## Upper Bounds for American Option Prices using Regression with Martingale Basis Functions (2004)

### BibTeX

@MISC{Firth04upperbounds,

author = {N. P. Firth},

title = {Upper Bounds for American Option Prices using Regression with Martingale Basis Functions},

year = {2004}

}

### OpenURL

### Abstract

High dimensional American options have no analytic solution and are di#cult to price numerically. Progress has been made in using Monte Carlo simulation to give both lower and upper bounds on the price. Building on an idea of Glasserman and Yu we investigate the utility of martingale basis functions in regression based approximation methods. Regression methods are known to give lower bounds easily, however upper bounds are usually computationally expensive.

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4 |
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4 |
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3 |
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Citation Context ...ow-discrepancy sequences [11]. Other methods include parameterization of the optimal exercise boundary [6, 24, 30], a quantization tree algorithm [3], wavelets [21, 22], irregular grid approximations =-=[5]-=-, and sparse grid methods [37]. Regression methods include [18, 33, 43]. The regression method of Longstaff and Schwartz [33] has proved particularly popular, due to its accuracy and simplicity. The p... |

2 |
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(Show Context)
Citation Context ...t [2, 16] and has been modified to use low-discrepancy sequences [11]. Other methods include parameterization of the optimal exercise boundary [6, 24, 30], a quantization tree algorithm [3], wavelets =-=[21, 22]-=-, irregular grid approximations [5], and sparse grid methods [37]. Regression methods include [18, 33, 43]. The regression method of Longstaff and Schwartz [33] has proved particularly popular, due to... |

2 |
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(Show Context)
Citation Context ...t [2, 16] and has been modified to use low-discrepancy sequences [11]. Other methods include parameterization of the optimal exercise boundary [6, 24, 30], a quantization tree algorithm [3], wavelets =-=[21, 22]-=-, irregular grid approximations [5], and sparse grid methods [37]. Regression methods include [18, 33, 43]. The regression method of Longstaff and Schwartz [33] has proved particularly popular, due to... |

1 |
Why use QuantLib? URL http://www.maths.ox.ac.uk/∼firth/research/quantlib.pdf
- Firth
(Show Context)
Citation Context ...pact of their work if both their papers and software implementations are available on the internet. For a survey of open–source derivatives pricing libraries and the benefits of adopting QuantLib se=-=e [23]. Fo-=-r instructions on how to download, install, run and contribute see the project website [36]. 8.2. Regression Precision. Under certain conditions on the residuals, ‘regression later’ gives an estim... |

1 | Monte Carlo methods for multiple exercise problems - Meinshausen, Hambly - 2004 |