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 develop approximating formulas for European options prices based on short term asymptotics, i.e. when time-to-maturity tends to zero. The analysis is performed in a general setting where stochastic volatility and jumps drive the dynamics of stock returns. In a numerical study we...