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- 7/22/13
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Hello,
I assume the BS market and that I work in the risk-neutral world. I want to price a Bermudan put option on a stock which pays no dividends using backward valuation method. The option has 2 exercise dates, the maturity T_2 and an early exercise date T_1.
1) To price this derivative, I work backwards starting from maturity at which I calculate the expected payoff and discount it till time T_1. In this time interval the option can be viewed as a European type option so we can use BS formula which will depend on the stock price at time T_1.
2) At time T_1, the payoff of the option is the expectation of the maximum between the discounted payoff of time T_2 and (K-S(T_1))_+.
Therefore, the fair price of the Bermudan put option the the expectation of the payoff at time T_1 discount till the present.
Now, the problem I have is the following:
When I use numerical integration with respect to the standard normal density where I have used the BS formula I get a "correct" price (between EU and American Put). However, if I replace the BS formula with the integral form, i.e. a second integral inside the maximum, and use some adaptive numerical integration method with depends on the value of S(T_1) the result I get is extremely high. I don't understand why.
If anyone can help me with this or can cite some material on this topic, I will really appreciate it.
PS: I implement the code in Matlab.
Thanks.
I assume the BS market and that I work in the risk-neutral world. I want to price a Bermudan put option on a stock which pays no dividends using backward valuation method. The option has 2 exercise dates, the maturity T_2 and an early exercise date T_1.
1) To price this derivative, I work backwards starting from maturity at which I calculate the expected payoff and discount it till time T_1. In this time interval the option can be viewed as a European type option so we can use BS formula which will depend on the stock price at time T_1.
2) At time T_1, the payoff of the option is the expectation of the maximum between the discounted payoff of time T_2 and (K-S(T_1))_+.
Therefore, the fair price of the Bermudan put option the the expectation of the payoff at time T_1 discount till the present.
Now, the problem I have is the following:
When I use numerical integration with respect to the standard normal density where I have used the BS formula I get a "correct" price (between EU and American Put). However, if I replace the BS formula with the integral form, i.e. a second integral inside the maximum, and use some adaptive numerical integration method with depends on the value of S(T_1) the result I get is extremely high. I don't understand why.
If anyone can help me with this or can cite some material on this topic, I will really appreciate it.
PS: I implement the code in Matlab.
Thanks.
