Cliquet Option

From ThetaWiki

Description

A cliquet or ratchet option can be seen as a series of at-the-money options with periodic settlement, resetting the strike value at the then-current price level, at which time the option locks-in the difference between the old and new strike and pays that out as profit. The profit can be accumulated until final maturity or paid out at each reset date. The option's lifetime is T. The floating strike look-back put gives the owner the right to sell the underlying at the highest price.

ThetaScript

Model cliquet
 
import S "Underlying stock"
import N "Notional"
import EUR "Numeraire"
import Cg "Global Cap"
import Fg "Global Floor"
import Cl "Local Cap"
import Fl "Local Floor"
export P "Option value"
 
    P = E(V!)
    sum=0
    loop 5
    	R = (S!-S)/S
 
        Theta 1
        Z=max(Fl,min(Cl,R))
        sum=sum+Z 
    end
    V=N*EUR*max(Fg,min(Cg,sum)) 
end

Thetagram

Numerical Example

The following table contains numerical results using a Theta with Geometric Brownian Motion and Jump Diffusion and compares the values to a reference given in the literature.

References

Numerical Methods and Volatility Models for Valuing Cliquet Options. H.A. Windcliff, P.A. Forsyth and K.R.Vetzal