Risk Neutral Measure Question

[mark_yao]

The derivation of the Black Scholes equations assumes the risk neutral measure for all the assets.

Yet, if we assume this risk neutral measure in the beginning, we can find out the price of an option by calculating the discounted expectation under this risk neutral measure. Why do we still need the BS equations for ?

Thanks!

 

[Keith Tan]

i guess it's something to do with time series. you don't need BS when you know when your option's expiry dates. but when the pricing of option goes towards infinity, who do ya call? no, not ghostbusters. don't put, but call, black scholes.

 

[DMD]

The derivation of the Black Scholes equations assumes the risk neutral measure for all the assets.

Yet, if we assume this risk neutral measure in the beginning, we can find out the price of an option by calculating the discounted expectation under this risk neutral measure. Why do we still need the BS equations for ?

Thanks!

Please rephrase your question.

 

[mark_yao]

Please rephrase your question.

We assume the stock follows a geometric brownian motion, which is \(S_t = e^{ (r-\frac{1}{2}\sigma^2 )t + \sigma dW_t}\), where r is the risk-free interest rate. We use this equation to derivate the BS equation, which determines the price of an option.

For example, if we are talking about European Call with strike K. Instead of solving the BS, we can just find out the expectation of \((S_T - K)^+\), since we know \(S_T\) is log-normal given the equation above. It looks like we never need BS?

 

[AndrewChang]

We assume the stock follows a geometric brownian motion, which is \(S_t = e^{ (r-\frac{1}{2}\sigma^2 )t + \sigma dW_t}\), where r is the risk-free interest rate. We use this equation to derivate the BS equation, which determines the price of an option.

For example, if we are talking about European Call with strike K. Instead of solving the BS, we can just find out the expectation of \(S_T - K)^+\), since we know \(S_T\) is log-normal given the equation above. It looks like we never need BS?

\((S_T - K)^+\), is the expected value of the option under any model of the underlying where as Black-Scholes assumes log-normal, constant volatility etc