The scope is the development of new mathematical tools for treating more complex and realistic financial models. Specifically, the focus is on local and stochastic volatility models and models with jumps for describing the evolution of stock price processes, LIBOR interest rates, and volatility surfaces. In the area of interest rates, after the financial crisis there is an emerging need for modeling multi-curve LIBOR models. Also FX LIBOR models are recently within the scope. To accomplish these goals new techniques in diverse mathematical fields such as the theory of Ito-Levy jump processes, non-stationary time series analysis, and ill-posed statistical inverse problems, are called for. For equity modeling, there is a new approach based on rough volatility. That is, (stochastic) volatility is modeled by a variety of the fractional Brownian motion with Hurst index less than ½. As only the volatility process, but not the price process itself is of fractional type, the resulting class of models do not violate the paradigm of no-arbitrage theory.




Highlights

Multivariate jump-diffusion extensions and stochastic volatility extensions of the EurIBOR market model are developed, implemented, and tested. It is shown that the extensions allow for flexible, systematic, and robust calibration to market quotes of "caps" and "swaptions" under incorporation of volatility "smile" and "skew" behavior. Highly accurate and efficient asymptotic formulas for prices of basket options are developed based on heat kernel expansions. These formulas are valid in a local volatility framework and offer surprisingly high precision over a wide range of strikes even in very high dimensions. These offer new possibilities for pricing, calibration and hedging. A rough stochastic volatility model (called "rough Bergomi model") was developed, which allows for precise matching of both implicit volatilities induced by the full range of put and call options and of realized variance time series data. As the first model of its kind, it even matches the implied volatility skew for very short maturities. At the same time, the model is very parsimonous and hence robust. Option prices can be computed by Monte Carlo simulation and by asymptotic pricing formulas. A perennial problem in the simulation of stochastic volatility Libor models and stochastic volatility asset price models such as the Heston model is the effective simulation of the square root process involved, also called the Cox--Ingersoll--Ross (CIR) diffusion process, Simulation of the CIR process is particularly difficult if the “volatility of volatility” parameter is so high that the Feller condition is violated. In this respect a novel simulation method is developed that applies regardless whether the Feller condition is violated or not. The corresponding simulation algorithm provides trajectories that are exact at random times and uniformly close to the exact ones at all times in between. Moreover, the method is developed such that it is applicable to rather general (one-dimensional) diffusions and is based on spectral series expansions connected with Sturm-Liouville problems.

Publications

  Monographs

  • CH. Bayer, J.G.M. Schoenmakers, Option Pricing in Affine Generalized Merton Models, in: Advanced Modelling in Mathematical Finance -- In Honour of Ernst Eberlein, J. Kallsen, A. Papapantoleon , eds., Springer Proceedings in Mathematics & Statistics, Springer International Publishing Switzerland, Cham, 2016, pp. 219--239, (Chapter Published).
    Abstract
    In this article we consider affine generalizations of the Merton jump diffusion model Merton (1976) and the respective pricing of European options. On the one hand, the Brownian motion part in the Merton model may be generalized to a log-Heston model, and on the other hand, the jump part may be generalized to an affine process with possibly state dependent jumps. While the characteristic function of the log-Heston component is known in closed form, the characteristic function of the second component may be unknown explicitly. For the latter component we propose an approximation procedure based on the method introduced in Belomestny, Kampen, Schoenmakers (2009). We conclude with some numerical examples.

  • J.G.M. Schoenmakers, Chapter 12: Coupling Local Currency Libor Models to FX Libor Models, in: Recent Developments in Computational Finance, Th. Gerstner, P. Kloeden, eds., 14 of Interdisciplinary Mathematical Sciences, World Scientific Publishers, Singapore, 2013, pp. 429--444, (Chapter Published).

  • J.G.M. Schoenmakers, Robust Libor Modelling and Pricing of Derivative Products, Chapman & Hall CRC Press, 2005, 202 pages, (Monograph Published).

  Articles in Refereed Journals

  • CH. Bayer, U. Horst, J. Qiu, A functional limit theorem for limit order books with state dependent price dynamics, The Annals of Applied Probability, 27 (2017), pp. 2753-2806.
    Abstract
    We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges to a continuous-time limit when the order arrival rates tend to infinity, the impact of an individual order arrival on the book as well as the tick size tend to zero. The limits of the standing buy and sell volume densities are described by two linear stochastic partial differential equations, which are coupled with a two-dimensional reflected Brownian motion that is the limit of the best bid and ask price processes.

  • D. Belomestny, J.G.M. Schoenmakers, Statistical inference for time-changed Lévy processes via Mellin transform approach, Stochastic Processes and their Applications, 126 (2016), pp. 2092--2122.

  • G.N. Milstein, J.G.M. Schoenmakers, Uniform approximation of the CIR process via exact simulation at random times, Advances in Applied Probability, 48 (2016), pp. 1095--1116.
    Abstract
    In this paper we uniformly approximate the trajectories of the Cox-Ingersoll-Ross (CIR) process. At a sequence of random times the approximate trajectories will be even exact. In between, the approximation will be uniformly close to the exact trajectory. From a conceptual point of view the proposed method gives a better quality of approximation in a path-wise sense than standard, or even exact simulation of the CIR dynamics at some deterministic time grid.

  • CH. Bayer, P. Friz, J. Gatheral, Pricing under rough volatility, Quantitative Finance, 16 (2016), pp. 887--904.
    Abstract
    From an analysis of the time series of volatility using recent high frequency data, Gatheral, Jaisson and Rosenbaum [SSRN 2509457, 2014] previously showed that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. The resulting Rough Fractional Stochastic Volatility (RFSV) model is remarkably consistent with financial time series data. We now show how the RFSV model can be used to price claims on both the underlying and integrated volatility. We analyze in detail a simple case of this model, the rBergomi model. In particular, we find that the rBergomi model fits the SPX volatility markedly better than conventional Markovian stochastic volatility models, and with fewer parameters. Finally, we show that actual SPX variance swap curves seem to be consistent with model forecasts, with particular dramatic examples from the weekend of the collapse of Lehman Brothers and the Flash Crash.

  • Z. Grbac, A. Papapantoleon, J.G.M. Schoenmakers, D. Skovmand, Affine LIBOR models with multiple curves: Theory, examples and calibration, SIAM Journal on Financial Mathematics, ISSN 1945-497X, 6 (2015), pp. 984--1025.
    Abstract
    We introduce a multiple curve LIBOR framework that combines tractable dynamics and semi-analytic pricing formulas with positive interest rates and basis spreads. The dynamics of OIS and LIBOR rates are specified following the methodology of the affine LIBOR models and are driven by the wide and flexible class of affine processes. The affine property is preserved under forward measures, which allows to derive Fourier pricing formulas for caps, swaptions and basis swaptions. A model specification with dependent LIBOR rates is developed, that allows for an efficient and accurate calibration to a system of caplet prices.

  • G.N. Milstein, J.G.M. Schoenmakers, Uniform approximation of the Cox--Ingersoll--Ross process, Advances in Applied Probability, 47 (2015), pp. 1132--1156.
    Abstract
    The Doss-Sussmann (DS) approach is used for simulating the Cox-Ingersoll-Ross (CIR) process. The DS formalism allows for expressing trajectories of the CIR process by solutions of some ordinary differential equation (ODE) that depend on realizations of the Wiener process involved. Via simulating the first-passage times of the increments of the Wiener process to the boundary of an interval and solving an ODE, we approximately construct the trajectories of the CIR process. From a conceptual point of view the proposed method may be considered as an exact simulation approach.

  • J.D. Deuschel, P. Friz, A. Jacquier, S. Violante , Marginal density expansions for diffusions and stochastic volatility: Part I, Communications on Pure and Applied Mathematics, 67 (2014), pp. 40--82.

  • J.D. Deuschel, P. Friz, A. Jacquier, S. Violante , Marginal density expansions for diffusions and stochastic volatility: Part II, Communications on Pure and Applied Mathematics, 67 (2014), pp. 321--350.

  • G. Milshteyn, V. Spokoiny, Construction of mean-self-financing strategies for European options under regime-switching, SIAM Journal on Financial Mathematics, ISSN 1945-497X, 5 (2014), pp. 532--556.
    Abstract
    The paper focuses on the problem of pricing and hedging a European contingent claim for an incomplete market model, in which evolution of price processes for a saving account and stocks depends on an observable Markov chain. The pricing function is evaluated using the martingale approach. The equivalent martingale measure is introduced in a way that the Markov chain remains the historical one. Due to the Markovian structure of the considered model, the pricing function satisfies the Cauchy problem for a system of linear parabolic partial differential equations. It is shown that any European contingent claim is attainable using a generalized replicating strategy which is self-financing in mean. For such a strategy, apart from the initial endowment and trading, some additional funds are required both step-wise at the jump moments of the Markov chain and continuously between the jump moments. The connection of the considered pricing and hedging problems with partial differential equations is very useful for computations.

  • CH. Bayer, B. Veliyev, Utility maximization in a binomial model with transaction costs: A duality approach based on the shadow price process, International Journal of Theoretical and Applied Finance, 17 (2014), pp. 1450022/1--1450022/27.

  • CH. Bayer, J. Gatheral, M. Karlsmark, Fast Ninomiya--Victoir calibration of the double-mean-reverting model, Quantitative Finance, 13 (2014), pp. 1813--1829.

  • CH. Bayer, P. Laurence, Asymptotics beats Monte Carlo: The case of correlated local vol baskets, Communications on Pure and Applied Mathematics, 67 (2014), pp. 1618--1657.

  • CH. Bayer, J.G.M. Schoenmakers, Simulation of forward-reverse stochastic representations for conditional diffusions, The Annals of Applied Probability, 24 (2014), pp. 1994--2032.
    Abstract
    In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced in Milstein et al. [Bernoulli, 10(2):281-312, 2004] in the context of a forward-reverse transition density estimator. The corresponding Monte Carlo estimators have essentially root-N accuracy, hence they do not suffer from the curse of dimensionality. We provide a detailed convergence analysis and give a numerical example involving the realized variance in a stochastic volatility asset model conditioned on a fixed terminal value of the asset.

  • M. Ladkau, J.G.M. Schoenmakers, J. Zhang, Libor model with expiry-wise stochastic volatility and displacement, International Journal of Portfolio Analysis and Management, 1 (2013), pp. 224--249.
    Abstract
    We develop a multi-factor stochastic volatility Libor model with displacement, where each individual forward Libor is driven by its own square-root stochastic volatility process. The main advantage of this approach is that, maturity-wise, each square-root process can be calibrated to the corresponding cap(let)vola-strike panel at the market. However, since even after freezing the Libors in the drift of this model, the Libor dynamics are not affine, new affine approximations have to be developed in order to obtain Fourier based (approximate) pricing procedures for caps and swaptions. As a result, we end up with a Libor modeling package that allows for efficient calibration to a complete system of cap/swaption market quotes that performs well even in crises times, where structural breaks in vola-strike-maturity panels are typically observed.

  • S. De Marco, P. Friz, S. Gerhold, Don't stay local -- Extrapolation analytics for Dupire's local volatility, Risk Magazine, 29 Jan (2013), pp. 82--87.

  • CH. Bayer, P. Friz, R.L. Loeffen, Semi-closed form cubature and applications to financial diffusion models, Quantitative Finance, 13 (2013), pp. 769--782.

  • A. Mahayni, J.G.M. Schoenmakers, Minimum return guarantees with funds switching rights --- An optimal stopping problem, Journal of Economic Dynamics & Control, 35 (2012), pp. 1880--1897.
    Abstract
    Recently, there is a growing trend to offer guarantee products where the investor is allowed to shift her account/investment value between multiple funds. The switching right is granted a finite number per year, i.e. it is American style with multiple exercise possibilities. In consequence, the pricing and the risk management is based on the switching strategy which maximizes the value of the guarantee put option. We analyze the optimal stopping problem in the case of one switching right within different model classes and compare the exact price with the lower price bound implied by the optimal deterministic switching time. We show that, within the class of log-price processes with independent increments, the stopping problem is solved by a deterministic stopping time if (and only if) the price process is in addition continuous. Thus, in a sense, the Black & Scholes model is the only (meaningful) pricing model where the lower price bound gives the exact price. It turns out that even moderate deviations from the Black & Scholes model assumptions give a lower price bound which is really below the exact price. This is illustrated by means of a stylized stochastic volatility model setup.

  • A. Papapantoleon, J.G.M. Schoenmakers, D. Skovmand, Efficient and accurate log-Lévy approximations to Lévy driven LIBOR models, Journal of Computational Finance, 15 (2012), pp. 3--44.
    Abstract
    The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a Lévy-driven LIBOR model and aim at developing accurate and efficient log-Lévy approximations for the dynamics of the rates. The approximations are based on truncation of the drift term and Picard approximation of suitable processes. Numerical experiments for FRAs, caps and swaptions show that the approximations perform very well. In addition, we also consider the log-Lévy approximation of annuities, which offers good approximations for high volatility regimes.

  • M. Beiglboeck, P. Friz, S. Sturm, Is the minimum value of an option on variance generated by local volatility?, SIAM Journal on Financial Mathematics, ISSN 1945-497X, 2 (2011), pp. 213--220.

  • P. Friz, S. Gerhold, A. Gulisashvili, S. Sturm, On refined volatility smile expansion in the Heston model, Quantitative Finance, 11 (2011), pp. 1151--1164.

  • P. Imkeller, A. Réveillac, J. Zhang, Solvability and numerical simulation of BSDEs related to BSPDEs with applications to utility maximization, International Journal of Theoretical and Applied Finance, 14 (2011), pp. 635--667.

  • D. Belomestny, J.G.M. Schoenmakers, A jump-diffusion Libor model and its robust calibration, Quantitative Finance, 11 (2011), pp. 529--546.

  • V. Krätschmer, H. Zähle, Sensitivity of risk measures with respect to the normal approximation of total claim distributions, Insurance: Mathematics & Economics, 49 (2011), pp. 335--344.
    Abstract
    A simple and commonly used method to approximate the total claim distribution of a (possible weakly dependent) insurance collective is the normal approximation. In this article, we investigate the error made when the normal approximation is plugged in a fairly general distribution-invariant risk measure. We focus on the rate of the convergence of the error relative to the number of clients, we specify the relative error's asymptotic distribution, and we illustrate our results by means of a numerical example. Regarding the risk measure, we take into account distortion risk measures as well as distribution-invariant coherent risk measures.

  • Y. Chen, W. Härdle, V. Spokoiny, GHICA --- Risk analysis with GH distributions and independent components, Journal of Empirical Finance, 17 (2010), pp. 255--269.

  • D. Belomestny, A. Kolodko, J.G.M. Schoenmakers, Pricing CMS spreads in the Libor market model, International Journal of Theoretical and Applied Finance, 13 (2010), pp. 45--62.
    Abstract
    We present two approximation methods for pricing of CMS spread options in Libor market models. Both approaches are based on approximating the underlying swap rates with lognormal processes under suitable measures. The first method is derived straightforwardly from the Libor market model. The second one uses a convexity adjustment technique under a linear swap model assumption. A numerical study demonstrates that both methods provide satisfactory approximations of spread option prices and can be used for calibration of a Libor market model to the CMS spread option market.

  • R.L. Loeffen, J.-F. Renaud, De Finetti's optimal dividends problem with an affine penalty function at ruin, Insurance: Mathematics & Economics, 46 (2010), pp. 98--108.

  • A. Weiss, Escaping the Brownian stalkers, Electronic Journal of Probability, 14 (2009), pp. 139-160.
    Abstract
    We propose a simple model for the behaviour of long-time investors on stock markets, consisting of three particles, which represent the current price of the stock, and the opinion of the buyers, or sellers resp., about the right trading price. As time evolves both groups of traders update their opinions with respect to the current price. The update speed is controled by a parameter $gamma$, the price process is described by a geometric Brownian motion. The stability of the market is governed by the difference of the buyers' opinion and the sellers' opinion. We prove that the distance

  • P. Friz, S. Benaim, Regular variation and smile asymptotics, Mathematical Finance. An International Journal of Mathematics, Statistics and Financial Economics, 19 (2009), pp. 1--12.

  • E. Giacomini, W. Härdle, V. Krätschmer, Dynamic semiparametric factor models in risk neutral density estimation, AStA. Advances in Statistical Analysis. A Journal of the German Statistical Society, 93 (2009), pp. 387--402.

  • D. Belomestny, J. Kampen, J.G.M. Schoenmakers, Holomorphic transforms with application to affine processes, Journal of Functional Analysis, 257 (2009), pp. 1222--1250.
    Abstract
    In a rather general setting of Itô?Lévy processes we study a class of transforms (Fourier for example) of the state variable of a process which are holomorphic in some disc around time zero in the complex plane. We show that such transforms are related to a system of analytic vectors for the generator of the process, and we state conditions which allow for holomorphic extension of these transforms into a strip which contains the positive real axis. Based on these extensions we develop a functional series expansion of these transforms in terms of the constituents of the generator. As application, we show that for multi-dimensional affine Itô?Lévy processes with state dependent jump part the Fourier transform is holomorphic in a time strip under some stationarity conditions, and give log-affine series representations for the transform

  • D. Belomestny, S. Mathew, J.G.M. Schoenmakers, Multiple stochastic volatility extension of the Libor market model and its implementation, Monte Carlo Methods and Applications, 15 (2009), pp. 285-310.
    Abstract
    In this paper we propose a Libor model with a high-dimensional specially structured system of driving CIR volatility processes. A stable calibration procedure which takes into account a given local correlation structure is presented. The calibration algorithm is FFT based, so fast and easy to implement.

  • D. Belomestny, G.N. Milstein, V. Spokoiny, Regression methods in pricing American and Bermudan options using consumption processes, Quantitative Finance, 9 (2009), pp. 315--327.
    Abstract
    Here we develop methods for efficient pricing multidimensional discrete-time American and Bermudan options by using regression based algorithms together with a new approach towards constructing upper bounds for the price of the option. Applying sample space with payoffs at the optimal stopping times, we propose sequential estimates for continuation values, values of the consumption process, and stopping times on the sample paths. The approach admits constructing both low and upper bounds for the price by Monte Carlo simulations. The methods are illustrated by pricing Bermudan swaptions and snowballs in the Libor market model.

  • V. Krätschmer, Compactness in spaces of inner regular measures and a general Portmanteau lemma, Journal of Mathematical Analysis and Applications, 351 (2009), pp. 792--803.

  • R.L. Loeffen, An optimal dividends problem with transaction costs for spectrally negative Lévy processes, Insurance: Mathematics & Economics, 45 (2009), pp. 41--48.

  • J. Kampen, A. Kolodko, J.G.M. Schoenmakers, Monte Carlo Greeks for financial products via approximative transition densities, SIAM Journal on Scientific Computing, 31 (2008), pp. 1--22.

  • R. Krämer, P. Mathé, Modulus of continuity of Nemytskiĭ operators with application to a problem of option pricing, Journal of Inverse and Ill-Posed Problems, 16 (2008), pp. 435--461.

  • Y. Chen, W. Härdle, V. Spokoiny, Portfolio value at risk based on independent components analysis, Journal of Computational and Applied Mathematics, 205 (2007), pp. 594--607.
    Abstract
    Risk management technology applied to high-dimensional portfolios needs simple and fast methods for calculation of value at risk (VaR). The multivariate normal framework provides a simple off-the-shelf methodology but lacks the heavy-tailed distributional properties that are observed in data. A principle component-based method (tied closely to the elliptical structure of the distribution) is therefore expected to be unsatisfactory. Here, we propose and analyze a technology that is based on independent component analysis (ICA). We study the proposed ICVaR methodology in an extensive simulation study and apply it to a high-dimensional portfolio situation. Our analysis yields very accurate VaRs.

  • CH. Fries, J. Kampen, Proxy simulation schemes for generic robust Monte Carlo sensitivities, process-oriented importance sampling and high-accuracy drift approximation, Journal of Computational Finance, 10 (2007), pp. 97--128.
    Abstract
    We consider a generic framework for generating likelihood ratio weighted Monte Carlo simulation paths, where we use one simulation scheme (proxy scheme) to generate realizations and then reinterpret them as realizations of another scheme (target scheme) by adjusting measure (via likelihood ratio) to match the distribution. This makes the approach independent of the product (the function f) and even of the model, it only depends on the numerical scheme. The approach is essentially a numerical version of the likelihood ratio method and Malliavin's Calculus reconsidered on the level of the discrete numerical simulation scheme. Since the numerical scheme represents a time discrete stochastic process sampled on a discrete probability space the essence of the method may be motivated without a deeper mathematical understanding of the time continuous theory (e.g. Malliavin's Calculus). The framework is completely generic and may be used for high accuracy drift approximations, process oriented importance sampling and the robust calculation of partial derivatives of expectations w.r.t. model parameters (i.e. sensitivities, aka. Greeks) by applying finite differences by reevaluating the expectation with a model with shifted parameters. We present numerical results using a Monte-Carlo simulation of the LIBOR Market Model for benchmarking.

  • O. Reiss, J.G.M. Schoenmakers, M. Schweizer, From structural assumptions to a link between assets and interest rates, Journal of Economic Dynamics & Control, 31 (2007), pp. 593--612.
    Abstract
    We derive a link between assets and interest rates in a standard multi-asset diffusion economy from two structural assumptions ? one on the volatility and one on the short rate function. Our main result is economically intuitive and testable from data since it only involves empirically observable quantities. A preliminary study illustrates how this could be done.

  • H. Haaf, O. Reiss, J.G.M. Schoenmakers, Numerically stable computation of CreditRisk+, Phys. Rev. E (3), 6 (2004), pp. 1--10.
    Abstract
    The CreditRisk+ model launched by Credit Suisse First Boston in 1997 is widely used by practitioners in the banking sector as a simple means for the quantification of credit risk, primarily of the loan book. We present an alternative numerical recursion scheme for CreditRisk+, equivalent to an algorithm recently proposed by Giese, that is based on well-known expansions of the logarithm and the exponential of a power series. We show that it is advantageous for the Panjer recursion advocated in the original CreditRisk+ document, in that it is numerically stable. The crucial stability arguments are explained in detail. We explain how to apply the suggested recursion scheme to incorporate stochastic exposures into the CreditRisk+ model as introduced by Tasche (2004). Finally, the computational complexity of the resulting algorithm is stated and compared with other methods for computing the CreditRisk+ loss distribution.

  • J.G.M. Schoenmakers, B. Coffey, Systematic generation of parametric correlation structures for the LIBOR market model, International Journal of Theoretical and Applied Finance, 6 (2003), pp. 507-519.
    Abstract
    We present a conceptual approach of deriving parsimonious correlation structures suitable for implementation in the LIBOR market model. By imposing additional constraints on a known ratio correlation structure, motivated by economically sensible assumptions concerning forward LIBOR correlations, we yield a semi-parametric framework of non-degenerate correlation structures with realistic properties. Within this framework we derive systematically low parametric structures with, in principal, any desired number of parameters. As illustrated, such structures may be used for smoothing a matrix of historically estimated LIBOR return correlations. In combination with a suitably parametrized deterministic LIBOR volatility norm we so obtain a parsimonious multi-factor market model which allows for joint calibration to caps and swaptions. See Schoenmakers [2002] for a stable full implied calibration procedure based on the correlation structures developed in this paper.

  • O. Kurbanmuradov, K. Sabelfeld, J.G.M. Schoenmakers, Lognormal approximations to LIBOR market models, Journal of Computational Finance, 6 (2002), pp. 69--100.
    Abstract
    We study several lognormal approximations for LIBOR market models, where special attention is paid to their simulation by direct methods and lognormal random fields. In contrast to conventional numerical solution of SDE's this approach simulates the solution directly at a desired point in time and therefore may be more efficient. As such the proposed approximations provide valuable alternatives to the Euler method, in particular for long dated instruments. We carry out a path-wise comparison of the different lognormal approximations with the 'exact' SDE solution obtained by the Euler scheme using sufficiently small time steps. Also we test approximations obtained via numerical solution of the SDE by the Euler method, using larger time steps. It turns out that for typical volatilities observed in practice, improved versions of the lognormal approximation proposed by Brace, Gatarek and Musiela, citeBrace, appear to have excellent path-wise accuracy. We found out that this accuracy can also be achieved by Euler stepping the SDE using larger time steps, however, from a comparative cost analysis it follows that, particularly for long maturity options, the latter method is more time consuming than the lognormal approximation. We conclude with applications to some example LIBOR derivatives.

  • G.N. Milstein, J.G.M. Schoenmakers, Numerical construction of hedging strategies against multi-asset European claims, Stochastics and Stochastics Reports, 73 (2002), pp. 125--157.
    Abstract
    For evaluating a hedging strategy we have to know at every moment the solution of the Cauchy problem for a corresponding parabolic equation (the value of the hedging portfolio) and its derivatives (the deltas). We suggest to find these quantities by Monte Carlo simulation of the corresponding system of stochastic differential equations using weak solution schemes. It turns out that with one and the same control function a variance reduction can be achieved simultaneously for the claim value as well as for the deltas. As illustrations we consider a Markovian multi-asset model with an instantaneously riskless saving bond and also some applications to the LIBOR rate model of Brace, Gatarek, Musiela and Jamshidian.

  Contributions to Collected Editions

  • CH. Bayer, P. Laurence, Small-time asymptotics for the at-the-money implied volatility in a multi-dimensional local volatility model, in: Large Deviations and Asymptotic Methods in Finance, P. Friz, J. Gatheral, A. Gulisashvili, A. Jaquier, J. Teichmann, eds., 110 of Springer Proceedings in Mathematics & Statistics, Springer, Berlin et al., 2015, pp. 213--237.

  • J.G.M. Schoenmakers, SHOWCASE 17 -- Expiry-wise Heston LIBOR model, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 314--315.

  • H.-G. Bartel, H.-J. Mucha, J. Dolata, Geochemical and statistical investigation of Roman stamped tiles of the Legio XXI Rapax, in: Classification as a Tool for Research. 11th IFCS Biennial Conference and 33rd Annual Conference of the Gesellschaft für Klassifikation e. V., Dresden, March 13--18, 2009, H. Locarek-Junge, C. Weihs, eds., Studies in Classification, Data Analysis, and Knowledge Organization, Springer, Berlin/Heidelberg, 2010, pp. 427--434.

  • P. Friz, M. Keller-Ressel, Moment explosions in financial models, in: Encyclopedia of Quantitative Finance, R. Cont, ed., Wiley, Chichester, 2010, pp. 1247--1253.

  • P. Friz, Implied volatility: Large strike asymptotics, in: Encyclopedia of Quantitative Finance, R. Cont, ed., Wiley, Chichester, 2010, pp. 909--913.

  • M. Elagin, V. Spokoiny, Locally time homogeneous time series modelling, in: Applied Quantitative Finance (2nd edition), W. Härdle, N. Hautsch, L. Overbeck, eds., Springer, Berlin, 2008, pp. 345--362.

  • J. Kampen, On optimal strategies of multivariate passport options, in: Progress in Industrial Mathematics at ECMI 2006, L.L. Bonilla, M. Moscoso, G. Platero, J.M. Vega, eds., 12 of Mathematics in Industry, Springer, Berlin, Heidelberg, 2008, pp. 666--670.

  • C. Croitoru, Ch. Fries, W. Jäger, J. Kampen, D.-J. Nonnenmacher, On the dynamics of the forward interest rate curve and the evaluation of interest rate derivatives and their sensitivities, in: Mathematics --- Key Technology for the Future, W. Jäger, H.-J. Krebs, eds., Springer, Heidelberg, 2008, pp. 343--357.

  • H. Haaf, O. Reiss, J.G.M. Schoenmakers, Numerically stable computation of Credit Risk+, in: CreditRisk+ in the Banking Industry, M. Gundlach, F. Lehrbass, eds., XII, Springer, Berlin Heidelberg, 2004, pp. 67-76.

  Preprints, Reports, Technical Reports

  • R. Hildebrand, J.G.M. Schoenmakers, J. Zhang, F. Dickmann, Regression based duality approach to optimal control with application to hydro electricity storage, Preprint no. 2330, WIAS, Berlin, 2016, DOI 10.5072/WIAS.PREPRINT.2330 .
    Abstract, PDF (341 kByte)
    In this paper we consider the problem of optimal control of stochastic processes. We employ the dual martingale method brought forward in [Brown, Smith, and Sun, 2010]. The martingale constituting the solution of the dual problem is determined by linear regression within a Monte-Carlo approach. We apply the solution algorithm to a model of a hydro electricity storage and production system coupled with a model of the electricity wholesale market.

  • CH. Bayer, M. Siebenmorgen, R. Tempone, Smoothing the payoff for efficient computation of basket option prices, Preprint no. 2280, WIAS, Berlin, 2016.
    Abstract, PDF (272 kByte)
    We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster compared to Monte Carlo or Quasi Monte Carlo in dimensions up to 25.

  Talks, Poster

  • CH. Bayer, Rough volatility models in finance, AMCS Seminar, King Abdullah University of Science and Technology (KAUST), Computer, Electrical and Mathematical Sciences & Engineering Division, Thuwal, Saudi Arabia, October 25, 2017.

  • CH. Bayer, Pricing under rough volatility, Statistics for Differential Equations driven by Rough Paths, September 7 - 8, 2016, University of Warwick, Centre for Research in Statistical Methodology, Coventry, UK, September 7, 2016.

  • CH. Bayer, Pricing under rough volatility, Vienna Congress on Mathematical Finance -- VCMF 2016, September 12 - 14, 2016, Vienna University of Economics and Business, Austria, September 12, 2016.

  • CH. Bayer, Pricing under rough volatility, Czech, Slovenian, Austrian, Slovak and Catalan Mathematical Societies Joint Meeting 2016, September 20 - 23, 2016, Societat Catalana de Matemàtiques, Institut d'Estudis Catalans, Barcelona, Spain, September 20, 2016.

  • CH. Bayer, Short dated option prices under rough volatility, Rough Volatility Meeting, October 7 - 8, 2016, Imperial College London, Department of Mathmatics, UK, October 7, 2016.

  • J.G.M. Schoenmakers, Financial Mathematics, The 9th Summer School in Financial Mathematics 2016, February 18 - 20, 2016, African Institute for Mathematical Sciences South Africa (AIMS), Cape Town.

  • J.G.M. Schoenmakers, Uniform approximation methods for the C.I.R. process, Stochastic Seminar, Charles University, Prague, Czech Republic, April 6, 2016.

  • J.G.M. Schoenmakers, Uniform approximation of the Cox--Ingersoll--Ross process, Frontiers in Stochastic Modelling for Finance, February 2 - 6, 2016, Università degli Studi di Padova, Padua, Italy, February 5, 2016.

  • CH. Bayer, Asymptotics beats Monte Carlo: The case of correlated local vol baskets, Groupe de Travail: Finance Mathématique, Probabilités Numériques et Statistique des Processus, Université Paris Diderot, Laboratoire de Probabilités et Modèles Aléatoires, France, February 19, 2015.

  • CH. Bayer, Pricing under rough volatility, Berlin-Princeton-Singapore Workshop on Quantitative Finance, June 29 - July 1, 2015, National University of Singapore, Centre for Quantitative Finance, Singapore, June 29, 2015.

  • CH. Bayer, Pricing under rough volatility, 38th Conference on Stochastic Processes and their Applications, July 13 - 17, 2015, University of Oxford, Oxford-Man Institute of Quantitative Finance, UK, July 15, 2015.

  • CH. Bayer, Pricing under rough volatility, Finanzmathematik, University of Vienna, Faculty of Mathematics, Austria, November 26, 2015.

  • CH. Bayer, Rough volatility, 3rd Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis, January 27 - 29, 2015, WIAS Berlin, January 29, 2015.

  • M. Ladkau, A new multi-factor stochastic volatility model with displacement, First Berlin-Singapore Workshop on Quantitative Finance and Financial Risk, May 21 - 24, 2014, WIAS-Berlin und Humboldt-Universität zu Berlin, May 22, 2014.

  • CH. Bayer, Asymptotics beats Monte Carlo: The case of correlated local vol baskets, International Workshop ``Advances in Optimization and Statistics'', May 15 - 16, 2014, Russian Academy of Sciences, Institute of Information Transmission Problems (Kharkevich Institute), Moscow, May 16, 2014.

  • CH. Bayer, Asymptotics beats Monte Carlo: The case of correlated local vol baskets, First Berlin-Singapore Workshop on Quantitative Finance and Financial Risk, May 21 - 24, 2014, WIAS-Berlin und Humboldt-Universität zu Berlin, May 21, 2014.

  • CH. Bayer, Asymptotics beats Monte Carlo: The case of correlated local vol baskets, Workshop on Stochastic and Quantitative Finance, November 28 - 29, 2014, Imperial College London, UK, November 29, 2014.

  • CH. Bayer, Asymptotics beats Monte Carlo: The case of correleated local vol baskets, Stochastic Analysis Seminar Series, Oxford-Man Institute, UK, January 27, 2014.

  • J.G.M. Schoenmakers, Affine LIBOR models with multiple curves: Theory, examples and calibration, 11th German Probability and Statistics Days 2014, March 5 - 7, 2014, Universität Ulm, March 6, 2014.

  • M. Ladkau, A new multi-factor stochastic volatility model with displacement, PreMoLab Workshop on: Advances in predictive modeling and optimization, May 16 - 17, 2013, WIAS-Berlin, May 16, 2013.

  • CH. Bayer, Asymptotics beats Monte Carlo: The case of correlated local volatility baskets, Stochastik-Seminar, Universität Heidelberg, Institut für angewandte Mathematik, June 18, 2013.

  • CH. Bayer, Asymptotics beats Monte Carlo: The case of correlated local volatility baskets, Seminar Finanzmathematik, Universität Wien, Austria, November 28, 2013.

  • CH. Bayer, Asymptotics can beat Monte Carlo, 20th Annual Global Derivatives & Risk Management, April 16 - 18, 2013, The International Centre for Business Information (ICBI), Amsterdam, Netherlands, April 18, 2013.

  • J.G.M. Schoenmakers, Simulation of conditional diffusions via forward-reverse stochastic representations, DynStoch 2013, April 17 - 19, 2013, University of Copenhagen, Department of Mathematical Sciences, Denmark, April 19, 2013.

  • J.G.M. Schoenmakers, Simulation of conditional diffusions via forward-reverse stochastic representations, PreMoLab Workshop on: Advances in predictive modeling and optimization, May 16 - 17, 2013, WIAS-Berlin, May 16, 2013.

  • CH. Bayer, Asymptotics beats Monte Carlo: The case of correlated local vol baskets, Applied Mathematics and Computational Science Seminar, King Abdullah University of Science and Technology, Saudi Arabia, December 5, 2012.

  • CH. Bayer, Some applications of the Ninomiya--Victoir scheme in the context of financial engineering, Talks in Financial and Insurance Mathematics, Eidgenössische Technische Hochschule Zürich, Switzerland, April 26, 2012.

  • CH. Bayer, Some applications of the Ninomiya--Victoir scheme in the context of financial engineering, Stochastic Analysis Seminar Series, Oxford University, Oxford-Man Institute of Quantitative Finance, UK, May 21, 2012.

  • H. Mai, Drift estimation for jump diffusion, Haindorf Seminar 2012 (Klausurtagung des SFB 649), February 9 - 12, 2012, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, Hejnice, Czech Republic, February 10, 2012.

  • H. Mai, Parametric and nonparametric estimation for stochastic volatility models with jumps, 10th German Probalility and Statistic Days 2012, March 6 - 9, 2012, Johannes Gutenberg Universität Mainz, March 7, 2012.

  • V. Krätschmer, Central limit theorems for law-invariant risk measures, Conference on ``Modeling and managing financial risks'', Université Paris VI, École Polytechnique, France, January 11, 2011.

  • V. Panov, Affine stochastic volatility models: asymptotic behavior of the characteristic function and estimation of the Blumenthal - Getoor index, Tagung des SFB 649 "Ökonomisches Risiko" in Motzen, June 30 - July 2, 2011, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, July 1, 2011.

  • R.L. Loeffen, Two methods for pricing European options, Colloquia on Probability and Statistics 2011, University of Bern, Institute of Mathematical Statistics and Actuarial Science, Switzerland, May 5, 2011.

  • R.L. Loeffen, Applying spectral representations for CBI processes to finance, Stochastic Networks and Related Topics III, May 22 - 25, 2011, Mathematical Research and Conference Center in Bedlewo, Poland, May 24, 2011.

  • R.L. Loeffen, Option pricing in affine term structure models via spectral representations, Seminar in Mathematical Finance, Universität Wien, Fakultät für Mathematik, Austria, January 31, 2011.

  • J.G.M. Schoenmakers, New dual methods for single and multiple exercise option, Universität Ulm, Institut für Numerische Mathematik, May 27, 2011.

  • J.G.M. Schoenmakers, New dual methods for single and multiple exercise options, Workshop ``Quantitative Methods in Financial and Insurance Mathematics'', April 18 - 21, 2011, Lorentz Center, Leiden, Netherlands, April 21, 2011.

  • J.G.M. Schoenmakers , New dual methods for single and multiple exercise options, International Workshop on Numerical Algorithms in Computational Finance, July 20 - 22, 2011, Goethe Universität Frankfurt, Goethe Center for Scientific Computing, July 22, 2011.

  • V. Krätschmer, A uniform central limit theorem for distortions of empirical distributions with applications to nonparametric estimation of distribution-invariant risk measures, Leipziger Stochastik Tage, March 1 - 5, 2010, Universität Leipzig, Fakultät für Mathematik und Informatik, March 2, 2010.

  • V. Krätschmer, Error caused by normal approximation of the total claim distribution when plugged in risk measures, 4th International Conference Mathematical and Statistical Methods for Actuarial Sciences and Finance, April 7 - 9, 2010, Università degli Studi di Salerno, Dipartimento di Scienze Economiche e Statistiche, Ravello, Italy, April 8, 2010.

  • V. Krätschmer, Error caused by normal approximation of the total claim distribution when plugged in risk measures, DAGStat2010, March 23 - 26, 2010, Technische Universität Dortmund, Fakultät Statistik, March 23, 2010.

  • V. Krätschmer, Nichtparametrische Schätzung verteilungsinvarianter Risikomaße, Universität Bayreuth, Fachbereich Mathematik, July 27, 2010.

  • V. Krätschmer, Nichtparametrische Schätzung verteilungsinvarianter Risikomaße, Universität Mannheim, Institut für Mathematik und Informatik, May 4, 2010.

  • V. Krätschmer, Nichtparametrische Schätzung verteilungsinvarianter Risikomaße, Heinrich Heine Universität Düsseldorf, Institut für Mathematik, April 23, 2010.

  • V. Krätschmer, Nonparametric estimation of low invariant risk measures for time series, Statistische Woche Nürnberg 2010, September 14 - 17, 2010, Deutschen Statistischen Gesellschaft (DStatG), September 16, 2010.

  • P. Friz, Stochastic analysis and quantitative finance, Microsoft Research Cambridge, UK, January 5, 2010.

  • R.L. Loeffen, Absolute ruin in the insurance risk model of Ornstein--Uhlenbeck type, 24th European Conference on Operational Research (EURO XXIV LISBON), July 11 - 14, 2010, Universidade de Lisboa, Faculdade de Ciéncias, Portugal, July 14, 2010.

  • R.L. Loeffen, The Ornstein--Uhlenbeck type risk model: Absolute ruin and spectral representation, Talks in Actuarial Sciences, Université Libre de Bruxelles, Département de Mathématiques, Belgium, November 18, 2010.

  • P. Mathé, Conjugate gradient iteration for statistical inverse problems, Rencontres de Statistiques Mathématiques 10, December 13 - 17, 2010, Centre International de Rencontres Mathématiques (CIRM), Luminy, France, December 15, 2010.

  • J.G.M. Schoenmakers, Advanced Libor modeling, Postbank Bonn, February 25, 2010.

  • J.G.M. Schoenmakers, Holomorphic transforms with application to affine processes, 5th General Conference in Advanced Mathematical Methods in Finance, May 4 - 8, 2010, University of Ljubljana, Faculty of Mathematics and Physics, Slovenia, May 6, 2010.

  • J.G.M. Schoenmakers, On three innovations in financial modeling, Colloquium, University of Twente, Faculty of Electrical Engineering, Mathematics and Computer Science, Netherlands, August 24, 2010.

  • B. Metzger, The discrete Gross--Pitaevskii model and condensation in the single particle ground state, Berlin-Leipzig Seminar on Analysis and Probability Theory, November 27, 2009, Technische Universität Berlin, Institut für Mathematik, November 27, 2009.

  • V. Panov, Pricing Bermudan options via dimension reduction, Klausurtagung des SFB 649, June 4 - 6, 2009, Humboldt-Universität zu Berlin, Motzen, June 5, 2009.

  • V. Panov, Solving classification task using detection of non-Gaussian components, Haindorf Seminar 2009, February 12 - 15, 2009, Humboldt-Universität zu Berlin, CASE --- Center for Applied Statistics and Economics, Hejnice, Czech Republic, February 14, 2009.

  • D. Peschka, Dewetting of thin liquid films on viscoelastic substrates, European Coating Symposium, September 7 - 9, 2009, Karlsruhe, September 7, 2009.

  • P. Friz, From numerical aspects of stochastic financial models to the foundations of stochastic differential equations (and back), Annual Meeting of the Deutsche Mathematiker-Vereinigung and 17th Congress of the Österreichische Mathematische Gesellschaft, Section ``Financial and Actuarial Mathematics'', September 20 - 25, 2009, Technische Universität Graz, Austria, September 25, 2009.

  • P. Friz, Rough paths and the gap between deterministic and stochastic differential equations, Berlin Mathematical School, Friday Colloquium, December 18, 2009.

  • R. Loeffen, De Finetti's optimal dividends problem with an affine penalty function at ruin, Université Libre de Bruxelles, Département de Mathématiques, Belgium, November 19, 2009.

  • CH. Meyer, Finite element error analysis for state-constrained optimal control of the Stokes problem, 80th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2009), Section ``Optimization of Differential Equations'', February 9 - 13, 2009, Gdansk University of Technology, Poland, February 10, 2009.

  • A. Mielke, BV solutions and parametrized solutions for rate-independent systems, 80th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2009), Session ``Applied Analysis'', February 9 - 13, 2009, Gdansk University of Technology, Poland, February 10, 2009.

  • J.G.M. Schoenmakers, Holomorphic transforms with application to affine processes, Workshop ``Computational Finance'', August 10 - 12, 2009, Kyoto University, Faculty of Sciences, Japan, August 10, 2009.

  • J.G.M. Schoenmakers, Statistical and numerical methods for evaluation for financial derivates and risk, Center Days 2009 (DFG Research Center scshape Matheon), March 30 - April 1, 2009, Technische Universität Berlin, March 31, 2009.

  • J. Kampen, Higher order WKB expansions of the fundamental solution and pricing of options, Credit Suisse, Zurich, Switzerland, March 28, 2008.

  • J. Kampen, Holomorphic transforms with application to affine feller processess in finance, 5th World Congress, Bachelier Finance Society, July 16 - 19, 2008, Royal Geographical Institute, London, UK, July 18, 2008.

  • J. Kampen, Monte carlo greeks for financial prods via approximate transition densities, 5th World Congress, Bachelier Finance Society, July 16 - 19, 2008, Royal Geographical Institute, London, UK, July 19, 2008.

  • A. Weiss, Limit order books and optimal portfolio liquidation, Summer School 2008 Pro$^*$Doc/IRTG Berlin-Zürich ``Stochastic Models of Complex Processes'', July 21 - 25, 2008, Disentis, Switzerland, July 22, 2008.

  • P. Mathé, On non-stability of some inverse problem in option pricing, Workshop on Inverse and Partial Information Problems: Methodology and Applications, October 27 - 31, 2008, Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, October 30, 2008.

  • J.G.M. Schoenmakers, Holomorphic transforms and affine processes, Technische Universität Braunschweig, May 20, 2008.

  • J.G.M. Schoenmakers, Holomorphic transforms with application to affine processes, 2nd Meeting in the winter semester 2008/2009 of the Research Seminar ``Stochastic Analysis and Stochastics of Financial Markets'', Technische Universität Berlin, November 6, 2008.

  • J. Kampen, Closed form analytic expansion formulas for characteristic functions of affine jump diffusion processes, Workshop on Numerics in Finance, November 5 - 6, 2007, Commerzbank AG, Frankfurt/Main, November 6, 2007.

  • J.G.M. Schoenmakers, Robust Libor modelling and calibration, International Multidisciplinary Workshop on Stochastic Modeling, June 25 - 29, 2007, Sevilla, Spain, June 29, 2007.

  • A. Weiss, Escaping the Brownian stalkers, BRG Workshop on Stochastic Models from Biology and Physics, October 9 - 10, 2006, Johann Wolfgang Goethe-Universität Frankfurt, October 10, 2006.

  • A. Weiss, Escaping the Brownian stalkers, 5th Prague Summer School 2006 "`Statistical Mathematical Mechanics"', September 10 - 23, 2006, Charles University, Center for Theoretical Study and Institute of Theoretical Computer Science, Prague, Czech Republic, September 20, 2006.

  • J.G.M. Schoenmakers, A jump-diffusion Libor model and its robust calibration, 4th World Congress of the Bachelier Finance Society, August 17 - 20, 2006, National Center of Sciences, Hitotsubashi University, ICS, Tokyo, Japan, August 20, 2006.

  • J.G.M. Schoenmakers, Interest rate modelling: Practical calibration and implementation techniques, June 15 - 16, 2006, Risk, London, UK.

  • J.G.M. Schoenmakers, Robust Libor modelling and pricing of derivative products, Delft University of Technology, Netherlands, June 9, 2005.

  • J.G.M. Schoenmakers, Interest rate modelling --- Practical calibration and implementation techniques, Incisive Media Events, Hong Kong, China, December 8, 2004.

  • J.G.M. Schoenmakers, Numerically stable computation of CreditRisk+, Karlsruher Stochastik-Tage 2004, March 23 - 26, 2004, Universität Karlsruhe, March 25, 2004.

  • J.G.M. Schoenmakers, Kreditrisiko Portfolio-Modelle, Kreditanstalt für Wiederaufbau, Frankfurt, July 18, 2003.

  • J.G.M. Schoenmakers, Robust calibration of LIBOR market models, Petit Dejeuner de la Finance, November 4 - 5, 2003, Paris, November 5, 2003.

  • J.G.M. Schoenmakers, Accuracy and stability of LIBOR model calibration via parametric correlation structures and approximative swaption pricing, Risk Conference 2002, April 23 - 24, 2002, Paris, France, April 23, 2002.

  • J.G.M. Schoenmakers, Calibration of LIBOR models to caps and swaptions: A way around intrinsic instabilities via parsimonious structures and a collateral market criterion, Johann Wolfgang Goethe-Universität, MathFinance Institute, Frankfurt am Main, November 7, 2002.

  • J.G.M. Schoenmakers, Calibration of LIBOR models to caps and swaptions: A way around intrinsic instabilities via parsimonious structures and a collateral market criterion, Quantitative Finance 2002, Risk Waters Group, London, UK, November 26, 2002.

  • J.G.M. Schoenmakers, Endogenous interest rates in asset markets, 2nd World Congress of the Bachelier Finance Society, June 12 - 15, 2002, Crete, Greece, June 14, 2002.

  • J.G.M. Schoenmakers, Kalibrierung im LIBOR Modell, Reuters AG, Düsseldorf, March 11, 2002.

  • J.G.M. Schoenmakers, Correlation structure in LIBOR market models, calibration to caps and swaptions, Technical University of Delft, Netherlands, May 8, 2001.

  • J.G.M. Schoenmakers, Term structure dynamics endogenously induced by multi-asset markets, Conference Risk 2001 Europe, April 10 - 11, 2001, Paris, France, April 10, 2001.

  • J.G.M. Schoenmakers, HJM term structure dynamics from a multi asset market; finite factor models, Hamburger Stochastik-Tage 2000, March 21 - 24, 2000, Universität Hamburg, March 21, 2000.

  • J.G.M. Schoenmakers, HJM term structure dynamics from a multi asset market; finite factor models, WIAS-Kolloquium, Berlin, May 15, 2000.

  • J.G.M. Schoenmakers, Stable calibration of multi-factor LIBOR market models via a semi-parametric correlation structure, "`ICBI 2000 Conference"', December 6 - 7, 2000, Genf, Switzerland, December 7, 2000.

  • J.G.M. Schoenmakers, Stable implied calibration of multi-factor LIBOR models by semi-parametric correlation structure, Risk Conference Math Week 2000, November 13 - 17, 2000, New York, USA, November 15, 2000.

  External Preprints

  • CH. Bayer, B. Veliyev, Utility maximization in a binomial model with transaction costs: A duality approach based on the shadow price process, Preprint no. arXiv:1209.5175, Cornell University Library, arXiv.org, 2012.

  • P. Friz, S. Gerhold, Don't stay local --- Extrapolation analytics for Dupire's local volatility, Preprint no. arXiv:1105.1267, Cornell University Library, arXiv.org, 2011.

  • J.D. Deuschel, P. Friz, A. Jacquier, S. Violante , Marginal density expansions for diffusions and stochastic volatility, Preprint no. arXiv:1111.2462, Cornell University Library, arXiv.org, 2011.

  • J.G.M. Schoenmakers, J. Huang, Optimal dual martingales, their analysis and application to new algorithms for Bermudan products, Preprint no. 1825944, Social Science Research Network (SSRN) Working Paper Series, 2011.

  • J. Kampen, Characteristic functions of affine processes via calculus of their operator symbols, Preprint no. arXiv:1002.2764, Cornell University Library, arXiv.org, 2010.

  • CH. Fries, J. Kampen, On a class of semi-elliptic diffusion models. Part I: A constructive analytical approach for global existence, densities, and numerical schemes with applications to the Libor market model, Preprint no. arXiv:1002.5031, Cornell University Library, arXiv.org, 2010.

  • P. Friz, S. Gerhold, A. Gulisashvili, S. Sturm, On refined volatility smile expansion in the Heston model, Preprint no. arXiv:1001.3003, Cornell University Library, arXiv.org, 2010.

  • R.L. Loeffen, P. Patie, Absolute ruin in the Ornstein--Uhlenbeck type risk model, Preprint no. arXiv:1006.2712, Cornell University Library, arXiv.org, 2010.
    Abstract
    We start by showing that the finite-time absolute ruin probability in the classical risk model with constant interest force can be expressed in terms of the transition probability of a positive Ornstein-Uhlenbeck type process, say X. Our methodology applies to the case when the dynamics of the aggregate claims process is a subordinator. From this expression, we easily deduce necessary and sufficient conditions for the infinite-time absolute ruin to occur. We proceed by showing that, under some technical conditions, the transition density of X admits a spectral type representation involving merely the limiting distribution of the process. As a by-product, we obtain a series expansions for the finite-time absolute ruin probability. On the way, we also derive, for the aforementioned risk process, the Laplace transform of the first-exit time from an interval from above. Finally, we illustrate our results by detailing some examples.

  • N. Serdyukova, Local parametric estimation under noise misspecification in regression, Preprint no. arXiv:0912.4489, Cornell University Library, arXiv.org, 2010.