Abstract
If we want to value a European-style option without dividend payment, several parameters have to be specified, some of which are simply given in the option contract, such as strike price K and time to maturity T. The other variables such as the stock price S(t), the interest rate r(t) and the volatility v(t), are strongly dependent on the market situation and change from day to day. The objective of an option pricing model is to specify these variables and then to value options. Obviously, the process of stock price S(t) plays a crucial and fundamental role since the interest rate and the volatility are merely two parameters of the process S(t) in a risk-neutral pricing framework. Additionally, we can extend the usual Brownian motion for S(t) by adding a discontinuous jump component, hoping that jump phenomena in the stock price movement, for instance, during the crash of 1987, could be described better and more realistically.
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