Option Millionaires

[dominik2]

So by lookin at delta that shows u ur probability of finishing in the money ?Do u guys ever trade solely based on Delta gamma vega thetha?



The Black Scholes equation is as follows:

c = S*N(d1) - PV(K)*N(d2)

delta is the sensitivity of the option price to changes in the underlying and by simply differentiation:

dc/dS = N(d1)

Mathematically speaking, the risk neutral probability that an option expires in the money is actually N(d2), not N(d1) as is often believed.

N(d2) = pr ( ln(S) > ln(x) ) at expiry

If we ignore discounting, and take the idea that N(d1) is the risk neutral probability as often believed, therefore we get N(d1) = N(d2)

c = S*N(d1) - K*N(d1) = N(d1)*(S - X)

but as you can see this can make the call option price negative if S < X. Therefore N(d1) will be strictly greater than N(d2).

The problem is that there are two uncertainties of expiration:
1. If we get anything at all: represented by N(d2)
2. How much we get: represented by N(d1)