Edited by Adrian R. Bell, Chris Brooks and Marcel Prokopczuk
Chapter 5: American option pricing using simulation with an application to the GARCH model
To date, pricing options in general and options with early exercise in particular remains a challenge and an area of interest in empirical finance. There are several reasons for this. In reality, many exchange traded options do have the possibility of early exercise and hence this feature needs to be considered when pricing these claims. This is the case for most if not all options written on individual stocks and if neglected their values could be severely underestimated. However, potentially much more important is the fact that many decisions made in real life, not only of the financial kind, can be regarded as problems of deciding on the optimal stopping time and hence correspond to the American option pricing situation. A classical example is that of real options – for instance, the option to develop an area for mining. The decision of when to develop the mine is essentially one of deciding on the optimal stopping time, and the value of the mine should be calculated taking this into consideration. As a result of the wide applicability of the American option pricing problem it is of immediate interest to develop a flexible pricing framework. For example, theoretically it is well known that the price of an equity option on a financial asset depends on multiple factors including the strike price and the maturity of the option, the interest rate, the value of the underlying asset, the volatility of this asset and the value of dividends paid on it.
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