Spread Option
A spread option is a derivative contract whose payoff is based on the difference between the prices (or rates) of two underlying assets rather than on a single asset price, providing the holder with a view on the relative performance of the two assets or the spread between two related commodities, interest rates, or credit instruments. Spread options are extensively used in energy markets (crack spreads, spark spreads), fixed income (yield curve spreads), and equity relative value strategies.
Key takeaways
- A call spread option pays max(S₁ - S₂ - K, 0) where S₁ and S₂ are the prices of the two underlying assets and K is the strike spread; a put spread option pays max(K - (S₁ - S₂), 0).
- Spread options cannot be valued with the standard Black-Scholes formula (which requires a single underlying); they require more complex models such as the Kirk approximation, Margrabe's formula (for zero-strike spreads), or Monte Carlo simulation.
- Correlation between the two underlying assets is the key additional input beyond individual volatilities; higher correlation reduces spread option premium by compressing the distribution of possible spread outcomes.
- Energy companies extensively use spread options to hedge or monetize the optionality in processing margins: a refinery 'owns' the crack spread option (the right to process crude into products), while a power generator 'owns' the spark spread option (the right to dispatch).
- Spread options on interest rate differentials (2s10s curve steepener/flattener options) allow fixed income investors to express yield curve views with defined downside, gaining convexity on curve positioning.
Explanation
Spread options represent a natural extension of single-asset options to the broader set of spread relationships that drive real economic decisions. A grain processor's profitability depends on the spread between corn prices and ethanol prices (the corn crush spread). A refiner's margin depends on the difference between product values (gasoline, heating oil) and crude oil costs (the crack spread). An electric utility's generation decision depends on the spark spread between electricity and gas prices. In each case, the business 'owns' an operational spread option — the real option to exercise or not exercise the spread by operating their processing or generation facility. Financial spread options allow these companies (and financial investors) to hedge or speculate on these spread relationships directly.
The mathematical challenge in spread option pricing arises from the need to model the joint distribution of two correlated stochastic processes. The standard Black-Scholes formula assumes a single lognormal underlying, but a spread of two lognormal assets is not itself lognormal — the distribution of S₁ - S₂ is more complex, especially near zero where the spread can be negative. Margrabe's exchange option formula (1978) provides an exact closed-form solution for the special case where the strike K = 0 (an option to exchange one asset for another): this is the appropriate model for commodity processing options where the operator can choose to process (receiving the spread) or not process (receiving nothing). For non-zero strikes, the Kirk approximation (1995) provides a fast and reasonably accurate semi-analytical solution by treating the spread approximately as a modified single-asset option.
Correlation is the key non-standard parameter in spread option pricing. In the standard Black-Scholes framework, the only inputs are the underlying price, strike, volatility, time, and risk-free rate. For spread options, the correlation between the two underlying assets is an additional critical input: a correlation of +1.0 would make the spread essentially deterministic (the two assets always move together), eliminating most option value; a correlation of -1.0 maximizes spread uncertainty and option premium. Implied correlation — backing out the correlation implied by observed spread option prices — is an important market indicator of market participants' consensus view on how closely related two commodities or instruments are expected to track each other.
In the fixed income context, yield curve spread options allow investors to efficiently express views on the yield curve's slope without the need to maintain complex delta-hedged positions in two different maturity bonds. A 2s10s steepener option — an option that pays the difference between the 10-year yield and the 2-year yield minus a strike spread, if positive — provides a clean, capped-downside way to bet on yield curve steepening. During periods of quantitative easing or yield curve control, these options may price cheaply (implied volatility of the spread is low), making them attractive for investors who believe policy normalization will steepen the curve.
For interest rate spread options across currencies (e.g., USD vs. EUR 10-year yield differential), the option simultaneously embeds interest rate risk and currency risk, requiring sophisticated cross-currency term structure models for accurate pricing. These instruments are primarily used by global macro hedge funds and bank proprietary trading desks.
Formula
Spread Call Payoff = max(S₁ - S₂ - K, 0); Spread Put Payoff = max(K - (S₁ - S₂), 0)
Example
A petroleum refinery buys a 3-month crack spread call option at a strike of $20/barrel (the spread between gasoline and crude oil). The current crack spread is $18/barrel. The option costs $2.50/barrel. Over the next 3 months, summer driving demand and a refinery disruption push the crack spread to $35/barrel. The refinery exercises the option, receiving $35 - $20 = $15/barrel. Net of the $2.50 option premium, the refinery earns $12.50/barrel via the option, effectively locking in a minimum processing margin of $15/barrel (its operational spread) plus the $12.50 option gain — supplementing its physical margin. If the crack spread had fallen to $10/barrel, the option expires worthless (the option only protects the upside on the hedge, not the downside — the refinery still operates at the lower margin for unhedged production).
Related terms
Call Option Chooser Option Correlation Crack Spread Crush Spread Delta Equity Equity Swap Exchange Global Macro Implied Volatility Interest Rate