PENENTUAN HARGA OPSI EROPA DI BAWAH MODEL BS-BHM-UPDATED BERDASARKAN PADA PENDEKATAN BHM; THE DETERMINING OF EUROPEAN OPTION PRICING UNDER THE BS-BHM-UPDATED MODEL BASED ON THE BHM APPROACH

MUTIJAH, Suryo Guritno

2016 | Tesis | FMIPA

Investors can use the technical and fundamental analysis to evaluate their invested stocks so that they obtain profits according to their wishes. The technical analysis is a way of the stocks assesment based on the information of stocks data at past time and the fundamental analysis is done by calculating the discounted cash flows. One of the advantage it is in the form of dividends. Therefore investors can evaluate stocks based on the dividends information. According to the background as above, then Brody, Hughston, and Macrina (BHM) developed an asset pricing model based on the dividend cash flows information and called the BHM Approach (BHM model). Generally, the BHM model is not a closed form expression. But for dividends distributed apriori Exponential and Gamma then the BHM model is a closed form expression. This research results the BHM model is a closed form expression for dividends distributed apriori is Rayleigh. Based on the idea that some frameworks of asset pricing model, generally can produce the kind of Black Scholes model as a special case. Related the idea then Brody, Hughston, and Macrina also developed a Black Scholes (BS) model from an information-based perspective by Brody, Hughston, and Macrina (BHM), and called BS-BHM model in this research. To obtain BS-BHM model is needed applying of Gaussian integral. By investigating of Gaussian integral is found imprecise in analyzing of the perfect square. The BS-BHM model that is improved in applying of Gaussian integral so called BS-BHM-Updated model. The BS-BHM-Updated model is a lognormal model. Parameters estimaton on the BS-BHM-Updated and BS-BHM model are done by using the momen method. Estimating of parameters under BSBHM- Updated model result an estimator in the quadratic equation and estimating of parameters under BS-BHM model result an estimator in the polynomial of four degree. Empirical studies to the parameters estimation are done by using the historical data of Microsoft (MSFT) stocks price. Option is the derivative asset of stock if the underlying asset is stock. The financial world has recognized the kinds of option, one of them is European option. Pricing of European option under the BS-BHM-Updated model and its good properties is determined in this research. The good properties are put-call parity, greeks, performance of implied volatility comparing of the historical volatility, and the European call option price for the extrem volatility. Empirical studies by calculating of the European option price and its properties are also done by using the data of Microsoft (MSFT) stocks price

Kata Kunci : BHM model, Closed form expression, BS-BHM model, Gaussian integral, BS-BHM-Updated model, and European Option.