A Horse Race Among Competing Option Pricing Models Using S P 500 Index Options
Download A Horse Race Among Competing Option Pricing Models Using S P 500 Index Options PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get A Horse Race Among Competing Option Pricing Models Using S P 500 Index Options book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Derivatives Pricing and Modeling
Author: Jonathan Batten
language: en
Publisher: Emerald Group Publishing
Release Date: 2012-07-02
Highlights research in derivatives modelling and markets in a post-crisis world across a number of dimensions or themes. This book addresses the following main areas: derivatives models and pricing, model application and performance backtesting, and new products and market features.
A 'Horse Race' Among Competing Option Pricing Models Using S&P 500 Index Options
The last three decades have witnessed a whole array of option pricing models. We compare the predictive performances of a selection of models by carrying out a horse race on Samp;P 500 index options along the lines of Jackwerth and Rubinstein (2001). The models we consider include: Black-Scholes, trader rules, Heston's stochastic volatility model, Merton's jump diffusion models with and without stochastic volatility, and more recent Levy type models. Trader rules still dominate mathematically more sophisticated models, and the performance of the trader rules is further improved by incorporating the stable index skew pattern documented in Li and Pearson (2005). Furthermore, after incorporating the stable index skew pattern, the Black-Scholes model beats all mathematically more sophisticated models in almost all cases. Mathematically more sophisticated models vary in their overall performance and their relative accuracy in forecasting future volatility levels and future volatility skew shapes.
Pricing S&P 500 Index Put Options
The primary purpose of this paper is to examine whether leverage has a significant statistical and economic effect on the pricing of Samp;P 500 index put options. The secondary purpose is to present information regarding the shape and persistent smile rather than skew of the implied volatility function. This is the first paper to directly test for leverage effects in stock index put options. To analyze these effects we use the Geske (1979) compound option model. The Geske model is closed form, implies stochastic equity volatility, is consistent with Modigliani and Miller, incorporates debt refinancing, and includes possibly differential default and bankruptcy. Black-Scholes (1973) is a special case of the Geske model. In this paper we show that during the years 1996-2004 the aggregate market based debt to equity (D/E) ratio of the firms comprising the Samp;P 500 equity index varies from about 40-120 percent. We believe that we are the first to present a market D/E ratio derived from option theory. We also present evidence that on an average of about 200,000 options during this 8 year period the implied volatility most often exhibits a smile not a smirk or skew. Next and more importantly we are the first to report the details of the statistically significant economic effects that market leverage has on pricing Samp;P 500 index put options. We measure that the Geske model improves the net option valuation of listed in the money (or out of the money) Samp;P 500 index put options on average by about 37% (19%) compared to Black-Scholes values. We demonstrate that the improvement is directly (and monotonically) related to both the time to expiration of the option and the amount of leverage in this market index. For options with longer expirations and/or periods of higher market leverage the improvement is greater, ranging from about 50% to 85%. We also demonstrate economic significance in basis points by showing that dealers making a book in index options can expect benefits of at least several 100 basis points using Geske instead of Black-Scholes. Finally we show that the per cent pricing errors compare very favorably with Heston-Nandi (2000).