Calibration to American options: numerical investigation of the de-Americanization method

Abstract

American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods for American options that are based on Monte Carlo, tree and partial differential equation methods. We present an alternative approach that has become popular under the name de-Americanization in the financial industry. The method is easy to implement and enjoys fast run-times (compared to a direct calibration to American options). Since it is based on ad hoc simplifications, however, theoretical results guaranteeing reliability are not available. To quantify the resulting methodological risk, we empirically test the performance of the de-Americanization method for calibration. We classify the scenarios in which de-Americanization performs very well. However, we also identify the cases where de-Americanization oversimplifies and can result in large errors.

Complexity reduction for calibration to American options

“…The resulting tree is used to price the associated so-called pseudo-European option with the same strike and maturity. A detailed description of the de-Americanization method is given in [11,Algorithm 1].…”

“…We observe especially for scenarios p 4 and p 5 , where the volatility of volatility ξ and correlation ρ have higher values, that the DAS has the strongest effect. Note that here we fix r = 5% as a particular case to highlight the de-Americanization effect, and we refer to [11] for a more detailed parameter study. 6.3.…”

“…These are obtained by perturbing the American put prices P obs j , i.e., P obs j := D(P obs j ), where D : R M → R M , and the corresponding model prices are the European put prices, P N j (Θ) = P N ,Eu j (Θ). As in [11], we use the binomial tree method, see [18], to transform American option prices into pseudo-European option prices. In a nutshell, once the observed market prices P obs j , j = 1, .…”

“…Whereas discretization techniques for PDEs and RDMs form a rather flexible and abstract framework, de-Americanization strategies are specially designed for the valuation of American options [13,11]. These strategies first transform the price into a pseudo-European option price and secondly calibrate the European option by directly applying the computationally less expensive closed-form solution.…”

“…These strategies first transform the price into a pseudo-European option price and secondly calibrate the European option by directly applying the computationally less expensive closed-form solution. In [11], the de-Americanization techniques are studied numerically, which also reveals their limitations. Both model reduction techniques, i.e., the RBM strategy and the de-Americanization strategy, are numerically studied and compared for the Heston model [33].…”