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

More documents

Recommendations

Info

Dynamic Programming ◮ Continuation value ◮ Backward induction Cm(x) = 0, Cn(x) = E[Vn+1(Stn+1 ) | Stn = x] Cn(x) = E[max{hn+1(Stn+1 ), Cn+1(Stn+1 )} | Stn = x]. ◮ Option value at time t0 is max{h0(St0 ), C0(St0 )}.
The Longstaff-Schwartz Algorithm ◮ Approximate optimal exercise strategy by dynamic programming ◮ Generate and store Monte Carlo paths ◮ Assumption: Continuation value is simple function of current value of state variables. ◮ Set up a linear combination of basis function ◮ Estimate coefficients by regression across all paths ◮ Similar ideas appeared in Carriere (1996) and Tsitsiklis & van Roy (2001)
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: Dynamic Programming ◮ Vn(x) = val
Page 11 and 12: 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

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

Create successful ePaper yourself

Delete template?

Save as template?