Spread Options
Derivatives-based Portfolio Solutions
OUTPERFORMANCE OPTIONS ARE USUALLY SHORT-DATED CALLSOutperformance 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 ‘r _{A} over r’ (as a put of ‘r_{B}_{A} over r’ can be structured as a call on ‘r_{B}_{B} over r_{A}’). Outperformance options are always European (like all light exotics) and are traded OTC.Payout = Max (r_{A} – r_{B}, 0) where r_{A} and r_{B} are the returns of assets A and B, respectivelyOPTIONS USUALLY ATM, CAN HAVE HURDLE AND ALLOWABLE LOSSWhile 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 (r_{A} over r_{B} – hurdle, – allowable loss)OUTPERFORMANCE OPTIONS ARE SHORT CORRELATIONThe 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.MARGRABE’S FORMULA CAN BE USED FOR PRICINGAn 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. TEND TO BE USED FOR CORRELATED ASSETSThe 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 σ _{A} and σ_{B} 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 2ρσ_{A}σ_{B} (reducing the outperformance volatility σ_{A-B}).LOWER FORWARD FLATTERS OUTPERFORMANCE PRICINGAssuming 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 underlyingIf two assets have the same volatility (σ _{A} = σ_{B}) and are 50% correlated (ρ = 50%), then the input for outperformance option pricing σ_{A-B} is equal to the volatilities of the two underlyings (σ_{A-B} = σ_{A} = σ_{B}). 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. |

### Spread Options

Selection | File type icon | File name | Description | Size | Revision | Time | User |
---|