The Cliquet option pricing engine uses Monte Carlo Simulation to estimate the value of Cliquet Option. Here, we assume the process of asset pricing applies to Black-Scholes process.
The Cliquet Option is an exotic option. It is constructed by a series of forward start options. The start dates, also called resets dates, are pre-determined in the contract in advance. Generally, the reset dates are periodical, such as semiannual or quarterly.
At every reset date, the option calculates the relative performance between the old and new underlying price and pays that out as a profit.
The payoff of the option at the maturity is the sum of the payout at every reset date.
The option price is calculated as:
Where \(N\) is the number or reset dates and it is equal to timesteps. \(r\) is the risk-free interest rate.