Notes on Options Pricing

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

d1=ln(F/k)σt+0.5σtd_1 = {\ln(F/k) \over \sigma \sqrt{t}} + 0.5*\sigma\sqrt{t}
d2=d1σtd_2 = d_1 - \sigma \sqrt{t}
Call=ert(FN(d1)kN(d2))Call = e^{-rt} ( F \mathcal{N}(d_1) - k \mathcal{N}(d_2) )
Put=ert(kN(d2)FN(d1))Put = e^{-rt} ( k \mathcal{N}(-d_2) - F \mathcal{N}(-d_1) )

And for Delta we compute:

ΔC=N(d1)ΔP=N(d1)\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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