**Cliquet Options**

A derivative is a financial instrument derived from another asset. Market participants enter into an agreement to exchange money, assets or some other value at some future date based on the underlying asset (Investopedia.com, 2007). Among different types of financial derivations, options/futures and swaps are the most common. Options are contracts where one party agrees to pay a fee to another for the right to buy something from or sell something to the other.

For example, a person who anticipates that the price of his Google stock may decline before he opts to sell it may pay a fee to another person who agrees to buy the stock from him at the strike price. The other person is called the writer of a put option. While the person with the stock is using a risk management option, the person who is the writer of the put option can benefit from the increase in the stock price and fee income. In contrast to a put option, a call option gives the buyer of the option the right to purchase the underlying asset at a later date and at the specified strike price.

There are two practical uses of options in general: speculation and hedging. For example, if one expects the price of $100 Microsoft stock to increase over the next three months, he can either buy the stock or call options on the stock. If a person has $10000 to invest, he can either buy 100 shares or 10000 call options on the stock. If the price actually rises to $120 in three months, there would be a profit of $2,000 if the stock had been bought directly and a profit of $100000 if the buyer had bought the options. Of course, if the price drops, the loss on the options will be greater than the loss on the stock (Marakani, 2000).

The hedger’s aim is to hold on to the value of his portfolio amidst price changes. If a person owns some Microsoft stock, he can sell call options on it. When there is a decline in the price below the strike, he will make a profit. If there is a rise in price, he incurs a loss as the options are called. This balances any decrease and increase in the stock value he holds and provides hedging (Marakani, 2000).

A forward start option is an advance purchases of a put or call option that will become active at some specified future time. The premium is paid in advance, and the asset and time to expiration are specified at that time. The strike price is determined when the option becomes active. Typically, it is set at-the-money based upon the asset value at that time. Alternatively, it can be set a pre-determined percentage in-the-money or out-of-the-money (Investopedia.com, 2007b).

A ratchet option (or cliquet option) is a series of consecutive forward start options. The first is active immediately. The second becomes active when the first expires, etc. Each option is struck at-the-money when it becomes active. The effect of the entire instrument is of an option that periodically “locks in” profits. Thus, cliquet option may be defined as “an extended option that periodically settles and resets its strike price at the level of the underlying during the time of settlement” (Investopedia.com, 2007a). “A Cliquet Option settles periodically and resets the strike at the then spot level. It is therefore a series of at-the-money options, but where the total premium is determined in advance. The payout on each option can either be paid at the final maturity or at the end of each reset period” (Cliquet Options, 2007).

For example, a 3 year cliquet option with a strike of 1000 would be rendered worthless if the value of the asset at the end of the first year happens to be 900. However, this value would then be the new strike for the following year and should the underlying on settlement be 1200, the contract holder would receive a payout and the strike would reset to this new level (Wilmott, 2002). Higher volatility provides better conditions for investors to earn profits. Cliquet options are currently very popular in the realm of equity derivatives. Their appeal is mainly due to the benefits they bring to the investor through their protection against downside risk, yet with significant upside potential (Windcliff et al, 2004). Due to this nature, cliquet options are in more demand due to recent turmoil in financial equity markets[1]. Cliquet options are also known as reset options, ratchet, and strike reset options.

The first cliquet options to be traded on a public exchange were S&P 500 bear market warrant with a periodic reset (Shparber and Resheff, 2004). They were introduced on the Chicago Board of Options Exchange in 1996. These reset warrants on the S&P 500 index are characterized by the fact that the exercise price is reset at a higher level if the index level is above the original exercise price on the reset date. But for this resetting characteristic, they otherwise work like regular equity or index puts (Shparber and Resheff, 2004).

**Types of Cliquet Options**

There are two kinds of cliquet options: regular and compound. Since both these types have similar properties, their values can be expressed using a single equation (Buetow, 1999). Moreover, the regular ratchet can be shown as a special case of the compound ratchet. Both these types of cliquet options have the characteristic that the amount of underlying asset is constant throughout the life of the ratchet (T years) and all the returns are locked in at the end of the resetting period (usually one year). Normally, the underlying asset is a specific equity index. The indices currently used range from the S&P 500 index to proprietary multi country indices. The chosen index in no way alters the derivation (Buetow, 1999).

In the usual European style cliquet entitles its holder upon exercise to the difference between the exercise price and the underlying stock price. However, the exercise price of a reset put is subject to change. On the issuance date, the exercise price is set to the current stock price, S0. Upon the reset date (specified in advance) if the stock price (St) is higher than the original exercise price (S0)

Five-year Reset Put on ABC Index

Option Buyer XXX

Option Seller YYY

Start Date dd/mm/yyyy

Maturity Date Start date + 5 years

Option Seller Pays at Maturity:

St – ST if St > X, ST ≤ St

X – ST if St ≤ X, ST ≤ X

0 if (St > X and ST > St) or (St ≤ X and ST > X)

Here, X is the original exercise price. This can be the closing stock price or index price on the date of issuance. St is the closing stock or index price on the reset date, and ST is the closing stock/index price on the expiration date. The exercise price is ‘reset’ to be equal to the prevailing stock price St. The value of a reset put with a single reset date is summarized in the above table. The time subscripts t and T represent the reset date and the expiration date of the put, respectively. In the second case, when the exercise price is greater than the stock price on the expiration date, ST ≤ X, the option holder receives the difference X – ST. In the third case, the put is out-of-the-money at expiration, independent of whether or not the put’s exercise price was reset (Wilmott, 2002).

**Valuating cliquet options**

- As already seen, a cliquet is a series of at-the-money options. The following facts may be considered while estimating cliquet options:
- The expected value of these options can be measured by generating the implied forward volatility curve.
- Cliquet options depend on special features of the implied volatility surface (e.g. forward implied volatility surface – especially forward skew).
- The Cliquet premium is the present value of the premiums for the option series.
- A cliquet call is always more expensive than a straight at-the-money call with the same final maturity.
- The buyer decides the number of reset periods knowing that more resets add to the cost of the cliquet option.

**Valuation of Cliquet Options**

The following are some numerical methods of valuating cliquet options. Closed-form solutions.

Gray & Whaley (1999) (GW) have suggested a different solution for the European cliquet option described above. The divided the end payoffs of the option to three possible outcomes and derived the overall expected value using the probabilities of each outcome. This approach can be used in the case of deriving the European cliquet option pricing formula as well (Shparber & Resheff, 2004).

Generally, the profit obtained through cliquet option can be allowed to accumulate till maturity or it can be paid out at each resent date. The difference between these cliquets and those analyzed by GW (1999) is that the strike of the former resets no matter what the stock price is. Otherwise, cliquet options can be priced as a series of forward-start options using the Rubinstein (1991) approach. Rubinstein showed that the value of a forward-start option is simply the current value of d-t vanillas which are currently at-the-money, with time to expiration T–t (where d is the continuous dividend payout rate).

It must be noted that this closed-form solution is not suitable for the GW type cliquet options that reset the strike price conditionally based on the underlying stock price. Thus we find that closed-form solutions are not flexible enough to be used to valuate a variety of exotic options and they are not simple enough. Because of these difficulties, HH (2001) has proposed the binomial method for pricing European cliquet options (Shparber & Resheff, 2004).

Binomial Solutions: HH used an analytical equation to value European cliquet options using a binomial tree. According to this binomial tree, the probabilities of ending at each node is calculated and then discounted at the risk free interest rate. This is a highly flexible solution that can be used widely and accurately. This solution can be used to value many kinds of cliquet options and the results are close to those obtained by GW method (Shparber & Resheff, 2004).

Other Solutions: Wilmott (2001) holds that cliquets are more sensitive to volatility than plain vanilla contracts. Based on this concept, Wilmott’s valuation model includes a changing volatility. He uses Monte Carlo simulation as well as partial differential equations to value the reset option. Monte-Carlo simulation pricing is highly flexible and can be very easily used to calculate the price for any kind of cliquet options: multiple-reset compound ratchets, coupe options, barrier cliquets, etc. Windcliff et al. (2003) use Merton’s jump diffusion model to value cliquet options. Other solutions are Schoutens and Symens (2002) and Buetow (1999) (Shparber & Resheff, 2004).

**Cliquet Option and Volatility**

A Cliquet option is most attractive when volatility is expected to increase. This statement can be illustrated with an example. The initial strike of a three year Cliquet Call on the FTSE with annual resets is set at say 3000. If at the end of year one, the FTSE closes at 3300, the first call matures 10% in-the-money and this amount is paid to the buyer. The call strike for year 2 is then reset at 3300. If at the end of year 2, the FTSE closes at 2900, the call will expire worthless.

The call strike for year 3 is then reset at 2900. Alternatively, it is possible to buy a one year at-the-money call and at the end of year one, buy another at-the-money one year call, and so on. The difference is that the cost of the Cliquet is known in advance, whereas the future cost of at-the-money calls is unknown. It is thus evident that if volatility is lower than expected, the Cliquet will be more expensive than buying the calls annually, if volatility is higher than expected, the Cliquet will be cheaper (Cliquet Options, 2007).

Target users of Cliquet Options: The cliquet option is ideal for medium term investors as it involves less risk than other medium term options. There is less specific risk as the buyer gets second and third chances due to the reset facility. The resetting increases the probability of payout the only drawback is that there is a higher premium cost involved. The cliquet option is also attractive to passive investors as it does not involve any kind of intermediate supervision or monitoring. Retail and private investors who deal in deposits and bonds consider cliquet options as a low risk exposure to equity and bond markets. Professional investors turn to cliquet options to take advantage of future assumptions regarding volatility.

Advantage of cliquet options: The major advantage of the Cliquet is that the probability of some payout is high. Over the 3 year period, there is less chance for the market to wind up lower for three consecutive years, than the chance for the market to close lower at the end of three years. Therefore, it is likely for the market to close higher in at least one of the three years even if the market is lower after three years (Cliquet Options, 2007).

**Conclusion**

Thus cliquet options, like all exotic options may be used in speculation and hedging. Though there are many kinds of cliquet options. Implied volatility curves showing the effect of correlation on option prices. One can see that positive correlation leads to an increase in the option price when the strike price is high and a decrease when the strike price is low while negative correlation has the opposite effect.

Implied volatility curves showing the effect of correlation on option prices for alpha = 1. It is clear that positive leads to an increase in the option price when the strike price is high and a decrease when the strike price is low while negative has the opposite effect

Example of call option ranges:

The prices of European call options on the S&P 500 Index whose maturity was on 21 Feb, 1998 on Jan 5, 1998 at 3:00 p.m.

Strike Price

Option Price

920

68.0

925

64.125

930

60.25

940

52.75

950

45.5 (trade at 3:20 p.m.)

960

39.0

970

31.5 (trade at 3:00 p.m.)

975

29.75

980

27.0

990

21.0 (trade at 3:00 p.m.)

1010

13.0 (trade at 3:20 p.m.)

**Bibliography**

- Marakani, Srikant (2000). Option Pricing with Stochastic Volatility. August 15, 2000. http://srikant.org/thesis/thesis.html
- Cliquet Options. Accessed March 2007. http://my.dreamwiz.com/stoneq/products/cliquet.htm
- Shparber, Michael and Resheff, Sharon (2004). Valuation of Cliquet Options. August 2004. http://www.global-derivatives.com/docs/ValuationOfCliquetOptions_Shparber_Resheff_2004.pdf
- Windcliff et al (2004). Numerical Methods and Volatility Models for Valuing Cliquet Options. http://www.cs.uwaterloo.ca/~paforsyt/cliquet.pdf
- “Selling Pessimism”, The Economist, March 8, 2003
- Buetow, W. Gerald (1999). Ratchet Options. Journal of Financial and Strategic Decisions. Volume 12, Number 2, Fall 1999. http://www.studyfinance.com/jfsd/pdffiles/v12n2/buetow.pdf
- Wilmott, Paul (2002). Cliquet Options and Volatility Models. Wilmott Magazine. December 2002. Page 78-83
- Investopedia.com (2007a). Cliquet. http://www.investopedia.com/terms/c/cliquet.asp
- Investopedia.com (2007b). Options Basics: Introduction. http://www.investopedia.com/university/options/