Equity Auto Delta Hedged Option

ORE introduces the product as follows:

This trade type represents a structured product consisting of one or more batches of European equity options with an embedded discrete delta-hedging strategy.

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

The trade is an option and its hedge sold as one contract. The option pays out in the usual way. The hedge leg replays a fixed hedging recipe: a stated volatility for the deltas, a stated drift for the forward, and daily rebalancing. The customer knows the hedge rules in advance.

The EquityAutoDeltaHedgedOptionData node is the trade data container for the EquityAutoDeltaHedgedOption trade type. Volatility is mandatory. It is the hedging volatility sigma_h used in the Black-Scholes delta computation for the daily delta-hedge rebalancing, expressed as a decimal. DriftRate is mandatory. It is the continuously compounded rate r used in the contractual forward formula F = S_t x e^(r x tau), where tau is the Actual/365 (Fixed) year fraction from the observation date to expiry. Underlyings is a container holding one or more Underlying child nodes. Each defines a single batch of options. The OptionData sub-node holds the option terms: LongShort, OptionType, Style, Settlement, exactly one ExerciseDate and one premium per underlying. The style must be European and the settlement must be Cash. The premium is included in the equity amount calculation at expiry. Each underlying also carries Name, Currency, Strike, StrikeCurrency and Quantity. ObservationStartDate is mandatory. It is the date from which the discrete delta-hedging observation begins. Historical fixings between this date and the valuation date are used to compute the realised hedge P&L.

The product combines the option payoffs of its batches with the P&L of a discrete delta-hedging strategy. Each day the hedge holds the Black-Scholes delta of the options, computed with the contractual hedging volatility. The contractual forward F = S_t x e^(r x tau) gives the drift of the hedge. The realised hedge P&L accumulates from the observation start date. At expiry the equity amount includes the premiums.

• The spot price of each underlying equity, through the option delta and the hedge.
• The implied volatility of each underlying.
• The contractual hedging volatility and drift rate.
• The strikes, quantities and exercise dates of the batches.
• The interest rates and dividends that drive the forward.

The hedge dampens the spot sensitivity of the raw option position. The choice of hedging volatility sets how the hedge behaves.

The hedge rebalances daily from the observation start date. Realised hedge P&L accumulates as the underlying moves. Near expiry the hedge tends toward the option deltas at expiry, and the batches settle in cash. After the last exercise date the product is settled and the exposure ends.

A customer who sells structured equity products wants the hedge economics inside the trade. The auto delta hedged option fixes the hedge parameters contractually, so the payoff and the hedge P&L are valued as one. In ORE Studio a customer books auto delta hedged options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a batch of long European calls on HSBC, with the hedging volatility at 5 percent and no drift:

<EquityAutoDeltaHedgedOptionData>
  <Volatility>0.05</Volatility>
  <DriftRate>0.00</DriftRate>
  <Underlyings>
    <Underlying>
      <OptionData>
        <LongShort>Long</LongShort>
        <OptionType>Call</OptionType>
        <Style>European</Style>
        <Settlement>Cash</Settlement>
        <ExerciseDates>
          <ExerciseDate>2021-01-29</ExerciseDate>
        </ExerciseDates>
        <PremiumAmount>9.36</PremiumAmount>
        <PremiumCurrency>USD</PremiumCurrency>
        <PremiumPayDate>2019-03-01</PremiumPayDate>
      </OptionData>
      <Name>RIC:HSBA.L</Name>
      <Currency>USD</Currency>
      <Strike>3.5</Strike>
      <StrikeCurrency>USD</StrikeCurrency>
      <Quantity>51400</Quantity>
    </Underlying>
    <Underlying>
      ...
    </Underlying>
  </Underlyings>
  <ObservationStartDate>2020-11-11</ObservationStartDate>
</EquityAutoDeltaHedgedOptionData>

Source: ORE User Guide, Products catalogue, equityautodeltahedgedoption.tex, listing Equity Auto Delta Hedged Option data, further batches elided.