Seminar Event Detail


Financial/Actuarial Mathematics

Date:  Wednesday, February 03, 2016
Location:  1360 East Hall (4:00 PM to 5:00 PM)

Title:  Small-time asymptotics for fast mean-reverting stochastic volatility models

Abstract:   We use stochastic volatility models, with fast mean-reverting volatility, to price out-of-the-money (OTM) European call options near maturity. The regime of interest is when time to maturity is small, but large compared to the mean-reversion time of the stochastic volatility. The different time scales of mean-reversion and time to maturity makes this a multi scale problem. To obtain asymptotics of the OTM option price and the corresponding implied volatility, we first prove a large deviation principle for stock price, as time to maturity approaches zero. The large deviation principle is obtained by PDE techniques rather than probabilistic methods. Due to the mutli-scale nature of the problem, the PDE techniques involve averaging viscosity solutions of nonlinear PDEs.

This is joint work with Jean-Pierre Fouque, Jin Feng and Lea Popovic.

Files: 3292_Talk-UM_AA.pdf


Speaker:  Rohini Kumar
Institution:  Wayne State University

Event Organizer:   Erhan Bayraktar    erhan@umich.edu

 

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