Cliquet

As cliquet is known in the financial world, a path-dependent exotic option whose payoff is determined by several interim observations at different, predetermined points in time. It consists of several at- the-money options, the first option with a strike price of 100 % of the current price, is active at the conclusion of the contract. Once this expires then, the next, again with a strike price of the current course, enabled. This process is repeated until the end of the term of the option.

Definition

A cliquet on a underlying is determined by the following parameters:

• The number of observations
• The timing of observations ( T corresponds to the expiration date )
• Local barriers
• The global barriers.

In the time between the run time returns are now observed. At the end time T, the following amount is paid:

The individual returns so it will initially be limited up and down ( by the local barriers), then summed and again limited ( by the global barriers).

If both the local and the global lower bound (engl: floor ) is negative, the amount paid may be negative. In this case, it is at cliquet no longer an option in the strict sense, but only to a contingent claim.

Assessment

An evaluation of a Cliquets is analytically feasible as with most path-dependent options, only in special cases. Thus, for example, in the Black- Scholes model, especially if the global barriers are not active, a simple solution. Then namely for the price of the option:

Where r is the risk-free interest rate and the expected value is calculated with respect to a martingale. The observation time points equidistant addition, as the expression is simplified to

:. However, if more complex capital market models used ( eg general Lévy processes or models with stochastic volatility ), often the only possibility is to estimate the option pricing using Monte Carlo simulation.

• Option trading