Closed-form pricers#

European option prices in closed form, from Bachelier’s normal model to Black-Scholes-Merton and its forward, futures and currency variants, and the model-free relations every price must obey.

Bachelier’s normal model

Bachelier's normal model

Stoll’s put-call parity

Stoll's put-call parity

The Black-Scholes formula

The Black-Scholes formula

Merton: dividends and no-arbitrage bounds

Merton: dividends and no-arbitrage bounds

Black-76: options on futures

Black-76: options on futures

Garman-Kohlhagen currency options

Garman-Kohlhagen currency options