# Option Pricing

Last updated

Last updated

The Black-Scholes pricing method is widely used in the financial industry to determine the fair price of options. It takes into account various factors such as the current price of the underlying asset, the option's strike price, time until expiration, volatility of the underlying asset, and risk-free interest rate.

$\boldsymbol{C(S_0,K,r,T,\sigma) = S_0\mathcal{N}(d_1)-K e^{-rT}\mathcal{N}(d_2)}$

with

$\boldsymbol{\mathrm d_1= \frac{1}{\sigma \sqrt{\mathrm T}} \left[\ln{\left(\frac{S_0}{K}\right)} + T\left(r + \frac{\sigma^2}{2} \right) \right]}$

$\boldsymbol{\mathrm d_2=d_1- {\sigma \sqrt{\mathrm T}}}$

S0 Current price of the underlying asset: This is the current market price of the asset on which the option is based.

K Option's strike price: The strike price is the predetermined price at which the option can be exercised.

T Time until expiration: The time remaining until the option expires plays a significant role in its pricing. The longer the time until expiration, the higher the option's price is likely to be.

Volatility of the underlying asset: Volatility measures the degree of fluctuation in the price of the underlying asset. Higher volatility typically leads to higher option prices, as there is more uncertainty in the market.

Risk-free interest rate: The risk-free interest rate is the return an investor can expect without taking on any risk.

While most parameters have known values for a given option, volatility is a unique factor that represents the market's expectation of the underlying asset's future price fluctuations.

Implied Volatility

At Polarity, the implied volatility for all strike prices and maturities is fetched from an on-chain oracle sourced from Deribit. This ensures that the options are priced accurately based on the market's expectations of future volatility in the underlying assets.

By incorporating implied volatility from reliable sources, the option pricing model accurately value options, reflecting the market's sentiment and expectations.

Fees

Opening Fee is charged when a trader opens a position, a fee equivalent to 0.03% of the notional value of the position is charged

Settlement Fee is charged when a trader closes a position, a fee equivalent to 0.03% of the notional value of the position is charged

The Opening Fee and Settlement Fee will be adjusted by the protocol’s decentralized governance over time.