Author: Melanie Cao
Publisher: Kingston, Ont. : Institute for Economic Research, Queen's University
Published: 1997
Total Pages: 32
ISBN-13:
DOWNLOAD EBOOK →Author: Melanie Cao
Publisher:
Published: 1997
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOK →This thesis consists of three essays which study the valuation of options in an equilibrium framework. The first essay uses a general equilibrium model to study the valuation of options on the market portfolio with predictable returns and stochastic volatility in a complete market. In a closed endowment economy where aggregate dividend is the only source of uncertainty, I investigate why the stock return exhibits certain predictable features. I also examine the equilibrium relationship between the price of the market portfolio and its volatility, as well as the relationship between the spot interest rate and the market volatility. Equilibrium conditions imply that the predictable feature of the market portfolio is induced by the mean-reverting of the rate of dividend growth. It is shown that there is strong interdependence between the stock price process and its volatility process. Using the Euler equation, I derive equilibrium pricing formulas for options on the market portfolio which incorporate both stochastic volatility and stochastic interest rates. Since there is only one source of uncertainty, this model preserves the completeness feature for hedging and risk management purposes. With realistic parameter values, numerical examples show that stochastic volatility and stochastic interest rates are both necessary for correcting the Black-Scholes pricing biases. The second essay focuses on the currency options in an incomplete market where the economy is subject to shocks in aggregate dividend and money supply. The key feature is that the exchange rate exhibits systematic jump risks which should be priced in the currency options. The closed-endowment equilibrium model in the first essay is extended to a small open monetary economy with stochastic jump-diffusion processes for both the money supply and aggregate dividend. It is shown that the exchange rate is affected by both government monetary policies and aggregate dividends. Since the jump in the exchange rate is correlated with aggregate consumption, the jump risk in the exchange rate derived from aggregate consumption must be priced by means of utility maximization. I further derive the foreign agents' risk-neutral valuation of the European currency option and provide restrictions that ensure the law of one price in currency option pricing. In general, these restrictions depend on the agent's risk preference. The objective of the third essay is to empirically study the existence of systematic jump risks in exchange rates and analyze their importance for currency option pricing. The empirical study is based on the theoretical model studied in the second essay, which argues that exchange rates are inherently correlated with the market and so must exhibit systematic jump risks. The third essay uses the maximum-likelihood method to estimate the joint distribution of exchange rates and the price of the market portfolio. Empirical results show that it is important to incorporate both systematic and non-systematic jump components in exchange rates in order to correctly price currency options.
Author: Jian Chen
Publisher: Springer
Published: 2018-04-10
Total Pages: 164
ISBN-13: 9811074283
DOWNLOAD EBOOK →This book mainly addresses the general equilibrium asset pricing method in two aspects: option pricing and variance risk premium. First, volatility smile and smirk is the famous puzzle in option pricing. Different from no arbitrage method, this book applies the general equilibrium approach in explaining the puzzle. In the presence of jump, investors impose more weights on the jump risk than the volatility risk, and as a result, investors require more jump risk premium which generates a pronounced volatility smirk. Second, based on the general equilibrium framework, this book proposes variance risk premium and empirically tests its predictive power for international stock market returns.
Author: Jerome Detemple
Publisher:
Published: 2008
Total Pages:
ISBN-13:
DOWNLOAD EBOOK →This paper examines the valuation of European- and American-style volatility options based on a general equilibrium stochastic volatility framework. Properties of the optimal exercise region and of the option price are provided when volatility follows a general diffusion process. Explicit valuation formulas are derived in four particular cases. Emphasis is placed on the MRLP (mean-reverting in the log) volatility model which has received considerable empirical support. In this context we examine the properties and hedging behavior of volatility options. Unlike American options, European call options on volatility are found to display concavity at high levels of volatility.
Author: Stylianos Perrakis
Publisher: Springer
Published: 2019-05-03
Total Pages: 277
ISBN-13: 3030115909
DOWNLOAD EBOOK →This book illustrates the application of the economic concept of stochastic dominance to option markets and presents an alternative option pricing paradigm to the prevailing no arbitrage simultaneous equilibrium in the frictionless underlying and option markets. This new methodology was developed primarily by the author, working independently or jointly with other co-authors, over the course of more than thirty years. Among others, it yields the fundamental Black-Scholes-Merton option value when markets are complete, presents a new approach to the pricing of rare event risk, and uncovers option mispricing that leads to tradeable strategies in the presence of transaction costs. In the latter case it shows how a utility-maximizing investor trading in the market and a riskless bond, subject to proportional transaction costs, can increase his/her expected utility by overlaying a zero-net-cost portfolio of options bought at their ask price and written at their bid price, irrespective of the specific form of the utility function. The book contains a unified presentation of these methods and results, making it a highly readable supplement for educators and sophisticated professionals working in the popular field of option pricing. It also features a foreword by George Constantinides, the Leo Melamed Professor of Finance at the Booth School of Business, University of Chicago, USA, who was a co-author in several parts of the book.