Spread Options
Derivatives-based Portfolio Solutions


Spread or outperformance options are options on the difference between returns on two different underlyings. They are a popular method of implementing relative value trades, as their cost is usually cheaper than an option on either underlying. The key unknown parameter for pricing outperformance options is implied correlation, as outperformance options are short correlation. The primary investor base for outperformance options is hedge funds, which are usually buyers of outperformance options on two correlated assets (to cheapen the price). Outperformance options are European and can always be priced as a call. Unless they are struck with a hurdle, they are an ATM option.

Outperformance options give a payout based on the difference between the returns of two underlyings. While any maturity can be used, they tend to be for maturities up to a year (maturities less than three months are rare). The payout formula for an outperformance option is below – by convention always quoted as a call of ‘rA over rB’ (as a put of ‘rA over rB’ can be structured as a call on ‘rB over rA’). Outperformance options are always European (like all light exotics) and are traded OTC.

Payout = Max (rA – rB, 0) where rA and rB are the returns of assets A and B, respectively

While outperformance options are normally structured ATM, they can be cheapened by making it OTM through a hurdle or by allowing an allowable loss at maturity (which simply defers the initial premium to maturity). While outperformance options can be structured ITM by having a negative hurdle, as this makes the option more expensive, this is rare. The formula for outperformance option payout with these features is:

Payout = Max (rA over rB – hurdle, – allowable loss)

The pricing of outperformance options depends on both the volatility of the two underlyings and the correlation between them. As there tends to be a more liquid and visible market for implied volatility than correlation, it is the implied correlation that is the key factor in determining pricing. Outperformance options are short correlation, which can be intuitively seen as: the price of an outperformance option must decline to zero if one assumes correlation rises towards 100% (two identical returns give a zero payout for the outperformance option).

As flow is to the buy side, some hedge funds outperformance call overwrite Outperformance options are ideal for implementing relative value trades, as they benefit from the upside, but the downside is floored to the initial premium paid. The primary investor base for outperformance options are hedge funds. While flow is normally to the buy side, the overpricing of outperformance options due to this imbalance has led some hedge funds to call overwrite their relative value position with an outperformance option.

An outperformance option volatility σA-B can be priced using Margrabe’s formula given the inputs of the volatilities σA and σB of assets A and B, respectively, and their correlation ρ. This formula is shown below.

The formula above confirms mathematically that outperformance options are short correlation (due to the negative sign of the final term with correlation ρ). From an investor perspective, it therefore makes sense to sell correlation at high levels; hence, outperformance options tend to be used for correlated assets (so cross-asset outperformance options are very rare). This is why outperformance options tend to be traded on indices with a 60%-90% correlation and on single stocks that are 30%-80% correlated. The pricing of an outperformance option offer tends to have an implied correlation 5% below realized for correlations of approx. 80%, and 10% below realized for correlations of approx. 50% (outperformance option offer is a bid for implied correlation).

Best pricing is with assets of similar volatility

The price of an outperformance is minimized if volatilities σA and σB of assets A and B are equal (assuming the average of the two volatilities is kept constant). Having two assets of equal volatility increases the value of the final term 2ρσAσB (reducing the outperformance volatility σA-B).

Assuming that the two assets have a similar interest rate and dividends, the forwards of the two assets approximately cancel each other out, and an ATM outperformance option is also ATMf (ATM forward or At The Money Forward). When comparing relative costs of outperformance options with call options on the individual underlyings, ATMf strikes must be used. If ATM strikes are used for the individual underlyings, the strikes will usually be lower than ATMf strikes and the call option will appear to be relatively more expensive compared to the ATMf (= ATM) outperformance option.

Pricing of ATM outperformance options is usually less than ATMf on either underlying
If two assets have the same volatility (σA = σB) and are 50% correlated (ρ = 50%), then the input for outperformance option pricing σA-B is equal to the volatilities of the two underlyings (σA-B = σA = σB). Hence, ATMf (ATM forward) options on either underlying will be the same as an ATMf (≈ATM) outperformance option. As outperformance options tend to be used on assets with higher than 50% correlation and whose volatilities are similar, outperformance options are usually cheaper than similar options on either underlying.
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