Research On Basket-Lookback Option Valuation

As a basic derivative security, the option takes an important position in financialmarket. For decades, it has been developing rapidly as an instrument for arbitrageand risk prevention. The fair price of option means the value judgment made by bothof counterparts, but it is rather di?cult to watch it in market. Hereby, the optionvaluation is always an important subject in financial mathematics.The basket option is usually used to hedge a basket of assets. In fact, it is anoption on the portfolio of various underlying assets. And the lookback option isanother exotic option whose payo? at expiry depends on asset price ?uctuationsduring the option's lifetime. Combination with these two options, there will be anew option named basket-lookback option with both properties of those optionsmentioned above. This new option is main object for which we care in this thesis.This thesis mainly include two core parts: 1. In Black-Scholes Model, where allunderlying asset price processes follow geometric Brownian motion with constantvolatilities, the formula in closed form for European basket-lookback call optionvaluation is given by martingale method. And the proof is given. 2. In Gaussian HJMframework, the formula in closed form for the valuation of European basket-lookbackcall option on coupon bonds is given by forward measure approach in forward ratemodel. And the proof is given.