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 the first part of the talk, I shall explain some basic concepts and preliminary results of Lévy processes, which are needed in the later results. I shall also provide some motivations for using Lévy processes in financial modeling. In the second part, 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. ( Slides)
Speaker: Ruoting Gong, Department of Mathematics, Rutgers University