LARGE-TIME OPTION PRICING USING THE DONSKER-VARADHAN LDP-CORRELATED STOCHASTIC VOLATILITY WITH STOCHASTIC INTEREST RATES AND JUMPS

• 成果类型: Article
• 署名作者: Forde, Martin; Kumar, Rohini
• 署名单位: University of London; King's College London; Wayne State University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1189
• 发表日期: 2016
• 页码: 3699-3726
• 关键词: markov process expectations; asymptotic evaluation; implied volatility; large deviations; MODEL; heston

摘要

We establish a large-time large deviation principle (LDP) for a general mean-reverting stochastic volatility model with nonzero correlation and sublinear growth for the volatility coefficient, using the Donsker-Varadhan [Comm. Pure Appl. Math. 36 (1983) 183-212] LDP for the occupation measure of a Feller process under mild ergodicity conditions. We verify that these conditions are satisfied when the process driving the volatility is an Ornstein Uhlenbeck (013) process with a perturbed (sublinear) drift. We then translate these results into large-time asymptotics for call options and implied volatility and we verify our results numerically using Monte Carlo simulation. Finally, we extend our analysis to include a CIR short rate process and an independent driving Levy process.