MCFAM Seminar - Lognormal Stochastic Volatility with Applications to Cryptocurrency Options

Speaker: Artur Sepp

Abstract: We introduce the log-normal stochastic volatility (SV) model with a quadratic drift to allow arbitrage-free valuation of options on assets under money-market account and inverse martingale measures. We show that the proposed volatility process has a unique strong solution, despite non-Lipschitz quadratic drift, and we establish the corresponding Feynman–Kac partial differential equation (PDE) for computation of conditional expectations under this SV model. We develop an analytic approach to compute an affine expansion for the moment generating function of the log-price, its quadratic variance (QV) and the instantaneous volatility. Our solution allows for semi-analytic valuation of vanilla options under log-normal SV models closing a gap in existing studies. We apply our approach for solving the joint valuation problem of vanilla and inverse options, which are popular in the cryptocurrency option markets. We demonstrate the accuracy of our solution for valuation of vanilla and inverse options. By calibrating the model to time series of options on Bitcoin over the past four years, we show that the log-normal SV model can work efficiently in different market regimes.

MCFAM Seminars