# Black-Scholes Model

Modified Black-Scholes model for digital assets

Portfolio modelling is centered around the Black-Scholes model with key modifications for digital assets. Modifications including the new Opportunity Cost (*O*) of collateral term have been introduced to reflect the characteristics of the 0xdx platform more accurately.

When you click on an option type within the orderbook, the order price field pre-populates with the value calculated by our modified Black-Scholes model.

Below is the modified Black-Scholes model used:

Premium price for calls:

Premium price for puts:

Where:

*C(S,t) = Call Option (Premium) Price*

*P(K,t) = Put Option (Premium) Price*

*N( ) = Cumulative Distribution (Density) Function*

*T = Time Left to Maturity (in years)*

*S = Underlying Asset Price*

*K = Strike Price*

*r = Risk Free Rate*

*O = Opportunity Cost of Collateral*

*Ļ = Volatility*

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