Abstract: This paper develops a simple yet general option pricing model that considers probability ambiguity. It formulates the state-probability price of Arrow Debreu security, continuous time equivalent martingale measure and pricing kernel in the risk-ambiguity paradigm, and applies them to the Black-Scholes-Merton (BSM) framework to derive analytical option pricing formula. Probability ambiguity significantly alleviates volatility smile, and reduces the BSM model's in-sample and 1-day out-of-sample pricing errors of the S&P 500 index options by 80% and 66%, respectively. We present the first approach to use the index options to estimate the market ambiguity premium that contains unique information.

Bio: Lihong Zhang is a professor of Finance in the School of Economics and Management at Tsinghua University. She holds a Ph.D. in Probability and Mathematical Statistics from the Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Science, and an M.S. in Probability and Mathematical Statistics and a B.S. in Probability and Mathematical Statistics from Nankai University. Before joining Tsinghua University, she conducted postdoctoral research in the School of Mathematical Science at Peking University.  Lihong’s research interests are on issues related to financial economics, stochastic calculus and its applications, actuarial science, and risk management. Her research has appeared in MIS Quarterly and Insurance: Mathematics and Economics.