Valuation For Lookback Options Embedded With Installment Paying

Option is a contract signed by the seller and the buyer, which gives the holder a right but noa obligation to buy or sell the underlying asset by a certain date in the future for a certain price.Option pricing problem has become an important research topic in financial engineering.It is well known that the conventional option product is that when the buyer pays the sellerall the money today he can acquires the right to exercise the option at the option maturity date.When the holder chooses the option exercising date only on the expiration date, the option iscalled a European-style. When the holder chooses the option exercising date at any time up tothe expiration date, the option is called an American-style. Today there exists a traded contractembedded with installment paying on exchanges in which the buyer pays a smaller up-front pre-mium and then a constant stream of installments at a certain rate per unit time. The buyer has theright of choosing at any time up to the maturity to stop making installment payments by eitherexercising the option or stopping the option contract. Based on the assumptions of the classicalBlack-Scholes model, this thesis considers pricing the Lookback options embedded with install-ment paying called installment lookback options. This thesis is organized as follows:Chapter 1 introduces simply the pricing theories and studied literatures for options, the look-back options and installment options.In Chapter 2, based on the assumption of the underlying stock's price satisfying the classicalBlack-Scholes model, we consider the pricing for the standard Lookback call option with discrete-installment paying. Some numerical results and the optimal stopping boundary with improvedCRR method are provided in the end.In Chapter 3, based on the assumption of the underlying stock's price satisfying the classi-cal Black-Scholes model, the standard Lookback options embedded with continuous-installmentpaying is considered. Some properties of both the options price function and the optimal stoppingboundary are proved. The quasi-analytical formulas for both the option value and the optimal stop-ping boundary for the continuous-installment Lookback put options with ?oating strike prices areobtained by using the decomposition technique which is used to make a nonlinear integral equa- tion of optimal stopping boundary. Using the extension of the above integral equation (EIE) andapproximating the optimal stopping boundary as step functions, we obtain the iterative schemesfor the optimal boundary with the Least-square or Newton-Raphson method, and then have theoption price based on this approaches. Some numerical examples are provided to indicate theeffects on the option price of the installment payments and practical significance of the optimalstopping boundary .Under the same market model in Chapter 3, pricing an American continuous-installmentLookback option are further considered in Chapter 4. Same arguments in Chapter 3, we ob-tain also two nonlinear integral equations for both optimal exercising boundary and the optimalstopping boundary which provide two iterative schemes to obtain these optimal boundaries. Weprovide also some numerical examples to indicate the effects on the option price of the installmentpayments and practical significance of the optimal boundaries.Conclusions and some future research works are proposed in Chapter 5.