Fabozzi et al free download

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That is, we introduce a new utility-based approach, which enables us to easily price both European and American options. In so doing, we circumvent the free-boundary problem and provide general solutions to the optimal option shares, optimal stock shares and the optimal hedge ratio. First, we present an option model without stocks, then we expand the model to include stocks.

W u is a standard Brownian motion on the probability space. The wealth is given by:. The firms's objective is to maximize the expected utility of total wealth with respect to the option quantity:. It is worth noting that the option writer is a not a price taker and therefore the price depends on the quantity, but the quantity does not depend on the price. It is well known that the price of the American option is defined as In this article, we redefine the price of the American option based on the price of its European counterpart as:.

The above equation holds with equality and thus the usual free-boundary problem is avoided. The solution yields. The value of a t can be calculated using historical data for the difference between the American price and the European price. In this section, we consider the case when the optimal option quantity and the optimal stock quantity are simultaneously determined. To determine the option price, we simply divide the initial wealth minus the stock portfolio by the optimal option quantity:.

In addition, the optimal hedge ratio has an explicit solution independent of preferences. Furthermore, from 28 , we obtain. Fabozzi, F. NJ: Prentice Hall.

Google Scholar. Epps, T. NJ: Wiley. Book Google Scholar. Focardi, F. Black, F.