# Option Pricing

## What is a premium?

A premium is the fee a writer receives when an option trader purchases their option.

## How is the premium priced?

Option writers are exposed to the risk of paying settlement in the event their options expire ITM. As such, the premiums they earn from purchasers must fairly reflect the probability of an ITM event occurring.

Dopex option premiums are derived from the Black-Scholes Model (*"BSM"*), the most common methodology used for pricing European options (i.e. options that are only exercisable on settlement date like our SSOVs).

The model when applied to a call option can be shown as follows:

The parameters that it takes into account are:

**Spot Price (S):**price of the underlying at time of option purchase**Strike Price****(K):**price of the underlying that the option will be settled against**Time to expiry****(t)**: how long till the option expires, as days till expiry365**Volatility****(σ):**degree of variance of underlying’s price**Risk-free interest rate (r):**interest rate earned on capital at zero underlying risk

## Dopex Black Scholes Model Assumptions

Dopex uses two assumptions in its application of the BSM:

The risk-free rate is assumed to be zero

Volatility is based on the 30-day historical volatility of the underlying*

### *Exceptions

$ETH and $BTC IV is taken directly from Deribit if strike prices match. If strike prices do not match, the closest upper and lower strikes from Deribit are weighted based on degree of offset to set IV on Dopex.

$CVX and $ARB use 30-day beta-based HV by calculating effective strike price of base asset against $ETH to extrapolate IV which is multiplied by beta of base asset against $ETH

Last updated