Essays on equilibrium valuation of options, theorem and empirical estimates

by Cao, Melanie

Abstract (Summary)
This thesis consists of three essays which stiidy the vduation of options in an eqiiilibriiun framework. The first eçsay uses a general eqitilibriiun model to stiidy the valiiation of options on the market portfolio with predictable retiirns and stochastic volatility in a complete market. In a closed endowment economy where aggregate dividend is the only source of imcertainty. 1 investigate why the stock retilrn extiibits certain predictable featiires. I also examine the eqidibriiun 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. Eqtdibriiun conditions imply that the predictable featiire of the market portfolio is indiiced 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 eqiiation. 1 derive eqiulibriim pricing formulas for options on the market portfoIio which incorporate bot,h stochastic volatility and stochastic interest rates. Since there is ody one source of imcertainty: this model preserves the completeness featiue for heùging and risk management piqoses. With realistic paramet er values, niimerical examples show that stochastic volatility and stochastic interest rates are both necessary for correcting the Black-Scholes pricing biases. The second essay fociises on the ciirrency options in an incomplete market where the economy is siibject to shocks in aggregate dividend and money siipply. The key featiire is that the exchange rate exhibits systematic jiunp risks which shoidd be priced in the cimency options. The closed-endowment eqidibriiim mode1 in the hst essay is extended to a small open monetary economy with stochastic jiunpdiffi~ion processes for bot h the money siipply and aggregate div- idend. It is shom that the exchange rate is dected by both government monetary policies and aggregate dividends. Since the jump in the exchange rate is corre- lated with aggregate con~iimption~ the jiunp risk in the exchange rate derived from aggregate coiisimption miist be priced by means of iitility maximization. 1 further derive the Foreign agents' risk-neiitrd vdiiation of the Eiuopean cimency option and provide restrictions that ensrue the law of one price in ciurency option pricing. In generd, these restrictions depend on the agent's risk preference. The objective of the third essay is to empirically stiidy the existence of sys- tematic jiunp risks in exchange rates and analyze their importance for ciurency option pricing. The ernpirical stiidy is based on the theoretical mode1 stiidied in the second essay, which argiles that exchanges rates are inherently correlateci with the market and so miist e'diibit systematic jimp risks. The thrd essay lises the maximiun-likelihood method to estirnate the joint distribution of exchange rates and the price of the market portfolio. Empirical residts show that it is important to incorporate both systernatic and non-systematic jimp components in eschange rates in order to correctly price ciirrency options. To rny parents
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Source Type:Master's Thesis



Date of Publication:01/01/1997

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