Equity Cliquet Option

ORE defines the product as follows:

A cliquet option is an exotic option consisting of a series of consecutive forward start options, with each option being struck at-the-money when it becomes active.

Source: ORE User Guide, Products catalogue, equitycliquetoption.tex.

ORE restates the setup as follows:

A cliquet option consists of a series of consecutive forward starting equity options, with each option being struck at a given moneyness (commonly at-the-money) when it becomes active.

Source: ORE User Guide, Products catalogue, equitycliquetoption.tex.

A cliquet option resets itself every period. Each period starts a new option at the then-current price. The gain of each period is added up. Caps and floors limit each period and the total. The buyer collects the sum of the good periods while the caps and floors control the cost.

The EquityCliquetOptionData node is the trade data container for the EquityCliquetOption trade type. The underlying comes from Name or an Underlying node. Currency is the currency of the notional and must equal the currency of the underlying equity. Notional scales the payoff. LongShort names the side and OptionType the call or put direction. Moneyness sets the strike of each forward starting option. A value of 1.0 is at the money, 1.1 is 110 percent of the at- the-money strike, 0.9 is 90 percent. LocalCap and LocalFloor limit each period's return. GlobalCap and GlobalFloor limit the total return. The ScheduleData node defines the valuation dates. The last date is the final valuation date. The whole payoff is paid at that date plus SettlementDays. SettlementDays defaults to zero. Premium is paid for the option and is expressed relative to the notional. If a premium is specified, a PremiumPaymentDate must also be specified. PremiumCurrency defaults to the currency of the notional.

The payoff is N x min(cap_g, max(floor_g, sum over the periods of the period returns)). Each period return is delta x min(cap_l, max(floor_l, S_ti / S_ti-1 - M)). S_ti is the price of the underlying at the period end. M is the moneyness. Delta is 1 for a call and -1 for a put. cap_l and floor_l are the local cap and floor. cap_g and floor_g are the global cap and floor over the whole product. The local limits bind period by period. The global limits bind the accumulated sum.

• The spot level of the underlying at each reset date.
• The implied volatility surface across the option tenors.
• The local caps and floors of each period.
• The global cap and floor of the product.
• The moneyness of the forward-start strikes.
• The interest rates and dividends of the underlying.

Each period is a new at-the-money option, so the structure is sensitive to the volatility term structure. The caps and floors set how much optionality each period keeps.

Period by period a return is locked in. A local cap or floor applies when the period return tries to exceed it. The accumulated total moves toward the global cap or floor. Once the global cap is reached, the remaining periods add nothing. Once the global floor binds, later gains rebuild the total. The number of live periods shrinks as the schedule advances. The final payoff settles at the last valuation date plus the settlement days.

A cliquet structure suits a customer who expects the market to grind upward with periodic setbacks. Each reset gives a fresh at-the-money option, so the customer never holds a deep out-of-the-money strike. The caps and floors shape the price. In ORE Studio a customer books equity cliquet options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a short call cliquet on the S&P 500 index with annual resets:

<EquityCliquetOptionData>
    <Underlying>
      <Type>Equity</Type>
      <Name>.SPX</Name>
      <IdentifierType>RIC</IdentifierType>
    </Underlying>
    <Currency>USD</Currency>
    <Notional>1000000.0</Notional>
    <LongShort>Short</LongShort>
    <OptionType>Call</OptionType>
    <Moneyness>1.0</Moneyness>
    <LocalCap>0.07</LocalCap>
    <LocalFloor>-0.06</LocalFloor>
    <GlobalCap>0.07</GlobalCap>
    <GlobalFloor>-0.07</GlobalFloor>
    <ScheduleData>
      <Dates>
        <Date>20171231</Date>
        <Date>20181231</Date>
        ...
      </Dates>
      <Calendar>USD</Calendar>
      <Convention>F</Convention>
    </ScheduleData>
    <SettlementDays>5</SettlementDays>
    <Premium>0.027</Premium>
    <PremiumPaymentDate>31-12-2017</PremiumPaymentDate>
    <PremiumCurrency>USD</PremiumCurrency>
</EquityCliquetOptionData>

Source: ORE User Guide, Products catalogue, equitycliquetoption.tex, listing Cliquet Option data, intermediate schedule dates elided.