Flexible Option Valuation Methods

Yin, Yun (2016) Flexible Option Valuation Methods. Masters thesis, University of East Anglia.

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Abstract

This thesis is concerned with methods of option valuation that fall completely outside of the Black-Scholes-Merton (BSM) framework. Data on S&P500 Index options are used to demonstrate the proposed methods. Some of our favoured methods are based on semi-parametric regression; others on simulation. The thesis consists of a number of chapters. In Chapter 2, we outline existing option valuation methods, with particular attention paid to the binomial-tree model and the Black-Scholes formula. We demonstrate that under some circumstances these two methods are equivalent. We also demonstrate using the binomial tree method that a “TGARCH effect” (which plays an important role in later chapters) can explain the well-known “smirk” pattern that is often observed in market option price data.

In Chapter 3, we use regression analysis to investigate the ways in which features of an option actually determine the market price. We start with polynomial regressions, and progress to additive models, with components obtained using the B-spline technique. The focus in these regression models is the role of volatility. Historical measures of volatility are used as explanatory variables in the regression, with one objective being to discover how far back into the past option traders are going when computing volatility. It is proposed that this approach gives rise to an alternative measure of implied volatility that is completely free of the Black-Scholes framework. We use the Practitioner Black Scholes (PBS) model as a Benchmark for comparison. The best of our regression models is found to perform better than the Black-Scholes formula in out-of-sample prediction of market prices.

In Chapter 4, we focus on the underlying (S&P500) Index, and consider a number of varying volatility models (ARCH, GARCH and TGARCH) of daily returns. We found that the TGARCH model is the best model to represent the volatility process. Then we simulated data from the models considered using the coefficients from the estimated models. After that, we found that the simulated ARCH family volatility models worked correctly, since the “true” parameter values are included in the confidence intervals.

Chapter 5 continues with the simulations of daily return data, in building a Monte Carlo program for the valuation of European options that allows for varying volatility. Of particular interest is whether superior models of the underlying stock price (i.e. ARCH, GARCH and TGARCH) result in option valuations that are superior to the Black-Scholes valuation. Superiority in this context is defined primarily in terms of ability to predict market prices. We find that all models perform better than the benchmark (PBS) model. Which model performs best depends on the type of market and time to expiry: ARCH is the best model for predicting the short and medium term put options for both bear and calm market and GARCH is the best one for predicting the long term put options in the bear market. In the crash market, TGARCH Monte Carlo simulation is the best model for predicting the long term European call and put options.

Item Type: Thesis (Masters)
Faculty \ School: Faculty of Social Sciences > School of Economics
Depositing User: Bruce Beckett
Date Deposited: 24 Jul 2018 09:46
Last Modified: 24 Jul 2018 09:46
URI: https://ueaeprints.uea.ac.uk/id/eprint/67830
DOI:

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