Name
Abstract | ||
|---|---|---|
We investigate and compare two dual formulations of the American option pricing problem based on two decompositions of supermartingales: the additive dual of Haugh and Kogan (Oper. Res. 52:258-270, 2004) and Rogers (Math. Finance 12:271-286, 2002) and the multiplicative dual of Jamshidian (Minimax optimality of Bermudan and American claims and their Monte- Carlo upper bound approximation. NIB Capital, The Hague, 2003). Both pro- vide upper bounds on American option prices; we show how to improve these bounds iteratively and use this to show that any multiplicative dual can be improved by an additive dual and vice versa. This iterative improvement con- verges to the optimal value function. We also compare bias and variance under the two dual formulations as the time horizon grows; either method may have smaller bias, but the variance of the multiplicative method typically grows much faster than that of the additive method. We show that in the case of a discrete state space, the additive dual coincides with the dual of the optimal stopping problem in the sense of linear programming duality and the multiplicative method arises through a nonlinear duality. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s00780-006-0031-3 | Finance and Stochastics |
Keywords | Field | DocType |
optimal stopping · monte carlo methods · variance reduction,monte carlo method,linear program,variance reduction,optimal stopping problem,optimal stopping,upper bound,monte carlo methods,state space,monte carlo | Financial economics,Mathematical optimization,Valuation of options,Optimal stopping,Multiplicative function,Dual polyhedron,Upper and lower bounds,Bellman equation,Duality (optimization),Linear programming,Mathematics | Journal |
Volume | Issue | ISSN |
11 | 2 | 1432-1122 |
Citations | PageRank | References |
16 | 1.22 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nan Chen | 1 | 16 | 1.22 |
| Paul Glasserman | 2 | 496 | 95.86 |