Hi,
I have a problem from my FM course that I need help with.
It's as follows:
The of pay-off from a European put option with strike price, K, and time to maturity T is given by max(0, K-S_T). ***(S_T as in "S sub T)***
The price of the asset is modeled by S_T= S_0*exp((r-q-0.5*sigma^2)*T+sigma*B_T), where B_T~N(0,T).
The put option price is computed by V=E[exp(-r*T)*max(0,K-K_T)].
1. Derive the formula for V in terms of the standard normal CDF (phi).
For S_0 = K=100, r=0.02, q=0.01, sigma=0.2, T=1, compute the put price.
**See the image for a clean version of what I typed above.**
I'm told that if I compute the expected value of the expression after I plug-in everything, that B_T will disappear, and that I will be able to find a closed form expression for V. From here, I'm lost...
Any help would be much appreciated.
I have a problem from my FM course that I need help with.
It's as follows:
The of pay-off from a European put option with strike price, K, and time to maturity T is given by max(0, K-S_T). ***(S_T as in "S sub T)***
The price of the asset is modeled by S_T= S_0*exp((r-q-0.5*sigma^2)*T+sigma*B_T), where B_T~N(0,T).
The put option price is computed by V=E[exp(-r*T)*max(0,K-K_T)].
1. Derive the formula for V in terms of the standard normal CDF (phi).
For S_0 = K=100, r=0.02, q=0.01, sigma=0.2, T=1, compute the put price.
**See the image for a clean version of what I typed above.**
I'm told that if I compute the expected value of the expression after I plug-in everything, that B_T will disappear, and that I will be able to find a closed form expression for V. From here, I'm lost...
Any help would be much appreciated.
Help with FM problem
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