2015/02/27 by Fabián Crocce, Juho Häppölä, Crocce, Fabián +5 · 1 citation
Economics, Econometrics and Finance · Engineering · #60J60 #60J65 #60J75 #65T50 #FOS: Economics and business #Financial Risk and Volatility Modeling #Fluid Dynamics and Turbulent Flows #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1503.00019
openalex publication_date 2015/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential \levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation that can be solved analytically in terms of the characteristic exponent of the \levy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a novel bound for the error and use this bound to set the parameters for the numerical method. We analyse the properties of the bound for a dissipative and pure-jump example. The bound presented is independent of the asymptotic behaviour of option prices at extreme asset prices. The error bound can be decomposed into a product of terms resulting from the dynamics and the option payoff, respectively. The analysis is supplemented by numerical examples that demonstrate results comparable to and superior to the existing literature.