Implied value-at-risk and model-free simulation

Abstract: We propose a novel model-free approach for extracting the risk-neutral quantile function of an asset using options written on this asset. We develop two applications. First, we show how for a given stochastic asset model our approach makes it possible to simulate the underlying terminal asset value under the risk-neutral probability measure directly from option prices. Specifically, our approach outperforms existing approaches for simulating asset values for stochastic volatility models such as the Heston, the SVI, and the SABR models. Second, we estimate the option implied value-at-risk (VaR) and the option implied tail value-at-risk (TVaR) of a financial asset in a direct manner. We also provide an empirical illustration in which we use S&P 500 Index options to construct an implied VaR Index and we compare it with the VIX Index.