Introducing two mixing fractions to a lognormal local-stochastic volatility model

Geoffrey Lee, Bowie Owens and Zili Zhu

Abstract

A single parameter, termed the mixing fraction, is used to calibrate current localstochastic volatility (LSV) models to traded exotic prices as well as vanilla options. This single parameter has been multiplied by both the volatility-of-volatility parameter and the correlation between spot and volatility of the original stochastic volatility model. In this paper, we introduce two mixing fractions that can be controlled separately to apply impact to the volatility-of-volatility and the correlation in a lognormal LSV model. For the case study using USD/JPY market data, we observe significant improvement in calibration accuracy to one-touch exotic option prices with the introduction of a second mixing fraction, without losing accuracy in the replication of European options. Importantly, when the LSV model with enhanced calibration accuracy is used to price other one-touch options, the discrepancy with market prices is not improved noticeably for the out-of-sample exotics, which indicates that either the market prices of traded one-touch options are not self-consistent or the LSV model does not capture the underlying dynamics exactly.