American Option Price Approximation for Real-Time Clearing
Abstract: American-style options are contracts traded on financial markets. These are derivatives of some underlying security or securities that in contrast to European-style options allow their holders to exercise at any point before the contracts expire. However, this advantage aggravates the mathematical formulation of an option's value considerably, explaining why essentially no exact closed-formed pricing formulas exist. Numerous price approximation methods are although available, but their possible areas of application as well as performance, measured by speed and accuracy, differ. A clearing house offering real-time solutions are especially dependent on fast pricing methods to calculate portfolio risk, where accuracy is assumed to be an important factor to guarantee low-discrepancy estimations. Conversely, overly biased risk estimates may worsen a clearing house's ability to manage great losses, endangering the stability of a financial market it operates. The purpose of this project was to find methods with optimal performance and to investigate if price approximation errors induce biases in option portfolios' risk estimates. Regarding performance, a Quasi-Monte Carlo least squares method was found suitable for at least one type of exotic option. Yet none of the analyzed closed-form approximation methods could be assessed as optimal because of their varying strengths, where although the Binomial Tree model performed most consistently. Moreover, the answer to which method entails the best risk estimates remains inconclusive since only one set of parameters was used due to heavy calculations. A larger study involving a broader range of parameter values must therefore be performed in order to answer this reliably. However, it was revealed that large errors in risk estimates are avoided only if American standard options are priced with any of the analyzed methods and not when a faster European formula is employed. Furthermore, those that were analyzed can yield rather different risk estimates, implying that relatively large errors may arise if an inadequate method is applied.
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