In this paper, we apply the Least-Squares Monte Carlo method intensively to price four different American Asian (Amerasian) options with four different polynomial basis. Although not dedicated to the task of pricing an American Asian option, other authors, such as Glasserman ( 2004) states that “accuracy depends on the choice of basis functions, which may require experimentation or good information about the structure of the problem”. They applied two different polynomial basis, i.e., exponential and Laguerre. Also to access the performance of this techniques, Cerrato and Cheung ( 2007) priced an American Asian Arithmetic Average call option using three sets of simulated trajectories. In their experiment, they used power polynomial basis. Chaudhary ( 2005) used quasi-random sequences to improve the performance of this technique by pricing an American Asian Arithmetic Average call option without varying the polynomial basis used. Moreno and Navas ( 2003) found that the choice of the polynomial basis and the degree of these polynomials influence the estimated prices. Moreno and Navas ( 2003) access the performance of Least Squares Monte Carlo Method numerically, by using two different polynomial basis, i.e., Laguerre and Hermite B, to value the same American Asian option priced by Longstaff and Schwartz ( 2001). Longstaff and Schwartz ( 2001) exemplified the use of their technique in pricing an American Asian Arithmetic Average Fixed Strike call option with a specific polynomial basis, i.e., power. The Least-Squares Monte Carlo Method has been used to price American Asian options. Besides being faster and more precise to compute than other methodologies, the LSM methodology helps assess path-dependent American options with multiple dimensions and multiple state variables, being also applied to Markovian and non-Markovian problems. This technique includes different methods, such as the Least-Squares Monte Carlo method (LSM), first introduced by Longstaff and Schwartz ( 2001). The most flexible technique for pricing exotic options, such as American options, is the use of stochastic simulation with optimization algorithm. Traditional techniques such as the finite-differences method and lattice become less attractive when dealing with pricing derivatives with multiple stochastic variables, problems with many dimensions, or even path-dependent American options, as it is the case of American Asian (Amerasian) options. The characteristics of the contract (subject, premium, strike price, deadlines and maturity) are freely agreed between the parties, emphasizing their non-standardization. Because they are complex (or exotic), the Asian options are usually traded over the counter. Its versatility is confirmed by its presence in markets like commodities, electric power, interest rates and currency rates (McDonald 2006). We find that when pricing an American Asian put option, Power A is better than the other basis we have studied here whereas when pricing an American Asian call, Hermite A is better.Īsian options are often used for cash flow hedges in companies whose purchase programming is set to mitigate the fluctuation of raw materials’ prices. However, our results does not confirm these. Theoretically all basis can be indistinctly used when pricing the derivative. Our results suggest that one polynomial basis is best suited to perform the method when pricing an American Asian option. In this article The Least-Squares Monte Carlo Method performance is assessed in pricing four different types of American Asian Options by using four different polynomial basis through three different sets of parameters. Such empirical outcome is theoretically unpredictable, since in principle all basis can be indistinctly used when pricing the derivative. For an Amerasian put option, the Power polynomial basis is recommended. In the case of an Amerasian call option, for example, we find that the preferable polynomial basis is Hermite A. We show that the choice of the basis interferes in the option's price by showing that one of them converges to the option's value faster than any other by using fewer simulated paths. To every American Asian Option priced, three sets of parameters are used in order to evaluate it properly. We assess Least-Squares Method performance in pricing four different American Asian Options by using four polynomial basis: Power, Laguerre, Legendre and Hermite A. By comparing four different polynomial basis we show that the choice of basis interferes in the option's price. The standard approach in the option pricing literature is to choose the basis arbitrarily. This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing.
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