The impact on option pricing of specification error in the underlying stock price returns

摘要: I. INTRODUCTION IN AN EARLIER PAPER,1 I briefly discussed the problem of errors in option pricing due to a misspecification stochastic process generating underlying stock's returns. While there are many ways which specification error can be introduced, particular form chosen that paper was compare prices arrived at by an investor who believes distribution unanticipated returns stock is lognormal, and hence he use classic Black-Scholes formula2, with "correct" if true for mixture lognormal jump process. This particularly important case because nature not just one magnitude, but indeed qualitiative characteristics two processes fundamentally different. In this paper, examine magnitude quantitative fashion using simulations. Before discussing simulations, it necessary summarize results deduced earlier paper. At heart derivation formula arbitrage technique investors follow dynamic portfolio strategy riskless borrowing exactly reproduce return structure option. By following combination short position option, eliminate all risk from total position, avoid opportunities, must priced such equal rate interest. However, carried out, able revise their portfolios frequently price generates continuous sample path. effect, requirement implies over interval time, cannot change much. my derived when path does satisfy continuity property. particular, assumed dynamics written as types changes: (1) "normal" vibrations price, examples, temporary imbalance between supply demand, changes capitalization rates, economic outlook, or other new information causes marginal * Professor Finance, Massachusetts Institute Technology. thank J. Ingersoll programming simulations general scientific assistance, F. Black M. Scholes helpful discussions. Aid National Science Foundation gratefully acknowledged.