2019/08/26 by Kenji Nagami, Nagami, Kenji
Economics, Econometrics and Finance · #Computational Finance (q-fin.CP) #FOS: Economics and business #Pricing of Securities (q-fin.PR) #q-fin.CP #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1908.09640
20 pages, 5 figures
arxiv created 2019/08/26 · arxiv updated 2019/08/27
Some expansion methods have been proposed for approximately pricing options which has no exact closed formula. Benhamou et al. (2010) presents the smart expansion method that directly expands the expectation value of payoff function with respect to the volatility of volatility, then uses it to price options in the stochastic volatility model. In this paper, we apply their method to the stochastic volatility model with stochastic interest rates, and present the expansion formula for pricing options up to the second order. Then the numerical studies are performed to compare our approximation formula with the Monte-Carlo simulation. It is found that our formula shows the numerically comparable results with the method proposed by Grzelak et al. (2012) which uses the approximation of characteristic function.