Numerical Examples of Everlasting Option Pricing
We have proved the following pricing formulae for everlasting options under the BSM assumptions.
Let’s divide the theoretical prices of everlasting call and put options, Cᵉᵛᵉʳ and Pᵉᵛᵉʳ, into intrinsic value and time value:
The call and put options at the same strike have the same time value
The details of the math can be found in this article. Here we provide some numerical examples. Let’s take the BTCUSD-50000-CALL with 7Day funding period as an example and assume volatility = 100%:
Then we have the key intermediate variable
The out-of-money scenario
Assuming BTCUSD = 40000, then we have intrinsic value I = 0, and time value
Therefore, the theoretical price of this 50000-Call is
Every day, a long (short) position of 1BTC of this EO pays (receives)
The at-the-money scenario
Assuming BTCUSD = 50000, then we have intrinsic value I = 0, and time value
Therefore, the theoretical price of this 50000-Call is
Every day, a long (short) position of 1BTC of this EO pays (receives)
The In-the-money scenario
Assuming BTCUSD = 60000, then we have intrinsic value I = 60000–50000=10000, and time value
Therefore, the theoretical price of this 50000-Call is
Every day, a long (short) position of 1BTC of this EO pays (receives)
About Deri Protocol
Deri Protocol = (Perpetual Futures + Everlasting Options) x Decentralized.
Deri is the DeFi way to trade derivatives: to hedge, to speculate, to arbitrage, all on chain. With Deri Protocol, trades are executed under AMM paradigm and positions are tokenized as NFTs, highly composable with other DeFi projects. Having provided an on-chain mechanism to exchange risk exposures precisely and capital-efficiently, Deri Protocol has minted one of the most important blocks of the DeFi infrastructure.
