Equity Option

ORE defines the European and American forms as follows:

A European Equity Option gives the buyer the right, but not the obligation, to buy a set number of shares of a single name equity or an equity index, at a predetermined strike price, at the end of the contract. For this right the buyer pays a premium to the seller.

An American Equity Option gives the buyer the right to buy at any time during the life of the option up until the expiration date. The right to buy the shares can only be exercised once.

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

ORE defines the quanto and composite forms as follows:

A Quanto European Equity Option is a European Equity Option where the currency that the underlying equity (or equity index) is quoted in and the option payoff currency are different. The implied FX rate between the underlying currency and payoff currency at the option settlement date is then equal to one.

In a European Equity Composite Option the strike currency is different from the underlying currency. This is unrelated to the CompositeTrade trade type.

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

An equity option is an insurance-like right on a share price. The buyer pays a premium up front. In return the buyer can buy at the strike if the price rises above it, or sell at the strike if the price falls below it. Losses never exceed the premium. A quanto option pays in a different currency and ignores the exchange rate at settlement. A composite option keeps its strike in a different currency.

The EquityOptionData node is the trade data container for the EquityOption trade type. It has one and only one OptionData trade component sub-node. LongShort names the side, OptionType the call or put right. Style takes European or American. Settlement takes Cash or Physical. A quanto payoff must settle in cash. PayOffAtExpiry is relevant for American options and defaults to PayOffAtExpiry true. Exactly one ExerciseDate must be given. For American options it is the last exercise date. PaymentData can set a payment date other than the exercise date, except for quanto and composite options. Premiums carries the premium amounts. The underlying comes from Name or an Underlying node. Currency is the payment currency. If it differs from the currency the equity is quoted in, a quanto payoff applies. For a quanto option, StrikeCurrency must equal the currency the equity is quoted in. For a composite option it must equal the payment currency. The strike can also sit in a StrikeData node, which supports StrikePrice only.

The call payoff per share is max(S - K, 0) and the put payoff is max(K - S, 0), scaled by the quantity of shares. A quanto option converts the payoff at an implied FX rate of one. For a composite call the payoff at expiry is max(X(t) x S(t) - K, 0). Here X(t) is the exchange rate at expiry that converts from the underlying currency into the strike currency. The payoff can take place at exercise or at expiry.

• The spot price of the underlying equity or index. It sets the moneyness.
• The implied volatility of the underlying.
• The strike, the expiry and the style of the option.
• The expected dividends of the underlying.
• The interest rates in the payment and underlying currencies.
• For quanto options, the FX volatility and the equity-FX correlation.
• For composite options, the FX spot level.

Calls gain when the spot rises. Puts gain when it falls. Time decay works against the option buyer.

An option loses time value as expiry approaches. Its value converges to the intrinsic value. A European option cannot exercise early. An American option can, and early exercise may be optimal just before a dividend. At expiry the option settles in cash or delivers the shares. The quanto and composite conversions apply at the settlement date.

An equity option caps the downside of a share position or a planned trade. The buyer pays a known premium and keeps unlimited upside potential. American exercise suits holders who may need to act before expiry. Quanto options give equity exposure in a home currency without FX risk. Composite options express a view on both the equity and the exchange rate. In ORE Studio a customer books equity options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows an American call on the S&P 500 index:

<EquityOptionData>
    <OptionData>
         <LongShort>Long</LongShort>
         <OptionType>Call</OptionType>
         <Style>American</Style>
         <Settlement>Cash</Settlement>
         <PayOffAtExpiry>true</PayOffAtExpiry>
         <ExerciseDates>
             <ExerciseDate>2022-03-01</ExerciseDate>
         </ExerciseDates>
         ...
    </OptionData>
    <Name>RIC:.SPX</Name>
    <Currency>USD</Currency>
    <Strike>2147.56</Strike>
    <StrikeCurrency>USD</StrikeCurrency>
    <Quantity>17000</Quantity>
</EquityOptionData>

Source: ORE User Guide, Products catalogue, equityoption.tex, listing Equity Option data.

The linear counterpart is the Equity Forward. The option-on-future variant is the Equity Futures Option.