What a Futures Option Prices When Exercise Creates a Futures Position

Summary

The document raises a question about the payoff represented by Black’s model for an option on a futures contract. It distinguishes the futures price agreed when the option is exercised from the later spot price at the futures contract’s own maturity. The concern is that exercising an in-the-money option creates a long futures position, whose eventual settlement depends on the underlying asset price at that later date, while that price does not appear explicitly in the option pricing formula.

The excerpt contains the question but no answer or supporting derivation. It therefore highlights the need to distinguish the option’s maturity payoff from the subsequent gains and losses on the futures position received through exercise. It does not resolve how the model’s valuation relates to that post-exercise position, nor specify the contract’s settlement conventions, so those points cannot be inferred from this document alone.

Key ideas

• The question distinguishes the futures option’s expiry from the underlying futures contract’s maturity.
• Exercising the option is described as creating a long futures position.
• The question asks why the later underlying price does not appear in the option pricing formula.
• The excerpt provides no answer or derivation to resolve the issue.

Tags

# Pricing of future options


# Pricing of future options












I have the following question on futures options:

There is a Black’s model, which is a variant of the Black-Scholes formula that is used to price stock options. The Black’s model prices future options.

https://en.m.wikipedia.org/wiki/Black_model

The approach in the pricing model uses Magrabe’s formula. Both the agreed strike futures price $K_1$ of the future contract and the market future price $K_2$ of the futures contract at the maturity date $T$ of the futures option are used. If $K_1 < K_2$, the futures option is exercised with immediate profit $K_2-K_1$.

> However, if the holder exercises the futures option at time $T$ of the futures option, he/she enters into a long position of the futures contract of the underlying asset, with maturity $T’ \geq T$. The problem is that the payoff at time $T’$ is $S_{T’}-K_2$, where $S_{T’}$ is the price of the underlying asset at time $T’$. The main problem is that $S_{T’}$ does not appear in the pricing formula. More precisely, the value of the futures option does not take the payoff at the maturity of the futures into account. Is that because the option is long gone at time $T’$ and this payoff is not “part” of the option?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.