Crypto options

European options on bitcoin, ether and other coins, paid in currency or coin-margined (Deribit style, premium in coins), on the forward from a futures basis; Black-76, Merton jump diffusion, Heston and Bates by the COS method, with the implied Black-76 vol, delta and the coin delta of an inverse book, gamma, vega and theta.

Inputs

AssetTypeSettlement

Strike

Expiry

Coins

Index price

Futures basis a year%

Model

Initial vol √v₀%

Jumps a year

Mean jump%

Jump vol%

θ (long-run variance)

Vol of vol

CurrencyCurve

Curve: flat rate% cc

Results

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Methodology

Conventions

A European option on the forward: given, or the index grown at the futures basis.
Inverse options pay max(S − K, 0)/S coins, worth the linear payoff in currency: the coin premium is the currency premium over the index.
Merton, Heston and Bates prices by the COS method; the Black-76 vol of the model price is shown.

References

Black (1976)
Bates (1996)
Fang and Oosterlee (2008)

Formulas

Inverse premium: V_coin = V / S
Coin delta: Δ_coin = Δ − V/S