westcoastbadger
04-30-2009, 01:38 PM
I know how to derive the Black-Scholes Equation for call options, but don't get why this works for put options.
When writing a put, the market-maker will sell delta shares. With the assumption that profit is 0 when the stock moves one standard deviation, the middle term in the following formula doesn't get cancelled out, and I can't use the same derivation as I do for calls.
Profit= -(Put1- Put0) - Delta*(S1-S0) + (Put0+Delta*S0)*rh
Put1 - Put0 = Delta*(S1-S0) + .5*gamma*(S1-S0)^2 + h*theta
In the solution for #5 in ASM exam 3, the exact BS Equation for calls is used for puts. Can someone help me out with why this works?
When writing a put, the market-maker will sell delta shares. With the assumption that profit is 0 when the stock moves one standard deviation, the middle term in the following formula doesn't get cancelled out, and I can't use the same derivation as I do for calls.
Profit= -(Put1- Put0) - Delta*(S1-S0) + (Put0+Delta*S0)*rh
Put1 - Put0 = Delta*(S1-S0) + .5*gamma*(S1-S0)^2 + h*theta
In the solution for #5 in ASM exam 3, the exact BS Equation for calls is used for puts. Can someone help me out with why this works?