Finance with Monte Carlo by Ronald W. Shonkwiler

Author:Ronald W. Shonkwiler
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

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With that background, we present an algorithm using geometric cooling.

The key step in the algorithm is the line in which the old state x is replaced by the new one y with probability p (as achieved by drawing a computer random number r and replacing if r < p). If the new energy E y is less than the old, then p as calculated is greater than 1 and the new state is accepted. But the new state can also be accepted even if the new state is worse. And this will happen with greater probability at high temperature than low. In this way the algorithm does not become trapped in local minima.

Another complication of the present application is that the energy calculation (i.e. the price calculation) is stochastic, see Fig. 3.11. What we want to maximize on is the mean of the option prices. A way to do so is to make the reported option price an average over several individual runs. By calculating the variance of the average, a confidence interval for the option prices can be worked out. For more information on this, see Section A.8.

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