Large Deviation Principles for Stochastic Volatility Models with Reflection and Three Faces of the Stein and Stein Model
29 Pages Posted: 3 Mar 2021
Date Written: December 30, 2020
We introduce stochastic volatility models, in which the volatility is described by a time-dependent nonnegative function of a reflecting diffusion. The idea to use reflecting diffusions as building blocks of the volatility came into being because of a certain volatility misspecification in the classical Stein and Stein model. A version of this model that uses the reflecting Ornstein-Uhlenbeck process as the volatility process is a special example of a stochastic volatility model with reflection. The main results obtained in the present paper are sample path and small-noise large deviation principles for the log-price process in a stochastic volatility model with reflection under rather mild restrictions. We use these results to study the asymptotic behavior of binary barrier options and call prices in the small-noise regime.
Keywords: stochastic volatility models with reflection, reflecting diffusions, large deviation principles, binary barrier options, call pricing functions.
JEL Classification: C02
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