Futures carry effect

Before expiry a futures price normally sits above the spot price. Carrying the goods costs money, and the futures buyer has not paid that cost yet.

Now put two options side by side. Both are on the same commodity. Both have the same strike. One is an option on futures. The other is an option on goods, which looks at the spot price.

A call gains when its reference price is high. The futures price is the higher of the two. So the call on futures has more intrinsic value.

A put is the mirror. A put gains when its reference price is low. Spot is the lower number. So the put on goods has more intrinsic value than the put on futures.

The workbook calls this difference the futures carry effect.

Nothing about the two options differs. Only the price each one looks at.

The workbook states it as two inequalities. In the normal situation F is greater than S before expiry of the futures contract. With X as the strike price:

So (F - X) is greater than (S - X) and (X - F) is less than (X - S). The entire effect follows from one fact: F exceeds S while carry remains to be paid.

Two boundaries stop this being a free lunch.

It dies at expiry. Convergence pulls F down to S on the delivery date. The workbook says that, all other things being the same, the call option price on futures and on goods on the expiry date will remain the same, technically.

Premium is not intrinsic value. Option premium equals intrinsic value plus time value, and the carry effect touches only the first part. The workbook gives separate reasons why an option on goods may in practice trade dearer overall in a relatively shallow market. Spot markets carry no daily price limit, so measured volatility is higher and protection demand pushes premiums up. And the writer of an option on goods faces full delivery of goods on a call, or full payment on a put, so sellers ask for compensation for that larger obligation. Where the option, futures and cash markets are all deep enough, the workbook says arbitrage forces keep the two premiums hypothetically the same.

The workbook attaches no figure to the carry effect itself — it is written purely as inequalities. The arithmetic below therefore borrows its moneyness example for the futures side and adds an illustrative spot price for the goods side.

Start from the workbook's own moneyness numbers. The current market price of the commodity futures is Rs 1,280 and a call struck at Rs 1,170 carries a premium of Rs 200, of which intrinsic value is 1,280 - 1,170 = Rs 110 and time value is the remaining Rs 90.

Now suppose the polled spot price the same day is Rs 1,250, so the carry built into the futures is Rs 30. (The spot figure is illustrative; the rest is the workbook's.)

The call on futures is Rs 30 richer in intrinsic value, and Rs 30 is precisely the carry.

Move the strike above both prices, to Rs 1,300, and look at the puts:

Now the put on goods is Rs 30 richer — the same Rs 30, working the other way.

Scale it. Guar seed trades in a lot of 1 MT, which is 10 quintals. At Rs 30 per quintal the carry effect is worth Rs 300 per lot on intrinsic value alone.

Finally, run the clock forward to expiry. Convergence brings F and S together at, say, Rs 1,265. Both calls struck at Rs 1,170 are now worth Rs 95 of intrinsic value, and both puts struck at Rs 1,300 are worth Rs 35. The Rs 30 gap has vanished, exactly as the workbook says it must.

Chapter 4 (Commodity Options), section 4.6 on Options on Goods, where the two inequalities and the phrase futures carry appear. It leans on the intrinsic value definitions from section 4.4.4, so the two sections are examined together.

Expect the direct pair: the intrinsic value of a call option on futures is ____ than that of a call option on goods — higher — and the reverse for puts. A harder version asks which option is costlier in a shallow market, where the answer is the option on goods, but for volatility and delivery-risk reasons rather than carry. A third version tests the expiry position: technically the same, because of convergence.

• Calls favour futures; puts favour goods. That one sentence is the whole page, and candidates reliably learn half of it.
• This is about intrinsic value, not premium. Premium also holds time value, and in a shallow market an option on goods can be dearer overall even though its call has less intrinsic value.
• It depends on F being above S. In backwardation the futures price is below spot and the ordering reverses. The workbook writes in normal situation for exactly this reason.
• At expiry the effect is zero. Convergence collapses F to S, so all else equal the two call prices are technically the same on the expiry date.
• It is not an arbitrage. Where the option, futures and cash markets are deep enough, arbitrage keeps options on goods and options on futures at hypothetically the same price.
• Futures carry is the ordinary cost of carry that also produces contango. It is not a separate charge levied on option holders.
• Do not confuse the two reasons an option on goods can be expensive. Carry makes its call intrinsic value smaller; spot volatility and the writer's delivery obligation make its premium bigger. They pull in opposite directions.