EUROPEAN CALL OPTION PRICING BY ESSCHER TRANSFORM

• Main Author: Hazna Latiefah, Efa
• Format: Theses
• Language: Indonesia
• Subjects: Matematika
• Online Access: https://digilib.itb.ac.id/gdl/view/32144
• Institution: Institut Teknologi Bandung

The Black-Scholes model has long been considered as the standard method for pricing options. This model assumes log-return of the stock prices are normally distributed. However, there is much empirical evidence for that these log-return are not normally distributed. Therefore, in this thesis the log return of stock prices are modelled with some stochastic process in the family of levy process. This thesis will consider four alternate levy process that included non zero skewness, kurtosis greater than 3 and jumps. They are Normal Inverse Gaussian Process, Shifted Poisson Process, Shifted Gamma Process, and Shifted Inverse Gaussian process. The Fundamental Theorem of Asset Pricing stated that the absence of arbitrage is equivalent to the existence of an equivalent martingale measure. Therefore, a method needed to obtain the equivalent martingale measure. In this thesis, the equivalent martingale measure obtained by Esscher transform. An Esscher transform of a stock-price process induces an equivalent probability measure on the process. The Esscher parameter is determined so that the discounted price of stock is a martingale under the new probability measure. The price of option is simply calculated as the expectation, with respect to the equivalent martingale measure, of the discounted payoffs. For simulation, the levy process are used to fit the log return of PT Astra International Tbk historical data, the log-return of Jakarta Composite Index historical data, and the log return of Alexion Pharmaceutical, Inc historical data. By means of both graphical and quantitative method, it shows that Normal Inverse Gaussian Process performs better than the other processes. At last, this thesis provides a comparison of the prices of European Call Options obtained by each model