This paper develops a general approximation scheme, henceforth called a hybrid asymptotic expansion scheme for the valuation of multi-factor European path-independent derivatives. Specifically, we apply it to pricing long-term currency options under a market model of interest rates and a general...

This paper proposes a unified method for precise estimates of the error bounds in asymptotic expansions of an option price and its Greeks (sensitivities) under a stochastic volatility model. More generally, we also derive an error estimate for an asymptotic expansion around a partially elliptic...

This paper derives a new semi closed-form approximation formula for pricing an up-and-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada (2012). We also demonstrate...

In this work, we apply our newly proposed perturbative expansion technique to a quadratic growth FBSDE appearing in an incomplete market with stochastic volatility that is not perfectly hedgeable. By combining standard asymptotic expansion technique for the underlying volatility process, we...