Speaker: Ruoting Gong, Department of Mathematics, Rutgers University
ABSTRACT
This talk is concerned with the small-time asymptotics and expansions of call option prices, when the log-return processes of the underlying stock prices follow several Lévy-based models. During the last decade, Lévy processes and other stochastic processes with jumps have become increasingly popular for modeling market fluctuations, both for risk management and option pricing purposes. In this talk, I shall present some recent results on the time-to-maturity asymptotic behavior for both at-the-money (ATM), out-of-the-money (OTM) and in-the-money (ITM) call-option prices under several exponential Lévy models. The asymptotic expansion of the corresponding Black-Scholes implied volatilities in both cases are also addressed as immediate consequences.