Testing option pricing with the Edgeworth expansion

✍ Scribed by Ruy Gabriel Balieiro Filho; Rogerio Rosenfeld

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 183 KB
• Volume: 344
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2004.06.018

✦ Synopsis

There is a well-developed framework, the Black-Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is observed in the market that this hypothesis is awed, leading to the introduction of a fudge factor, the so-called volatility smile. Therefore, it would be interesting to explore extensions of the Black-Scholes theory to non-Gaussian distributions. In this paper, we provide an explicit formula for the price of an option when the distributions of the returns of the underlying asset is parametrized by an Edgeworth expansion, which allows for the introduction of higher independent moments of the probability distribution, namely skewness and kurtosis. We test our formula with options in the Brazilian and American markets, showing that the volatility smile can be reduced. We also check whether our approach leads to more e cient hedging strategies of these instruments.