Valuing American Asian Options with Least Squares Monte Carlo and Low Discrepancy Sequences PDF Download
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Author: Andries Jacobus Van Niekerk
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Languages : en
Pages :
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Book Description
There exists no closed form approximation for arithmetically calculated Asian options, but research has shown that closed form approximations are possible for Geometrically calculated Asian options. The aim of this dissertation is to effectively price American Asian options with the least squares Monte Carlo approach (Longstaff & Schwartz, 2001), applying Low discrepancy sequences and variance reduction techniques. We evaluate how these techniques affect the pricing of American options and American Asian options in terms of accuracy, computational efficiency, and computational time used to implement these techniques. We consider the effect of, Laguerre-, weighted Laguerre- , Hermite-, and Monomial-basis functions on the Longstaff and Schwartz (2001) model. We briefly investigate GPU optimization of the Longstaff and Schwartz algorithm within Matlab. We also graph the associated implied and Local volatility surfaces of the American Asian options to assist in the practical applicability of these options.
Author: Andries Jacobus Van Niekerk
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
There exists no closed form approximation for arithmetically calculated Asian options, but research has shown that closed form approximations are possible for Geometrically calculated Asian options. The aim of this dissertation is to effectively price American Asian options with the least squares Monte Carlo approach (Longstaff & Schwartz, 2001), applying Low discrepancy sequences and variance reduction techniques. We evaluate how these techniques affect the pricing of American options and American Asian options in terms of accuracy, computational efficiency, and computational time used to implement these techniques. We consider the effect of, Laguerre-, weighted Laguerre- , Hermite-, and Monomial-basis functions on the Longstaff and Schwartz (2001) model. We briefly investigate GPU optimization of the Longstaff and Schwartz algorithm within Matlab. We also graph the associated implied and Local volatility surfaces of the American Asian options to assist in the practical applicability of these options.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 152
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Author: Jennifer X.F. Jiang
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Category :
Languages : en
Pages : 17
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Book Description
Quasi-Monte Carlo sequences have been shown to provide accurate option price approximations for a variety of options. In this paper, we apply quasi-Monte Carlo sequences in a duality approach to value American options. We compare the results using different low discrepancy sequences and estimate error bounds and computational effort. The results demonstrate the value of sequences using expansions of irrationals.
Author: Nelson Areal
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ISBN:
Category :
Languages : en
Pages : 36
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Book Description
This paper studies various possible approaches to improving the least squares Monte Carlo option valuation method. We test different regression algorithms and suggest a variation to estimating the option continuation value, which can reduce the execution time of the algorithm by one third. We test the choice of varying polynomial families with different number of basis functions. We compare several variance reduction techniques, and find that using low discrepancy sequences can improve the accuracy up to four times. We also extend our analysis to compound and mutually exclusive options. For the latter, we propose an improved algorithm which is faster and more accurate.
Author: Phuc Phan
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Languages : en
Pages : 11
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Book Description
In this report, we evaluate the use of the Least Squares Monte Carlo (LSM) method, which was proposed by Longstaff and Schwartz in 2001. The holder of an American option has the right to exercise the option anytime, which makes the option much more difficult to price compared to a European style option. LSM is a simple and powerful method to price American style options and utilizes the use of least squares to estimate the conditional expected payoff to the option holder from continuation value. I provide a simple version of the LSM algorithm using second degree polynomials as basis functions with working code in Matlab to price American put option. I illustrate how the model is affected when input parameter such as risk free interest rate, volatility, underlying stock price, time to maturity are perturbed. After that, I construct the quasi Monte Carlo version of the Least Square algorithm by using Halton sequence and compare the performance of both quasi Monte Carlo and Monte Carlo algorithm.
Author: Lars Stentoft
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Languages : en
Pages :
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Author: Lars Stentoft
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Languages : en
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Author: Shiguang Han
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Category :
Languages : en
Pages : 65
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Author: Diego Garcia
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Category :
Languages : en
Pages : 132
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Author: Qiang Liu
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Category :
Languages : en
Pages : 9
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Book Description
Options pricing and hedging under canonical valuation have recently been demonstrated to be quite effective, but unfortunately are only applicable to European options. In this paper, a variation of canonical valuation called canonical least-squares Monte Carlo is proposed to price American options, which proceeds in three stages. First, given a set of historical gross returns (or price ratios) of the underlying for a chosen time interval, a discrete risk-neutral distribution is obtained via the canonical approach. Second, from this canonical distribution independent random samples of gross returns are taken to simulate future price paths for the underlying. Third, to those paths the least-squares Monte Carlo method is then applied to compute a price for an American option. Numerical results obtained from using simulated gross returns under geometric Brownian motion (GBM) show that this new approach yields reasonably accurate prices for American put options and can be utilized as an alternative to pricing American options, whether the underlying follows GBM or not.
