Option Pricing and Distribution Characteristics

• Activity Number: 662
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): David Mauler*+ and James McDonald
• Companies: Brigham Young University and Brigham Young University
• Keywords: Black-Scholes ; return distributions ; Inverse Hyperbolic Sine ; option pricing ; generalized distributions

Abstract

The subject of extensive examination and research in financial literature, the Black-Scholes (B-S) option pricing model has inherent limitations which have been identified and corrected for with varying success. Foremost among these is its assumption of lognormal returns on the underlying asset-frequently shown in empirical studies to be invalid. In response to this, a series of efforts have been made to make use of other more flexible distributions. Following precedent set by papers which have investigated the GB2, Burr-3, Weibull, and g-and-h distributions in this setting, we evaluate the performance of the B-S model when assuming the Inverse Hyperbolic Sine (IHS) distribution. The IHS distribution has been shown to exhibit flexibility comparable to other generalized distributions, but has yet to be formally investigated in this setting. Our findings are consistent with previous studies, in that the B-S model prices options with greater accuracy when assuming the IHS rather than lognormal distribution. We use historical S&P 500 call option prices for our empirical evaluation, and include a comparison to previously examined general distributions in addition to the lognormal.