The Black-Scholes formula and volatility smile.

Black-Scholes;Implied volatility;Binomial model;Option pricing;Arrow-Debreu

Brian Michael Butler, 1969-

University:University of Louisville

Department:Mathematics

关键词: Black-Scholes;    Implied volatility;    Binomial model;    Option pricing;    Arrow-Debreu;   

Others  :  https://ir.library.louisville.edu/cgi/viewcontent.cgi?article=1187&context=etd

美国|英语

来源: The Universite of Louisville's Institutional Repository

【 摘 要 】

This paper investigates the development and applications of the Black-Scholesformula. This well-known formula is a continuous time model used primarily to priceEuropean style options. However in recent decades, observations in financial market datahave brought into question some of the basic assumptions that the model relies on. Ofparticular interest is the prevalence of the volatility smile in asset option prices. This is aviolation of one of the key assumptions under this model, and as a result alternatives toand modifications of Black-Scholes have been suggested, some continuous and somediscrete. This paper researches one such modification, proposed by Derman and Kani(1994), in which observed market data is used to create a discrete time implied asset pricetree that correctly reflects changing volatilities, risk-neutral probabilities, and observedoption prices. The results are then used to price a less conventional derivativearrangement.