Perpetual Options

Perpetual Options Explained

Perpetual Options combine features of traditional options with a funding mechanism that allows them to exist without expiration dates.

Core Concepts

Option Valuation

The mark price of a Perpetual Option depends on 6 major inputs:

Option Type

Call or Put option

Spot Oracle Price

Current price of the underlying asset

Strike Price

Predetermined price at which the option can be exercised

Mark Implied Volatility (Mark IV)

Estimated volatility used in price calculations

Interest Rate

Derived from Paradex Futures Funding Rate

Funding Period

Set at 24 hours for continuous funding

Paradex calculates prices using the Black-Scholes formula adapted for perpetual options with continuous funding.

Implied Volatiility (IV)

Paradex maintains a Mark Implied Volatility that reflects a fair estimate of market IV even when the perpetual option may be illiquid. Mark IV is derived from 4 inputs:

Time Value

In Perpetual Options, Time Value is the difference between the mark price of the option and its intrinsic value:

Time Value=Mark Price−Intrinsic Value\text{Time Value} = \text{Mark Price} - \text{Intrinsic Value}

Core Idea

Time Value represents the premium or value traders are willing to pay for the option’s potential future value.

Funding Mechanism

The funding mechanism is how Perpetual Options maintain their perpetual nature. Long positions continuously pay short positions a funding rate based on the option’s time value.

  • Funding Period: 24 hours (funding is paid continuously)

  • Funding Premium: The total amount of funding paid over the funding period, equal to the time value of the option:

    Funding Premium = Time Value = Mark Price - Intrinsic Value

Core Idea

The Funding Period is a critical concept to understand. It represents the expected period of time over which a user will pay the time value of the option via Funding. This is a parameter chosen by Paradex and is what makes the current Perpetual Option similar (but not equal to) a 24 hour dated option.

Example

For a BTC-USD-101000-C with:

  • Spot Price: $100,000
  • Mark Price: $500
  • Intrinsic Value: $0 (out-of-the-money)
  • Time Value: $500

If Dave buys 5 contracts and holds for 1 hour with unchanged prices:

  • Funding PnL = -5 × (500×1/24)=−500 × 1/24) = -104.17

Funding accrues continuously as unrealized PnL and is realized whenever the position is updated.

Option Types

Similar to a traditional dated call option, a Perpetual Call Option gives the holder the right to benefit from price increases above the strike price. The intrinsic value of a Call option is:

max(Spot Price−Strike Price,0)\text{max}(\text{Spot Price} - \text{Strike Price}, 0)

  • When Spot Price > Strike Price: The option is “in-the-money” (ITM)
  • When Spot Price < Strike Price: The option is “out-of-the-money” (OTM)