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# Option Pricing Models

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Introduction

Research Proposal Title: Option Pricing Models Introduction It is known that most of the option pricing models and techniques employeed by today's analysts are rooted in a model developed by Fischer Black and Myron Scholes in 1973. One basic assumption of BS model is that the stock price is log-normally distributed with constant volatility. However, Fama (1965) and Mandelbrot (1966) found that stock returns exhibit both fat-tailed marginal distributions and volatility clustering. These features are interpreted as evidence of stochastic volatility of financial asset prices. To overcome the shortcoming, many researchers have contributed to substantial new models that incorporate stochastic volatility in the last two decades. It is thus interesting to examine whether the stochastic-volatility option pricing models provide improvements to the BS model. During the past decade, researchers have begun to study generalized autoregressive conditional heteroskedasticitic (GARCH) models for option pricing due to the superior ability of this class of models to describe asset return dynamics. Duan (1995) developed a theory with respect to which options can be priced when the evolution of the asset return follows the GARCH process. Empirically, Duan (1996), Heston and Nandi (2000), Hsieh and Ritchken (2000), Hardle and Hafner (2000), Duan and Zhang (2001) and Christoffersen and Jacobs (2002) have showed that the GARCH model can be used to capture the pricing behavior of exchange-traded European options. ...read more.

Middle

The basic idea of the numeraire approach can be described as follows. Suppose that an option's price depends on several (say, n) sources of risk. We may then compute the price of the option according to this scheme: * Pick a security that embodies one of the sources of risk, and choose this security as the numeraire. * Express all prices in the market, including that of the option, in terms of the chosen numeraire. In other words, perform all the computations in a relative price system. * Since the numeraire asset in the new price system is riskless (by definition), we have reduced the number of risk factors by one, from n to n-1. * We thus derive the option price in terms of numeraire. A simple translation from the numeraire back to the local currency will then give the price of the option in monetary terms. Assumption 1. Given a priori are: * An empirically observable (k+1)-dimensional stochastic process: X = (X1, ..., Xk+1) with the notational convention that the process k+1 is the riskless rate: Xk+1(t) = r(t) * We assume that under a fixed risk-neutral martingale measure Q the factor dynamics have the form: dXi(t) = �i(t, X(t))dt + ?i(t, X(t))dW(t) i = 1, ..., k+1 where W = (W1, ..., Wd)� is a standard d-dimensional Q-Wiener process and ?i = (?i1, ?i2, ..., ?id) ...read more.

Conclusion

There will be an emphasis on a highly structured methodology to facilitate replication (Gill and Johnson, 1997) and on quantifiable observations that lend themselves to statistical analysis. Interpretivism, it claims that rich insights into this complex world are lost if such complexity is reduced entirely to a series of law-like generalizations. And for realism, it is based on the belief that a reality exists that is independent of human thoughts and beliefs. According to the different characters of these three philosophies, I choose the positivism to do may research work. In this research, I assume the role of an objective analyst, coolly making detached interpretations about those data that have been collected in an apparently value-free manner. Most of the data collected are the quantitative data. To be useful these data need to be analysed and interpreted. And the quantitative data can be incorporated into relatively inexpensive personal-computer-based analysis software. These range from spreadsheets such as Excel and Lotus 1-2-3 to more advanced data management and statistical analysis software packages such as Minitab, SAS, SPSS for Windows and Statiew, and the software from the website as well, such as Excel add-in, options strategy evaluation model, and on-line pricing calculators. Data Resources 1. Use computer service, hardware and software . 2. Get primary data and secondary data from internet. 3. Information and data from library and book shop. ...read more.

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