Exact Sampling of Jump Diffusions

Kay Giesecke · Dmitry Smelov

48 citations0/0 files storedOperations Research

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Stochastic processes and financial applications Probability and Risk Models Markov Chains and Monte Carlo Methods

Abstract

This paper develops a method for the exact simulation of a skeleton, a hitting time, and other functionals of a one-dimensional jump diffusion with state-dependent drift, volatility, jump intensity, and jump size. The method requires the drift function to be C 1 , the volatility function to be C 2 , and the jump intensity function to be locally bounded. No further structure is imposed on these functions. The method leads to unbiased simulation estimators of security prices, transition densities, hitting probabilities, and other quantities. Numerical results illustrate its features.

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References

1976Option pricing when underlying stock returns are discontinuous 2000Transform Analysis and Asset Pricing for Affine Jump-diffusions 1999Modeling Term Structures of Defaultable Bonds 1976VALUING CORPORATE SECURITIES: SOME EFFECTS OF BOND INDENTURE PROVISIONS 2002A Jump-Diffusion Model for Option Pricing 2004Option Pricing Under a Double Exponential Jump Diffusion Model 2001The term structure of credit spreads with jump risk 2006Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes

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2020Efficient Simulation of Generalized SABR and Stochastic Local Volatility Models based on Markov Chain Approximations 2015On the exact and $\varepsilon$-strong simulation of (jump) diffusions 2014Fluctuation analysis for the loss from default 2017Efficient Simulation of Clustering Jumps with CIR Intensity 2018Exact simulation of the Ornstein–Uhlenbeck driven stochastic volatility model

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