Dynamically Hedging a Futures Spread Option

Summary

The document explains why an option on a spread of two futures cannot generally be replicated statically using options on the individual futures. It uses a gasoline crack spread option as an example of this contract type. The proposed approach is to price the spread option as a function of both futures prices, using a two-dimensional partial differential equation or Monte Carlo simulation.

After calculating the option value, the method derives a hedge for each underlying futures contract from the option’s sensitivity to that contract’s price. The trader adjusts those futures positions over time to replicate the option payoff dynamically. This requires a pricing model and repeated rebalancing; the document does not specify model inputs, rebalancing frequency, transaction costs, or how closely the hedge performs in practice.

Key ideas

• A spread option depends on the prices of both underlying futures contracts.
• The document says it cannot generally be replicated with a static portfolio of options on the individual futures.
• A two-dimensional pricing model or Monte Carlo simulation can estimate the option value.
• Dynamic replication uses a separate delta hedge in each futures contract and requires rebalancing.

Tags

# How to synthesize a futures spread option?


# How to synthesize a futures spread option?












Is it possible to synthesize a futures spread option using only the options on the spread's underlyings? If so, how? If not, is there another way?

As an example, please show me how to synthesize NYMEX's RBOB Gasoline Crack Spread Options.

## Answer by Chris Taylor (score 2)

https://quant.stackexchange.com/a/9444

This spread can't be statically synthesized. However you can synthesize it dynamically by trading in the underlying contracts. You would first value the option using standard theory (this involves solving a two-dimensional PDE, or using Monte Carlo) to get a price $V(F_1,F_2)$ in terms of the prices of the underlying futures contracts. Then the holdings in each of the underlyings are given by the deltas

$$\Delta_1 = \frac{\partial V}{\partial F_1}$$

$$\Delta_2 = \frac{\partial V}{\partial F_2}$$

By re-adjusting your holdings at some specified frequency, you can replicate the payoff of the option.

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.