Cliquet Option
FinPricing offers:
Four user interfaces:
- Data API.
- Excel Add-ins.
- Model Analytic API.
- GUI APP.
Cliquet or Ratchet or Forward Start Option Valuation
FinPricing provides valuation models for:
- Forward Start Option
- Cliquet Option
- Cliquet Option with Cap Floor
- Cliquet Option with Locks
- Skipton Digital Option (Cliquet of Digitals)
- Check FinPricing valuation models
All the equity models in FinPricing take volatility skew/smile and dividend into account.
| 1. Cliquet Option Valuation Introduction |
A cliquet option or ratchet option is an exotic option consisting of a series of consecutive forward start options. Each cliquet period is settled as soon as it fixes. In other words, each cliquet period has its own fixing date, independent of the other cliquets.
The product payoff in each of these periods is determined by the rate of return on the underlying asset during that time interval. A cliquet may be subject to a cap and a floor where the payoff for each period is the better of a floor level and a capped period return of the underlying index.
Cliquets are volatility-sensitive products. A good volatility model not only has to be able to calibrate to the spot implied volatilities but also to the forward start options. A Cliquet model is designed to take the term structure of volatility and the volatility smile into account
Cliquet options are popular. They consist of financial derivatives that provide a guaranteed minimum return in exchange for a capping of the maximal return over the life of the contract. A cliquet option is equivalent to a series of forward-starting at-the-money options.
We consider standard forward start options on domestic equity stock prices. These products are characterized by prevailing market conditions and by the following deal-specific inputs: Percentage strike, Forward start date, Maturity date.
Cliquet options are appealing to investors because they can protect holders against downside risks. Possible variants include reverse cliquet which amounts to a cash flow minus a capped cliquet of puts, and digital cliquet. Digital cliquet is a forward-starting digital option.
The Cliquet option may have an optional Lock feature, that pays a Total Coupon equal to a guaranteed Coupon plus the sum of a series of Weighted Individual Coupons at maturity. The Coupon Sum is subject to both a Global Floor and a Global Cap. The cap or floor is applied periodically to the entire trade period.
We model the respective forward equity price process to each fixing time, but use a calibration procedure, based on an underlying capital gains process, to determine the appropriate forward-forward volatility term structure for each fixing process.
Another type of cliquet option is reverse cliquet option that is usually embedded in an index linked note. The payoff of a reverse cliquet option at maturity is the better of a floor level and the sum of capped percentage changes in the prices of the Index for each quarterly period throughout the term of the Notes.
In the reverse cliquet case, we assume that the risk-neutral index price process follows a geometric Brownian motion with stochastic volatility. Moreover, the variance process satisfies an SDE of the CIR form.
| 2. Valuation |
In valuation, stock prices into stochastic and deterministic components. The deterministic component is defined to be the present value of dividend payments to the option’s maturity, while The stochastic component, which we will denote by G, is modeled as a log-normal process under the risk-neutral probability measure
The payoff in each period is determined by the excess return above a local hurdle, and constraint by a local cap and a local floor. At expiry, the total payoff depends on the excess return above a global hurdle. It may also be constraint by a global cap and a global floor.
A cliquet may also pay a minimum coupon b to the face value F , regardless of the return on the underlying asset.
We use the stochastic local volatility (SLV) model calibrated to local volatility surface with given model inputs. The stochastic differential equation (SDE) of an SLV model is given by
Sensitivities are important for hedging and risk assessment. Delta is computed as the derivative of the option premium with respect to the equity underlier spot level at valuation date. Gamma is computed as the second derivative of the option premium with respect to the equity underlier spot level at valuation date. Vega is computed as the sum, over each fixing date, of the derivative of the option price with respect to the term volatility to the fixing date. Rho is the sum, over each bootstrap key maturity point, of the derivative of the option price with respect to the effective continuously compounded zero rate to the maturity point.
| 3. Related Topics |