Pricing Options with Vanishing Stochastic Volatility

In the past years, there has been an extensive investigation of class stochastic volatility models for evaluation options and complex derivatives. These have proven to be extremely useful in generalizing classic Black–Scholes economy accounting discrepancies between observation predictions simple log-normal, constant-volatility model. this paper, we study structure market with a that will eventually vanish (i.e., reaches zero) very short periods time probability one. We investigate form pricing measures situation, first binomial case, then diffusion model, by constructing weak approximation discrete space continuous time. The described allows fleeting arbitrage opportunities, since vanishing prevents construction equivalent measure, so contingent claims are, priori, not obvious. Nevertheless, can still produce fair equation. Let us note issue is only theoretical relevance, as phenomenon low indeed observed financial markets quite long recent past.