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標題: Apply the Least Squares Monte Carlo Approach to Extremely Complex Options: A Building Block Methodology
運用最小平方蒙地卡羅模擬評價複雜選擇權: 區塊建構法
作者: 簡志宏
Chien, Chih-Hung
關鍵字: Least-Squares Monte Carlo;最小平方蒙地卡羅;Convertible Bond;Exotic Option;可轉換公司債;新奇選擇權
出版社: 財務金融系所
引用: Avellaneda, Marco, and Lixin Wu, 1999, Pricing Parisian-style Options with a Lattice Method, International Journal of Theoretical and Applied Finance, 2, 1-16. Boyle, Phelim P., and Sok-Hoon Lau, 1994, Bumping up against the Barrier with the Binomial Method, The Journal of Derivatives , 1(4), 6-14. Brennan, Michael J., and Eduardo S. Schwartz, 1977, Convertible bonds: Valuation optimal strategies for call and conversion, Journal of Finance, 6, 1699-1715. Brennan, Michael J., and Eduardo S. Schwartz, 1980, Analyzing convertible bonds, Journal of Financial and Quantitative Analysis, 15, 907-929. Cheng, Wai-yan, and Shugang Zhang, 2000, The Analytics of Reset Options, Journal of Derivatives, 59-71. Chesney, Marc, Monique Jeanblanc-Picqu´e, and Marc Yor, 1997, Brownian Excursion and Parisian Barrier Options, Advances in Applied Probability, 29, 165-184 Costabile, Massimo, 2002, A Combinatorial Approach for Pricing Parisian Options, Decisions in Economics and Finance, 25, 111-125. Gray, Stephen F., and Robert E. Whalely, 1997, Valuing S&P 500 Bear Market Warrants with a Periodic Reset, Journal of Derivatives, 5, 99-106. Haber, Richard J., Philipp Schonbucher, and Paul Wilmott, 1999, Pricing Parisian Options, Journal of Derivatives, 6(3), 71-79. Hull, John C., 2003, Options, Futures, and Other Derivatives. Ingersoll, Jonathan, 1977, A Contingent-claims Valuation of Convertible Securities, Journal of Financial Economics, 4, 289-322. Kim, In-Joon, Geun-Hyuk Chang, and Suk-Joon Byun, 2003, Valuation of Arithmetic Average Reset Options, Journal of Derivatives, 11(1), 70-80. Liao, Szu-Lang, and Chou-Wen Wang, 2002, Pricing Arithmetic Average Reset Options with Control Variates, Journal of Derivatives, 10, 59-74. Longstaff, Francis A., and Eduardo S. Schwartz, 2001, Valuing American Options by Simulation: A Simple Least-squares Approach, The Review of Financial Studies, 14, 113-147. McConnell, John J., and Eduardo S. Schwartz, 1986, LYON Taming, Journal of Finance, 14, 561-576. Merton, Robert C., 1973, Theory of Rational Option Pricing, The Bell Journal of Economics and Management Science, 4, 141-183. Moreno, Manuel, and Javier F. Navas, 2003, On the Robustness of Least-squares Monte Carlo (LSM) for Pricing American Derivatives, Review of Derivatives Research, 6, 107-128. Reiner, Eric, and Mark Rubinstein, 1991, Breaking Down the Barriers, Risk, 4, 28-35. Ritchken, Peter, 1995, On Pricing Barrier Options, Journal of Derivatives, 3, 19-28. Stentoft, Lars, 2004, Assessing the Least-squares Monte-Carlo approach to American Options Valuation, Review of Derivatives Research, 7, 129-168. Tsiveriotis, Kostas, and Chris Fernandes, 1998, Valuing Convertible Bonds wtih Cedit Risk, The Journal of Fixed Income, 8, 95-102.
The least-squares Monte Carlo simulation proposed by Longstaff and Schwartz (2001)
is claimed to price any American options even with very complicated provisions in the
contract. However, the main problem is how to choose the optimal regression settings,
including the explanatory variables, different basis functions, and the degree of these basis
functions. For some complex exotic options without other numerical solutions, such
as Taiwanese convertible bonds, it is difficult to determine optimal regression settings.
To deal with this problem, a building-block method is adopted to determining the optimal
regression settings of the least-squares Monte Carlo simulation model for pricing
Taiwanese convertible bonds. We separate the Taiwanese convertible bond into several
market-observed exotic options, and find the optimal regression settings in the leastsquares
Monte Carlo simulation model to deal with the exotic features via comparing the
results from the lattice models. We will apply the least-squares Monte Carlo simulation
methods to pricing a simple convertible bond with hard call and put provisions, a Parisian
option, and an arithmetic average reset option respectively. According to the optimal regression
settings for each exotic option, a pricing framework based on the least-squares
Monte Carlo simulation model is constructed to price Taiwanese convertible bonds. This
method overcomes the shortcoming of the least-squares Monte Carlo simulation that how
to determine the optimal regression settings on the exotic options without numerical solutions.
Furthermore, this framework also affords a direction to value more complicated
derivatives in the future.
其他識別: U0005-2908200607214100
Appears in Collections:財務金融學系所

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