Estimating Volatility and Correlation for Futures Spread Options
Summary
The document discusses how to estimate risk inputs for an option on the difference between two futures. It presents three approaches to spread volatility: calculate it from historical spread returns, combine the futures’ implied volatilities with a historical correlation estimate, or infer correlation from market prices for spread or basket options. The choice between historical and implied volatility depends on which is expected to better represent future realized volatility.
For a currency-translated spread, the method depends on what can be traded and priced. If the converted asset and its option are available, treat it like the basic spread. If the asset trades but its option does not, estimate spread volatility historically. If the converted asset itself is unavailable, model the component volatilities and correlations because the underlying assets require separate hedges. The answers give no calibration examples or performance evidence, and the appropriate inputs depend on available instruments and hedging needs.
Key ideas
- Historical spread returns can provide an estimate of spread volatility.
- Combining component implied volatilities requires an estimate of their correlation.
- Market prices for spread or basket options can be used to infer correlation.
- Currency conversion can require additional volatility and correlation inputs when components must be hedged separately.
Tags
Full text
# Pricing an option on the spread of two contracts, what correlation parameter? # Pricing an option on the spread of two contracts, what correlation parameter? I must price an option on the spread of two futures (A-B) the model I must use uses the IV on the options of each futures. Another parameter I need is the correlation of these, what would be a suitable way to find this please? Is there a concept of "volatility of the spread"? Could it be done by applying the cosine rule to the IVs and the correlation parameter? In addition how could this be extended to a cross currency spread i.e. (A*C - B) where C is the adequate currnecy future (or forward)? Thanks ## Answer by Arshdeep (score 1) https://quant.stackexchange.com/a/80247 If you don't care about vega hedging (spread options are not vega hedged typically) then you only need to look at the spread volatility, which you can get as: (i) historical vol of spread (ii) specifying correlation historically and using implied vols of A and B, if you believe implied vols are a better representation of realized vols. Really depends on what you think better approximates realized vol. For the FX product, (i) if AC is tradeable and option on AC is tradeable, its the same thing as above. (ii) If AC is tradeable but an option on AC is not tradeable, you will have to get the vol of the spread historically (iii) If AC is not tradeable then you need vols of A and C individually (as you need to delta hedge A and C separately now) and thus you will also need vol of B, and the correlation matrix. This will decide the deltas. ## Answer by ir7 (score 0) https://quant.stackexchange.com/a/80526 The third way (continuing the previous answer) is to get some market or consensus prices of the option on the futures price spread (or prices of basket options, if available) and, given implied vols, imply a correlation level. For a currency-translated asset, imply a FX rate/asset price correlation from, say, market or consensus quanto forward/options prices (or compo option prices, if available).
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.