#TITLE_ALTERNATIVE#

• Main Author: PARULIAN JOSAPHAT MARBUN (NIM 20105008), BONY
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/7450
• Institution: Institut Teknologi Bandung

Exotic option or path-dependent option is whose payoff depends on the behavior of the price of the underlying between time 0 and maturity time, rather than merely on the final price of the underlying, such as compound option. In this thesis, a generalization of the formula for compound options is obtained by using martingale method and the change of probability measure. Besides, compound options that discussed here, are compound options with two strike prices, two maturity time and the underlying asset is stock. Compound options have four main types, namely call option on call option, put option on call option, call option on put option, and put option on put option. In order to understand more easily, the difference between compound option and underlying option needs to be stressed. The options mentioned first is compound option and the option mentioned secondly is underlying option. Compund option is in the form European option or American one. As for with underlying option. Thus, generally speaking, sixteen types of compound option are obtained.<p> <br /> <br /> <br /> Derivation of analytical formula is executed in Black-Scholes framework that is the underlying stock is assumed follows geometric Brownian motion. Analytical formula can be obtained only for European option on European option case. Meanwhile for other cases than European option on European option, analytical formula can not be obtained. The pricing of compound option for other cases than European option on European option can be done only numerically. In this thesis numerical method used to obtain the price of compound option, either European option on European option or not, is binomial method. For European option on Eropean option, numerical price is compared to exact price and numerical price converges to exact price.