I am unpleased with current Interactive Brokers risk graph for option strategies, so I'm planning on writing an application myself to plot it.
My initial idea is to get the option greek values from the broker's data feed, so I would have the following data:
- Strike price
- Current underlying price
- Time to expiration
- Delta, Gamma, Theta, Rho, Vega
Since the Black-Scholes formula is as follows: $$C=SN(d_1)-e^{-rT}KN(d_2)$$
And assuming the greeks formulas as described in this paper, I can conclude that: $$N(d_1)=delta$$$$N(d_1)=\delta$$ $$e^{-rT}N(d_2)=\frac{rho}{KT}$$$$e^{-rT}N(d_2)=\frac{\rho}{KT}$$ And therefore I can calculate the Black-Scholes formula knowing only delta, rho, current underlying price, strike price and time to expiration: $$C=Sdelta-Krho$$$$C=S \delta-K \rho$$
The problem is that of course this must be wrong. It cannot be possible that I am able to calculate option price using only 2 greeks, or at least it looks hard to believe from what I know.
So, which assumption of those I'm taking is wrong? Is there any resource somewhere of how to calculate the option price from greeks (I searched but couldn't find one, that's why I started playing with these equations).
