An Improved Method for Pricing and Hedging American Options

Tommaso Paletta, Silvia Stanescu, R. Tunaru
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Abstract

The majority of quasi-analytic pricing methods for American options are efficient near-maturity but are prone to larger errors when time-to-maturity increases. A new methodology, called the "extension"-method, is introduced to increase the accuracy of almost any existing quasi-analytic approach in pricing long-maturity American options. It relies on an approximation of the optimal exercise price near the beginning of the contract combined with existing pricing approaches so that the maturity range for which small errors are attainable is extended. The new methodology retains the quasi-analytic nature of the methods it improves on and we derive generic quasi-analytic formulae for the price of an American put as well as for its delta parameter. Our numerical study indicates that the proposed methodology considerably improves both the pricing and the hedging performance of a number of established approaches for a wide range of maturities. Furthermore, the pricing improvements are most sizeable at longer maturities, where existing approaches do not perform well.
一种改进的美式期权定价和套期保值方法
多数美式期权的准解析定价方法在接近到期时是有效的,但当到期时间增加时,容易产生较大的误差。一种被称为“扩展”方法的新方法被引入,以提高几乎所有现有的准解析方法在长期美国期权定价中的准确性。它依赖于合约开始时最优行权价格的近似值与现有定价方法相结合,从而扩大了可实现小误差的期限范围。新方法保留了它改进的方法的准解析性质,我们为美国看跌期权的价格及其delta参数导出了一般的准解析公式。我们的数值研究表明,所提出的方法大大提高了定价和套期保值性能的一些既定方法的期限范围很广。此外,在现有方法表现不佳的较长期限债券上,定价方面的改善最为显著。
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