A new analytical approximation for European puts with stochastic volatility

In this paper, we apply singular perturbation techniques to price European puts with a stochastic volatility model, and derive a simple and elegant analytical formula as an approximation for the value of European put options. In contrast to the existing Heston’s semi-analytical formula, this approximation has the following unique feature: the latter only involves the standard normal distribution function, which is as fast and easy to implement as the Black–Scholes formula; whereas the former requires the evaluation of a logarithm with a complex argument during the involved Fourier inverse transform, which may sometimes result in numerical instability. Various numerical experiments suggest that our new formula can achieve a high order of accuracy for a large class of option derivatives with relatively short tenor.