Notes on Options Pricing

Optio uses Black-Scholes pricing assumptions, and the Black-76 options pricing model, specifically:

$$d_1 = {\ln(F/k) \over \sigma \sqrt{t}} + 0.5*\sigma\sqrt{t}$$

$$d_2 = d_1 - \sigma \sqrt{t}$$

$$Call = e^{-rt} ( F \mathcal{N}(d_1) - k \mathcal{N}(d_2) )$$

$$Put = e^{-rt} ( k \mathcal{N}(-d_2) - F \mathcal{N}(-d_1) )$$

And for Delta we compute:

$$\Delta_C = \mathcal{N}(d_1) \\ \Delta_P = -\mathcal{N}(-d_1)$$

Where: t is the time to expiration in years

σ is the volatility of the asset

F is the forward price of the asset

k is the strike price of the option

r is the risk free interest rate

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