Black–Scholes Option Pricing Model
Simple, generally accepted economic assumptions are insufficient to develop a rational option pricing theory. Assuming a perfect financial market (Section2.1) leads to elementary arbitrage relations which the options have to fulfill. While these relations can be used as a verification tool for sophisticated mathematical models, they do not provide an explicit option pricing function depending on parameters such as time, stock price and the options underlying parameters K, T. To obtain such a pricing function the value of the underlying financial instrument (stock, currency,...) has to be modelled. In general, the underlying instrument is assumed to follow a stochastic process either in discrete or in continuous time. While the latter is analytically easier to handle, the former, which we will consider as an approximation of a continuous time process for the time being, is particularly useful for numerical computations. In the second part of this text, the discrete time version will be discussed as a financial time series model.
KeywordsStock Price Option Price Call Option Implied Volatility Future Contract
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