Question about Lookback Option. Several people are under the impression that the lattice for pricing lookback option is not recombining. Answer: Recall that we keep track of the stock_price and the max of the stock price at each node. So each node in the lattice is characterized by: (time,stock_price,max) where time: time corresponding to the node stock_price: stock price at that node max: Maximum stock price on the path from the root to that node. Consider the situation where initial stock price is 1 and u=1/d and u=2. Assume time horizon of T=5. I will show two paths of length 5 such that the final stock price and the maximum on these paths is the same, i.e., showing recombination. up-tick,down-tick,up-tick,up-tick,up-tick up-tick,up-tick,up-tick,down-tick,up-tick I suggest that you print out the lattice for the lookback option with T=5 (the method to be called in AbstractOption.cpp is PrintLattice). I got the following result for T=10. Please plot this lattice and see. --------------------------PRINT OUT BEGIN---------------------------------- Nodes at time 0 ------------BEGIN----------------- Time: 0 Stock Price: 1 Aux Process: 1 Option Value: 1.47723 ------------END------------------- Nodes at time 1 ------------BEGIN----------------- Time: 1 Stock Price: 2 Aux Process: 2 Option Value: 2.94126 Time: 1 Stock Price: 0.5 Aux Process: 1 Option Value: 0.751829 ------------END------------------- Nodes at time 2 ------------BEGIN----------------- Time: 2 Stock Price: 4 Aux Process: 4 Option Value: 5.84581 Time: 2 Stock Price: 1 Aux Process: 2 Option Value: 1.50733 Time: 2 Stock Price: 1 Aux Process: 1 Option Value: 1.46145 Time: 2 Stock Price: 0.25 Aux Process: 1 Option Value: 0.41812 ------------END------------------- Nodes at time 3 ------------BEGIN----------------- Time: 3 Stock Price: 8 Aux Process: 8 Option Value: 11.5999 Time: 3 Stock Price: 2 Aux Process: 4 Option Value: 3.01466 Time: 3 Stock Price: 2 Aux Process: 2 Option Value: 2.89997 Time: 3 Stock Price: 0.5 Aux Process: 2 Option Value: 0.868352 Time: 3 Stock Price: 0.5 Aux Process: 1 Option Value: 0.753664 Time: 3 Stock Price: 0.125 Aux Process: 1 Option Value: 0.291635 ------------END------------------- Nodes at time 4 ------------BEGIN----------------- Time: 4 Stock Price: 16 Aux Process: 16 Option Value: 22.9376 Time: 4 Stock Price: 4 Aux Process: 8 Option Value: 6.06208 Time: 4 Stock Price: 4 Aux Process: 4 Option Value: 5.7344 Time: 4 Stock Price: 1 Aux Process: 4 Option Value: 1.80224 Time: 4 Stock Price: 1 Aux Process: 2 Option Value: 1.51552 Time: 4 Stock Price: 0.25 Aux Process: 2 Option Value: 0.65536 Time: 4 Stock Price: 1 Aux Process: 1 Option Value: 1.4336 Time: 4 Stock Price: 0.25 Aux Process: 1 Option Value: 0.45056 Time: 4 Stock Price: 0.0625 Aux Process: 1 Option Value: 0.278528 ------------END------------------- Nodes at time 5 ------------BEGIN----------------- Time: 5 Stock Price: 32 Aux Process: 32 Option Value: 45.2198 Time: 5 Stock Price: 8 Aux Process: 16 Option Value: 12.1242 Time: 5 Stock Price: 8 Aux Process: 8 Option Value: 11.305 Time: 5 Stock Price: 2 Aux Process: 8 Option Value: 3.85024 Time: 5 Stock Price: 2 Aux Process: 4 Option Value: 3.03104 Time: 5 Stock Price: 0.5 Aux Process: 4 Option Value: 1.47456 Time: 5 Stock Price: 2 Aux Process: 2 Option Value: 2.82624 Time: 5 Stock Price: 0.5 Aux Process: 2 Option Value: 0.96256 Time: 5 Stock Price: 0.125 Aux Process: 2 Option Value: 0.67584 Time: 5 Stock Price: 0.5 Aux Process: 1 Option Value: 0.75776 Time: 5 Stock Price: 0.125 Aux Process: 1 Option Value: 0.36864 Time: 5 Stock Price: 0.03125 Aux Process: 1 Option Value: 0.32768 ------------END------------------- Nodes at time 6 ------------BEGIN----------------- Time: 6 Stock Price: 64 Aux Process: 64 Option Value: 88.4736 Time: 6 Stock Price: 16 Aux Process: 32 Option Value: 24.576 Time: 6 Stock Price: 16 Aux Process: 16 Option Value: 22.1184 Time: 6 Stock Price: 4 Aux Process: 16 Option Value: 8.192 Time: 6 Stock Price: 4 Aux Process: 8 Option Value: 6.144 Time: 6 Stock Price: 1 Aux Process: 8 Option Value: 3.4816 Time: 6 Stock Price: 4 Aux Process: 4 Option Value: 5.5296 Time: 6 Stock Price: 1 Aux Process: 4 Option Value: 2.048 Time: 6 Stock Price: 0.25 Aux Process: 4 Option Value: 1.6384 Time: 6 Stock Price: 1 Aux Process: 2 Option Value: 1.536 Time: 6 Stock Price: 0.25 Aux Process: 2 Option Value: 0.8704 Time: 6 Stock Price: 0.0625 Aux Process: 2 Option Value: 0.8192 Time: 6 Stock Price: 1 Aux Process: 1 Option Value: 1.3824 Time: 6 Stock Price: 0.25 Aux Process: 1 Option Value: 0.512 Time: 6 Stock Price: 0.0625 Aux Process: 1 Option Value: 0.4096 Time: 6 Stock Price: 0.015625 Aux Process: 1 Option Value: 0.4096 ------------END------------------- Nodes at time 7 ------------BEGIN----------------- Time: 7 Stock Price: 128 Aux Process: 128 Option Value: 172.032 Time: 7 Stock Price: 32 Aux Process: 64 Option Value: 49.152 Time: 7 Stock Price: 32 Aux Process: 32 Option Value: 43.008 Time: 7 Stock Price: 8 Aux Process: 32 Option Value: 18.432 Time: 7 Stock Price: 8 Aux Process: 16 Option Value: 12.288 Time: 7 Stock Price: 2 Aux Process: 16 Option Value: 8.192 Time: 7 Stock Price: 8 Aux Process: 8 Option Value: 10.752 Time: 7 Stock Price: 2 Aux Process: 8 Option Value: 4.608 Time: 7 Stock Price: 0.5 Aux Process: 8 Option Value: 4.096 Time: 7 Stock Price: 2 Aux Process: 4 Option Value: 3.072 Time: 7 Stock Price: 0.5 Aux Process: 4 Option Value: 2.048 Time: 7 Stock Price: 0.125 Aux Process: 4 Option Value: 2.048 Time: 7 Stock Price: 2 Aux Process: 2 Option Value: 2.688 Time: 7 Stock Price: 0.5 Aux Process: 2 Option Value: 1.152 Time: 7 Stock Price: 0.125 Aux Process: 2 Option Value: 1.024 Time: 7 Stock Price: 0.03125 Aux Process: 2 Option Value: 1.024 Time: 7 Stock Price: 0.5 Aux Process: 1 Option Value: 0.768 Time: 7 Stock Price: 0.125 Aux Process: 1 Option Value: 0.512 Time: 7 Stock Price: 0.03125 Aux Process: 1 Option Value: 0.512 Time: 7 Stock Price: 0.0078125 Aux Process: 1 Option Value: 0.512 ------------END------------------- Nodes at time 8 ------------BEGIN----------------- Time: 8 Stock Price: 256 Aux Process: 256 Option Value: 327.68 Time: 8 Stock Price: 64 Aux Process: 128 Option Value: 102.4 Time: 8 Stock Price: 64 Aux Process: 64 Option Value: 81.92 Time: 8 Stock Price: 16 Aux Process: 64 Option Value: 40.96 Time: 8 Stock Price: 16 Aux Process: 32 Option Value: 25.6 Time: 8 Stock Price: 4 Aux Process: 32 Option Value: 20.48 Time: 8 Stock Price: 16 Aux Process: 16 Option Value: 20.48 Time: 8 Stock Price: 4 Aux Process: 16 Option Value: 10.24 Time: 8 Stock Price: 1 Aux Process: 16 Option Value: 10.24 Time: 8 Stock Price: 4 Aux Process: 8 Option Value: 6.4 Time: 8 Stock Price: 1 Aux Process: 8 Option Value: 5.12 Time: 8 Stock Price: 0.25 Aux Process: 8 Option Value: 5.12 Time: 8 Stock Price: 4 Aux Process: 4 Option Value: 5.12 Time: 8 Stock Price: 1 Aux Process: 4 Option Value: 2.56 Time: 8 Stock Price: 0.25 Aux Process: 4 Option Value: 2.56 Time: 8 Stock Price: 0.0625 Aux Process: 4 Option Value: 2.56 Time: 8 Stock Price: 1 Aux Process: 2 Option Value: 1.6 Time: 8 Stock Price: 0.25 Aux Process: 2 Option Value: 1.28 Time: 8 Stock Price: 0.0625 Aux Process: 2 Option Value: 1.28 Time: 8 Stock Price: 0.015625 Aux Process: 2 Option Value: 1.28 Time: 8 Stock Price: 1 Aux Process: 1 Option Value: 1.28 Time: 8 Stock Price: 0.25 Aux Process: 1 Option Value: 0.64 Time: 8 Stock Price: 0.0625 Aux Process: 1 Option Value: 0.64 Time: 8 Stock Price: 0.015625 Aux Process: 1 Option Value: 0.64 Time: 8 Stock Price: 0.00390625 Aux Process: 1 Option Value: 0.64 ------------END------------------- Nodes at time 9 ------------BEGIN----------------- Time: 9 Stock Price: 512 Aux Process: 512 Option Value: 614.4 Time: 9 Stock Price: 128 Aux Process: 256 Option Value: 204.8 Time: 9 Stock Price: 128 Aux Process: 128 Option Value: 153.6 Time: 9 Stock Price: 32 Aux Process: 128 Option Value: 102.4 Time: 9 Stock Price: 32 Aux Process: 64 Option Value: 51.2 Time: 9 Stock Price: 8 Aux Process: 64 Option Value: 51.2 Time: 9 Stock Price: 32 Aux Process: 32 Option Value: 38.4 Time: 9 Stock Price: 8 Aux Process: 32 Option Value: 25.6 Time: 9 Stock Price: 2 Aux Process: 32 Option Value: 25.6 Time: 9 Stock Price: 8 Aux Process: 16 Option Value: 12.8 Time: 9 Stock Price: 2 Aux Process: 16 Option Value: 12.8 Time: 9 Stock Price: 0.5 Aux Process: 16 Option Value: 12.8 Time: 9 Stock Price: 8 Aux Process: 8 Option Value: 9.6 Time: 9 Stock Price: 2 Aux Process: 8 Option Value: 6.4 Time: 9 Stock Price: 0.5 Aux Process: 8 Option Value: 6.4 Time: 9 Stock Price: 0.125 Aux Process: 8 Option Value: 6.4 Time: 9 Stock Price: 2 Aux Process: 4 Option Value: 3.2 Time: 9 Stock Price: 0.5 Aux Process: 4 Option Value: 3.2 Time: 9 Stock Price: 0.125 Aux Process: 4 Option Value: 3.2 Time: 9 Stock Price: 0.03125 Aux Process: 4 Option Value: 3.2 Time: 9 Stock Price: 2 Aux Process: 2 Option Value: 2.4 Time: 9 Stock Price: 0.5 Aux Process: 2 Option Value: 1.6 Time: 9 Stock Price: 0.125 Aux Process: 2 Option Value: 1.6 Time: 9 Stock Price: 0.03125 Aux Process: 2 Option Value: 1.6 Time: 9 Stock Price: 0.0078125 Aux Process: 2 Option Value: 1.6 Time: 9 Stock Price: 0.5 Aux Process: 1 Option Value: 0.8 Time: 9 Stock Price: 0.125 Aux Process: 1 Option Value: 0.8 Time: 9 Stock Price: 0.03125 Aux Process: 1 Option Value: 0.8 Time: 9 Stock Price: 0.0078125 Aux Process: 1 Option Value: 0.8 Time: 9 Stock Price: 0.00195313 Aux Process: 1 Option Value: 0.8 ------------END------------------- Nodes at time 10 ------------BEGIN----------------- Time: 10 Stock Price: 1024 Aux Process: 1024 Option Value: 1024 Time: 10 Stock Price: 256 Aux Process: 512 Option Value: 512 Time: 10 Stock Price: 256 Aux Process: 256 Option Value: 256 Time: 10 Stock Price: 64 Aux Process: 256 Option Value: 256 Time: 10 Stock Price: 64 Aux Process: 128 Option Value: 128 Time: 10 Stock Price: 16 Aux Process: 128 Option Value: 128 Time: 10 Stock Price: 64 Aux Process: 64 Option Value: 64 Time: 10 Stock Price: 16 Aux Process: 64 Option Value: 64 Time: 10 Stock Price: 4 Aux Process: 64 Option Value: 64 Time: 10 Stock Price: 16 Aux Process: 32 Option Value: 32 Time: 10 Stock Price: 4 Aux Process: 32 Option Value: 32 Time: 10 Stock Price: 1 Aux Process: 32 Option Value: 32 Time: 10 Stock Price: 16 Aux Process: 16 Option Value: 16 Time: 10 Stock Price: 4 Aux Process: 16 Option Value: 16 Time: 10 Stock Price: 1 Aux Process: 16 Option Value: 16 Time: 10 Stock Price: 0.25 Aux Process: 16 Option Value: 16 Time: 10 Stock Price: 4 Aux Process: 8 Option Value: 8 Time: 10 Stock Price: 1 Aux Process: 8 Option Value: 8 Time: 10 Stock Price: 0.25 Aux Process: 8 Option Value: 8 Time: 10 Stock Price: 0.0625 Aux Process: 8 Option Value: 8 Time: 10 Stock Price: 4 Aux Process: 4 Option Value: 4 Time: 10 Stock Price: 1 Aux Process: 4 Option Value: 4 Time: 10 Stock Price: 0.25 Aux Process: 4 Option Value: 4 Time: 10 Stock Price: 0.0625 Aux Process: 4 Option Value: 4 Time: 10 Stock Price: 0.015625 Aux Process: 4 Option Value: 4 Time: 10 Stock Price: 1 Aux Process: 2 Option Value: 2 Time: 10 Stock Price: 0.25 Aux Process: 2 Option Value: 2 Time: 10 Stock Price: 0.0625 Aux Process: 2 Option Value: 2 Time: 10 Stock Price: 0.015625 Aux Process: 2 Option Value: 2 Time: 10 Stock Price: 0.00390625 Aux Process: 2 Option Value: 2 Time: 10 Stock Price: 1 Aux Process: 1 Option Value: 1 Time: 10 Stock Price: 0.25 Aux Process: 1 Option Value: 1 Time: 10 Stock Price: 0.0625 Aux Process: 1 Option Value: 1 Time: 10 Stock Price: 0.015625 Aux Process: 1 Option Value: 1 Time: 10 Stock Price: 0.00390625 Aux Process: 1 Option Value: 1 Time: 10 Stock Price: 0.000976563 Aux Process: 1 Option Value: 1 ------------END-------------------