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paulchen


Total Posts: 2
Joined: Apr 2020
 
Posted: 2020-04-27 14:14
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 2-10 of my textbook,




Based on 2-11 of my textbook,

= =

Thus,
C=

[Denote d1_K2
= plug into K in d1(by BS model)]

C= e^(-rT)*{(S_0e^[(r-q)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
 
Posted: 2020-04-27 14:18
Answer 1: your implementation of MC has a bug.

paulchen


Total Posts: 2
Joined: Apr 2020
 
Posted: 2020-05-03 08:04
I have found the mistake, thanks.
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