Lévy-Sheffer Systems and the Longstaff-Schwartz Algorithm for ...

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The Longstaff-Schwartz Algorithm ◮ Approximate continuation values Cn(x) ≈ ◮ Regression coefficients ◮ Basis functions K k=0 βnkψnk(x) = β T n ψn(x), βn = (βn0, . . . , βnK ) T ψn(x) = (ψn0(x), . . . , ψnK (x)) T
The Longstaff-Schwartz Algorithm ◮ n exercise dates, K basis functions, N Monte Carlo paths ◮ Estimate coefficients of continuation values by cross-sectional regression ◮ High bias from peeking ahead ◮ Low bias from suboptimality ◮ Typical regressors in interest rate modeling: three forward (or swap) rates, of short, middle, and long tenor
Page 1 and 2: Lévy-Sheffer Systems and the Longs
Page 3 and 4: Motivation ◮ Many financial instr
Page 5 and 6: Algorithms ◮ An optimal stopping
Page 7 and 8: Dynamic Programming ◮ Vn(x) = val
Page 9: The Longstaff-Schwartz Algorithm
Page 13 and 14: Convergence Results ◮ K basis fun
Page 15 and 16: Results of Glasserman and Yu (2004)
Page 17 and 18: Results of Glasserman and Yu (2004)
Page 19 and 20: The Models ◮ Geometric Poisson pr
Page 21 and 22: Properties of the Meixner Process
Page 23 and 24: Lévy-Sheffer Systems ◮ Sheffer S
Page 25 and 26: Examples of Lévy-Sheffer Systems
Page 27 and 28: Convergence Results (SG 2008) ◮ N
Page 29 and 30: Proof Ingredients of the Convergenc
Page 31: References ◮ J.F. Carriere: Valua

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