Two Counters of Jumps

Abstract

This paper introduces a class of two counters of jumps option pricing models. The stock price follows a jump-diffusion process with price jumps up and price jumps down, where each type of jumps can have different means and standard deviations. Price jumps can be negatively autocorrelated as it has been observed in practice. We investigate the volatility surfaces generated by this class of two counters of jumps option pricing models. Our formulae, like the jump-diffusion models with a single counter of jumps, are able to generate smiles, and skews with similar shapes to those observed in the options markets. More importantly, unlike the jump-diffusion models with a single counter of jumps, our formulae are able to generate term structures of implied volatilities of at-the-money options with ∩-shaped patterns similar to those observed in the marketplace.