Pricing Options in Jump-Diffusion Models: An Extrapolation Approach

Feng, Liping; Linetsky, Vadim

doi:10.1287/opre.1070.0419

Cited by 151 publications

(121 citation statements)

References 52 publications

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“…Firstly, Bates model is a stochastic jump diffusion model. Jump diffusion are capable of modeling large and sudden changes in the state variable [12]. Default and risk factors are correlated through jump.…”

Section: Comparing To Heston Model Bates Extended Heston Model By Admentioning

confidence: 99%

CVA under Bates Model with Stochastic Default Intensity

Feng¹

2017

JMF

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Counterparty credit risk has received increasing attention and become a topical issue since 2007 credit crisis, particularly for its impact on the valuation of the OTC derivatives. Credit Value Adjustment (CVA) has become an import field and it is required in Basel III. This paper studies CVA for European options under Bates model with stochastic default intensity. We develop a Monte Carlo and finite difference method framework for assessing exposure profiles and impact of counterparty credit risk in pricing. The exposures are computed by solving a partial integro-differential Equation (PIDE) using implicit-explicit (IMEX) time discretization schemes. CVA in presence of wrong way risk (WWR) is embedded in the correlation between risk factor and default intensity. Meanwhile, the jump-at-default feature of the models offers an effective means to assess WWR. Our results show that both jump and WWR play an important role in evaluating CVA and exposures. The impact is significant and it is crucial for risk management purpose.

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Section: Comparing To Heston Model Bates Extended Heston Model By Admentioning

confidence: 99%

CVA under Bates Model with Stochastic Default Intensity

Feng¹

2017

JMF

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“…See the appendices of Feng and Linetsky (2008a), Feng and Linetsky (2008b) for more details. We would like to remark that, to use the fast Fourier transform based on the Toeplitz matrix vector multiplication, the step sizes h > 0 and η > 0 can be arbitrary.…”

Section: Hilbert Transform Representation For the Cdfmentioning

confidence: 99%

Inverse transform method for simulating levy processes and discrete Asian options pricing

Chen

Feng

Lin

2011

Proceedings of the 2011 Winter Simulation Conference (WSC)

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The simulation of a Lévy process on a discrete time grid reduces to simulating from the distribution of a Lévy increment. For a general Lévy process with no explicit transition density, it is often desirable to simulate from the characteristic function of the Lévy increment. We show that the inverse transform method, when combined with a Hilbert transform approach for computing the cdf of the Lévy increment, is reliable and efficient. The Hilbert transform representation for the cdf is easy to implement and highly accurate, with approximation errors decaying exponentially. The inverse transform method can be combined with quasi-Monte Carlo methods and variance reduction techniques to greatly increase the efficiency of the scheme. As an illustration, discrete Asian options pricing in the CGMY model is considered, where the combination of the Hilbert transform inversion of characteristic functions, quasi-Monte Carlo methods and the control variate technique proves to be very efficient.

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“…Pricing derivatives, especially exotic options, is a challenging problem in the operations research literature [to cite a few, see 11,17,18,20,27,34,54,58]. The application of transform techniques in mathematical finance is rather recent.…”

Section: Introductionmentioning

confidence: 99%

Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options

Fusai

Germano

Marazzina

2016

European Journal of Operational Research

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The Wiener-Hopf factorization of a complex function arises in a variety of fields in applied mathematics such as probability, finance, insurance, queuing theory, radio engineering and fluid mechanics. The factorization fully characterizes the distribution of functionals of a random walk or a Lévy process, such as the maximum, the minimum and hitting times. Here we propose a constructive procedure for the computation of the Wiener-Hopf factors, valid for both single and double barriers, based on the combined use of the Hilbert and the z-transform. The numerical implementation can be simply performed via the fast Fourier transform and the Euler summation. Given that the information in the Wiener-Hopf factors is strictly related to the distributions of the first passage times, as a concrete application in mathematical finance we consider the pricing of discretely monitored exotic options, such as lookback and barrier options, when the underlying price evolves according to an exponential Lévy process. We show that the computational cost of our procedure is independent of the number of monitoring dates and * Corresponding author Email addresses: gianluca.fusai@unipmn.it, gianluca.fusai.1@city.ac.uk (Gianluca Fusai), g.germano@ucl.ac.uk, g.germano@lse.ac.uk (Guido Germano), daniele.marazzina@polimi.it (Daniele Marazzina) Preprint submitted to ElsevierNovember 27, 2015the error decays exponentially with the number of grid points.

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Pricing Options in Jump-Diffusion Models: An Extrapolation Approach

Cited by 151 publications

References 52 publications

CVA under Bates Model with Stochastic Default Intensity

CVA under Bates Model with Stochastic Default Intensity

Inverse transform method for simulating levy processes and discrete Asian options pricing

Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options

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