FX options pricing in logarithmic mean-reversion jump-diffusion model with stochastic volatility

摘要

As a tradable asset, foreign currency has the particular property of mean-reversion, which should be reasonably included in FX dynamic modeling. From observation of FX historical data, jump takes frequently and it should be considered as modeling factor as well. The implied volatility smile/skew in FX options market is very significant, thus stochastic volatility is necessary in FX options models. Combining the three factors together, a new model named logarithmic mean-reversion jump-diffusion model with stochastic volatility is constructed. Conditional characteristic function under this model is derived by expectation approach, and Attari’s pricing formula is further attained. At last, we give some empirical results to show the good performance of our model.