ncku-talk2010-12-22

NCTS(South)/ NCKU Math Colloquium

DATE 2010-12-22　16:10-17:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Tai-Ho Wang（Department of Mathematics and Financial Engineering Baruch College, City University of New York）

TITLE Small time asymptotics for implied volatilities

ABSTRACT In this talk we start with a brief review on short time asymptotic behavior of implied volatility under various models. Particularly in the case of one dimensional diffusion model, using an expansion of the transition density function, we obtain the first and second order terms in the short time asymptotics of European call option prices.
The method described can be generalized to any order. We then use these option prices approximations to calculate the first order and second order deviation of the implied volatility from its leading value and obtain approximations which we numerically demonstrate to be highly accurate.
The analysis is extended to degenerate diffusions using probabilistic methods, i.e., the so called principle of not feeling the boundary. This is based on a joint work with Jim Gatheral, Elton Hsu, Peter Laurence, and Cheng Ouyang.

NCTS(South)/ NCKU Math Colloquium

DATE	2010-12-22　16:10-17:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Tai-Ho Wang（Department of Mathematics and Financial Engineering Baruch College, City University of New York）

TITLE	Small time asymptotics for implied volatilities

ABSTRACT	In this talk we start with a brief review on short time asymptotic behavior of implied volatility under various models. Particularly in the case of one dimensional diffusion model, using an expansion of the transition density function, we obtain the first and second order terms in the short time asymptotics of European call option prices. The method described can be generalized to any order. We then use these option prices approximations to calculate the first order and second order deviation of the implied volatility from its leading value and obtain approximations which we numerically demonstrate to be highly accurate. The analysis is extended to degenerate diffusions using probabilistic methods, i.e., the so called principle of not feeling the boundary. This is based on a joint work with Jim Gatheral, Elton Hsu, Peter Laurence, and Cheng Ouyang.