BUILDING A CONSISTENT PRICING MODEL FROM OBSERVED OPTION PRICES

Jean-Paul Laurent and Dietmar P. J. Leisen
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Jean-Paul Laurent: Center for Research in Economics and Statistics, Finance Department, 15 Boulevard Gabriel Péri, 92245 Malakoff Cedex, France
Dietmar P. J. Leisen: Stanford University, Hoover Institution, Stanford, CA 94305, USA

Chapter 8 in Quantitative Analysis in Financial Markets:Collected Papers of the New York University Mathematical Finance Seminar(Volume II), 2001, pp 216-238 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractThis paper constructs a model for the evolution of a risky security that is consistent with a set of observed call option prices. It explicitly treats the fact that only a discrete data set can be observed in practice. The framework is general and allows for state dependent volatility and jumps. The theoretical properties are studied. An easy procedure to check for arbitrage opportunities in market data is proven and then used to ensure the feasibility of our approach. The implementation is discussed: testing on market data reveals a U-shaped form for the "local volatility" depending on the state and surprisingly, a large probability for strong price movements.

Date: 2001
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