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Journal of Undergraduate Research

Keywords

Inverse Hyperbolic Sine distribution, IHS, price formula

College

Family, Home, and Social Sciences

Department

Economics

Abstract

My BYU ORCA grant provided valuable funding which allowed me to spend significant time on an interesting research question Dr. McDonald and I had considered late last year. We wanted to investigate whether the Inverse Hyperbolic Sine (IHS) distribution would allow for a more accurate option-pricing formula, extending the Black-Scholes formula which assumes a lognormal distribution. The project widened in scope as we worked on it during the summer. We eventually expanded our original proposal and included a number of other flexible distributions (GB2, g-and-h, Burr-3, Burr-12, Weibull). We derived price formulas specific to each assumed distributional form. The IHS option price formula had not previously been presented in the literature. We then undertook an empirical application where implied risk-neutral density functions for each distribution are estimated from options on the S&P 500 Index. Upon evaluating the distributions’ performance relative to one another, the GB2 appeared to be the most attractive choice.

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