# Leverage Trading: Options Pricing & The AMM

The zkVault option pricing algorithm presents an enhanced implementation of the Black-Scholes pricing model. It leverages on-chain implied volatility and incorporates supply and demand utilization modifiers to determine accurate pricing. By synergizing pool activities and considering time decay, the algorithm dynamically navigates pricing to achieve market equilibriums between liquidity makers and takers. This approach ensures optimal pricing and efficient utilization of pool liquidity within the zkVault ecosystem.

### How zkVault uses Black-Scholes

In zkVault's automated market maker (AMM), options are quoted across a range of strike prices and expiration dates. This is achieved through the generation of an implied volatility value, known as tradeVol, which is determined by market dynamics and varies based on both the expiry and strike price of the option. To calculate the tradeVol, the expiry's baseIV and the strike's skewRatio are multiplied together.

Let's consider an example to illustrate how the zkVault AMM quotes options:

Suppose we have the August expiry with a baseIV of 120% and the 3500 strike with a skewRatio of 0.9. In this case, the tradeVol for the August 3500 call would be calculated as 120% * 0.9 = 108%. This means that the option's implied volatility, taking into account both the expiration and strike price, is 108%.

When a trade is executed, this tradeVol value is fed into the Black-Scholes pricing equation along with the other relevant parameters (such as underlying asset price, time to expiry, risk-free interest rate, and option contract specifications). The equation then generates the option price based on the given tradeVol and other input variables.

By incorporating tradeVol that varies by expiry and strike, the zkVault AMM ensures that option prices accurately reflect market conditions and the specific attributes of each option contract.

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