We introduce a new analytical approach to price American options. Using an explicit and intuitive proxy for the exercise rule, we derive tractable pricing formulas using a short-maturity asymptotic expansion. Depending on model parameters, this method can accurately price options with...

We derive a closed-form asymptotic expansion formula for option implied volatility under a two-factor jump-diffusion stochastic volatility model when time-to-maturity is small. Based on numerical experiments we describe the range of time-to-maturity and moneyness for which the approximation is...

In this paper we propose analytical approximations for computing implied volatilities when time-to-maturity t is small. The analysis is performed in the framework of a two-factor model with local and stochastic volatility. We describe an algorithm for building the power series approximation of...