Analytic Financial“Asset-or-nothing digitals”

Mahamadi OuobaAmina El GaabiryDavid Johansson

Definition of Asset-or-Nothing:

An exotic option

Binary

The Asset-or-Nothing Call option The Asset-or-Nothing Put option

Payoff graphs:

Figure 1 Payoff of binary asset-or-nothing call option with strike price 40 .

Figure 2 Payoff of binary asset-or-nothing put option with strike price 40.

The price of a binary asset-or-nothing :

Call option :

Put option:

The Greeks

Definition of Greeks

The PDE of d :

Delta (∆)

Call option: =

Put option:

Gamma (Γ)

Call/Put option:

Rho (ρ)

Call option:=

Put option:

Vega (ϒ)

Call option:

Put option:

Theta (Θ)

Call option:

Put option:

Numerical derivatives