David Mauler and Dr. James McDonald, Department of Economics

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.

With the exception of the introduction of the IHS distribution in the context of option-pricing, our empirical evaluation can be considered a synthesis of previous literature where, in most cases, a given distribution is pitted individually against the lognormal. Our empirical application not only confirms the accepted conclusion in the literature that additional flexibility allows for increased accuracy in option-pricing, but also provides insight regarding the relative performance of the tested distributions. Of all the considered distributions, the g-and-h and IHS distributions are among the most flexible in terms of feasible skewness and kurtosis values and yield almost identical results. Also having a large moment space–albeit much more restrictive than that of the IHS and g-and-h for data with negative skewness–the GB2 is a particularly attractive choice given its relative accuracy in price forecasting and domain which only permits positive values. Its special and limiting cases, which include the GG, Burr-3, Burr-12, Weibull, and lognormal, allow for slightly faster computation at the expense of accuracy in forecasting (with the exception of the GG). However, given available computing capacity, selection of the GB2 would seem reasonable in practice despite the added dimensionality in the estimation procedure.

This project was computationally challenging, but offered a great learning experience for me. It was informative for me to experience the research process in its entirety, beginning with an idea and ending with us submitting our results to a peer-reviewed financial journal. I had the opportunity to travel with Dr. McDonald to the American Statistical Association’s Joint Statistical Meetings in San Diego this past August and present our paper there. I was the only undergraduate in our session, and was even more appreciative of the level of involvement in our research the ORCA grant had allowed me to experience.