paulchen


Total Posts: 2 
Joined: Apr 2020 


Hi,
My problem is here.
At first, I segmented the payoff diagram into 3 parts and I defined = 1 if = 0 otherwise = 1 if = 0 otherwise = 1 if = 0 otherwise
I have applied the Martingale Pricing Method to price this option.
Denote Q: risk neutral probability measure
C= =
Based on 210 of my textbook,
Based on 211 of my textbook,
= =
Thus, C=
[Denote d1_K2 = plug into K in d1(by BS model)]
C= e^(rT)*{(S_0e^[(rq)T][N(d1_K1)N(d1_K2)N(d1_K3)+N(d1_K4)]K1[N(d2_K1)N(d2_K4)]+K2[N(d2_K2)N(d2_K4)]+K3[N(d2_K3)N(d2_K4)]}
However, I used Monte Carlo Simulation to price this option and got a different answer.
I wonder what mistakes I have made, thank you. 



nikol


Total Posts: 1143 
Joined: Jun 2005 


Answer 1: your implementation of MC has a bug.



paulchen


Total Posts: 2 
Joined: Apr 2020 


I have found the mistake, thanks. 


