2014/09/03 by Pablo Olivares, Olivares, Pablo, Matthew Cane +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · Social Sciences · #91G20 #91G60 #Algorithm #Computer science #Econometrics #Exotic option #FOS: Economics and business #Fast Fourier transform #Financial Risk and Volatility Modeling #Fourier transform #Insurance, Mortality, Demography, Risk Management #Jump #Jump diffusion #Jump process #Mathematics #Monte Carlo method #Physics #Poisson distribution #Pricing of Securities (q-fin.PR) #Statistical physics #Statistics #Stochastic process #Stochastic processes and financial applications #Stochastic volatility #Valuation of options #Volatility (finance) #msc:91G20 #msc:91G60 #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1409.1175
published in arXiv (Cornell University) (Cornell University) · 9 figures
arxiv created 2014/09/03 · openalex publication_date 2014/09/03 · arxiv updated 2014/09/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
This paper examines the problem of pricing spread options under some models with jumps driven by Compound Poisson Processes and stochastic volatilities in the form of Cox-Ingersoll-Ross(CIR) processes. We derive the characteristic function for two market models featuring joint normally distributed jumps, stochastic volatility, and different stochastic dependence structures. With the use of Fast Fourier Transform(FFT) we accurately compute spread option prices across a variety of strikes and initial price vectors at a very low computational cost when compared to Monte Carlo pricing methods. We also look at the sensitivities of the prices to the model specifications and find strong dependence on the selection of the jump and stochastic volatility parameters. Our numerical implementation is based on the method developed by Hurd and Zhou (2009).