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)
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