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.
Auto market making
In NFTCall Surge, the auto market making will also consider the position of the vault, delta and PnL of each NFT collection and make corresponding adjustments to produce fair prices, decreasing the risks of the vault.
The AMM's core mechanism is to adjust the cost of NFT options based on demand and supply. When demand for options is high, the cost increases; when supply is high, it decreases. This approach enables the AMM to establish a market-clearing value for NFT options with any strike and expiry while effectively managing risks associated with LPs' options trading.
Adjusted Volatility
The AMM model uses adjusted volatility to calculate the options premium because according to the Black-Scholes formula, the most effect way to tune the premium is to adjust volatility given the strike price and expiration time.
When a user opens an options position, the protocol will adjust volatility by calculating the impact of the position on the vault. The adjusted volatility will be put into the formula to calculate the tuned premium.
Minimum Premium
When an option is opened, the ncETH vault will lock the corresponding maximum payout amount to ensure the trader's profit at expiration. According to the Black-Scholes formula, when the expiration time is set to be long and the position size is large, a trader can use a small premium to lock a large amount of liquidity, resulting in low capital utilization. Therefore, we introduce a minimum premium to address this situation.
We set a pre-determined annualized return rate for the ncETH vault, then calculate the minimum premium using the following formula:
Currently, the annualized return rate of the insurance vault is set at 5%.
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