Options Pricing

NFT options pricing fundamentally comes down to finding a market-value for implied volatility (IV), the expected volatility of the NFT floor price from now until expiration. When implied volatility is high (low), the cost to buy (sell) an option increases (decreases).

We'll get into more details as to how:

• How implied volatility translates into the price of an option

• How IV varies across strikes and expiries

in the following sections.

Black Scholes

The Black-Scholes model is the foundation of options pricing. It takes in the following 5 inputs:

• Asset price (S)

• Strike price (K)

• Risk-free interest rate (r)

• Time to expiry (T)

• Implied volatility (sigma)

and outputs the price of an option. Knowing the inputs to the model is a good enough starting point to begin to reason about options - but interested readers can read more about the model and its derivation here.

The important point to notice here is that, of the 5 inputs to the model, 4 are widely known to all market participants. The current price of the asset, the strike/expiry of the options contract, and the risk-free rate are all 'known' inputs to the equation.

The only input that is not observable is implied volatility. This means that when market participants are trading options, what they are really trading is implied volatility. Therefore, the major work of NFTCall is to calculate implied volatility of NFT floor prices.

Volatility

Volatility is a metric that measures the magnitude of the change in floor prices in an NFT collection. Generally speaking, the higher the volatility—and, therefore, the risk—the greater the reward. If volatility is low, options' premium is low as well.

There are several ways to measure volatility, but options traders generally work with two metrics: implied volatility and historical volatility.

• Implied Volatility: Implied, or projected, volatility is a forward-looking metric used by options traders to calculate probability.

• Historical Volatility: Also referred to as statistical volatility, historical volatility gauges the fluctuations of underlying assets by measuring price changes over predetermined periods of time.

Implied volatility, as its name suggests, uses supply and demand, and represents the expected fluctuations of an underlying asset over a specific time frame. However in NFTCall, once created, NFT options cannot be freely traded like traditional stock options. Hence, implied volatility is difficult to calculate due to the absence of market prices of NFT options. This leads us to choose historical volatility to evaluate volatility.

Historical volatility of an asset can be computed by looking at the variance of its returns over a certain period of time. It is computed by multiplying the standard deviation (which is the square root of the variance) by the square root of the number of time periods in question, T.

Here is how historical volatility is computed in detail.

How NFTCall uses Black-Scholes

NFTCall quotes options over a range of strikes and expiries. When a trade is made, the relevant historical volatility is fed into a Black-Scholes pricing equation (which takes in the other 4 parameters), yielding the option price.