Articlegreen2007

Accurate Evaluation of European and American Options Under the CGMY Process

70 citations0/0 files storedSIAM Journal on Scientific Computing

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Stochastic processes and financial applications Fractional Differential Equations Solutions Fuzzy Systems and Optimization

Abstract

A finite‐difference method for integro‐differential equations arising from Lévy driven asset processes in finance is discussed. The equations are discretized in space by the collocation method and in time by an explicit backward differentiation formula. The discretization is shown to be second‐order accurate for a relevant parameter range determining the degree of the singularity in the Lévy measure. The singularity is dealt with by means of an integration by parts technique. An application of the fast Fourier transform gives the overall amount of work $O(N_t N\log N)$, rendering the method fast.

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References

1973The Pricing of Options and Corporate Liabilities 1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1976Option pricing when underlying stock returns are discontinuous 2012The Econometrics of Financial Markets 1987The Pricing of Options on Assets with Stochastic Volatilities 2003Financial Modelling with Jump Processes 1976The valuation of options for alternative stochastic processes 1999Option valuation using the fast Fourier transform

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