Abstract
This paper discusses various extensions and implementation aspects of the primal-dual algorithm of Andersen and Broadie for the pricing of Bermudan options. The main emphasis is on a generalization of the dual lower and upper bounds to the case of mixed buyer and seller exercise, along with a detailed analysis of the sharpness of the bounds. As it turns out, the method as well as the convergence analysis can even be extended to conditional exercise rights and autotrigger strategies. These theoretical results are accompanied by a detailed description of the algorithmic implementation, including a robust regression method and the choice of suitable basis functions. Detailed numerical examples show that the algorithm leads to surprisingly tight bounds even for the case of high-dimensional callable Bermudan pricing problems.
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References
Andersen L., Broadie M. (2004) Primal-dual simulation algorithm for pricing multidimensional american options. Managment Science 50(9): 1222–1234
Belomestny D., Bender C., Schoenmakers J. (2009) True upper bounds for bermudan products via non-nested monte carlo. Mathematical Finance 19: 53–71
Black F., Scholes M. (1973) The pricing of options and corporate liabilities. Journal of Political Economy 81: 637–659
Broadie M., Cao M. (2008) Improved lower and upper bound algorithms for pricing american options by simulation. Quantitative Finance 8(8): 845–861
Carriere J. (1996) Valuation of early-exercise price of options using simulations and non-parametric regression. Insurance: Mathematics and Economics 19: 19–30
Clément E., Lamberton D., Protter P. (2002) An analysis of a least squares regression method for american option pricing. Finance and Stochastics 6(4): 449–471
Elliott R. J., Kopp P. E. (2009) Mathematics of financial markets. Springer, Berlin
Föllmer H., Schied A. (2004) Stochastic finance 2nd edn. de Gruyter, Berlin
Haugh M., Kogan L. (2004) Pricing american options: A duality approach. Operations Research 52: 258–270
Heston S. L. (1993) A closed-form solution for options with stochastic volatitlity with applications to bond and currency options. The Review of Financial Studies 6(2): 327–343
Jessup E.R., Sorensen D.C. (1994) A parallel algorithm for computing the singular value decomposition of a matrix. SIAM Journal on Matrix Analysis and Applications 15(2): 530–548
Jonen C. (2009) An efficient implementation of a least squares monte carlo method for valuing american-style options. International Journal of Computer Mathematics 86(6): 1024–1039
Longstaff F. A., Schwartz E. S. (2001) Valuing American options by simulation: A simple least-squares approach. The Review of Financial Studies 14(1): 113–147
Pizzi C., Pellizzari P. (2002) Monte carlo pricing of american options using nonparametric regression. Rendiconti per gli Studi Economici Quantitativi 1: 75–91
Rogers L. C. G. (2002) Monte carlo evaluation of american options. Mathematical Finance 12: 271–286
Tsitsiklis J., Van Roy B. (1999) Regression methods for pricing complex amercian style options. IEEE Transactions on Neural Networks 12: 694–703
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Mair, M.L., Maruhn, J.H. On the primal-dual algorithm for callable Bermudan options. Rev Deriv Res 16, 79–110 (2013). https://doi.org/10.1007/s11147-012-9078-9
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DOI: https://doi.org/10.1007/s11147-012-9078-9