6.4 Option Quotations, Delta, and Return on Equity

6.4 Option Quotations, Delta, and Return on Equity

An option quote is normally stated in the price units of the underlying futures contract, but the customer's cash premium equals the quote times the contract multiplier or unit size. Series 3 calculations become much easier when every problem is separated into per-unit value and total contract value.

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Reading an Option Quote

A futures-option chain identifies the underlying futures month, option expiration, strike, call or put, premium, and often volume and open interest. The option does not represent a fractional claim on the cash commodity; one option normally covers one underlying futures contract.

For a 5,000-bushel corn option quoted at $0.18 per bushel:

$\text{Total Premium} = \$0.18 \times 5{,}000 = \$900$

The buyer pays $900 plus transaction costs. The writer receives $900 before transaction costs but must meet margin requirements because assignment can create an adverse futures position. The quoted premium should not be confused with the futures performance bond. Premium is the option's price; futures margin is collateral.

A quotation can be expressed in cents, index points, or another convention. If an option premium is 12 index points and the multiplier is $50, the contract premium is $600. Use the multiplier provided by the question rather than importing a size from another contract.

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Intrinsic and Time Value Review

At a given moment:

$\text{Option Premium} = \text{Intrinsic Value} + \text{Time Value}$

For calls, intrinsic value is the greater of zero or futures price minus strike. For puts, it is the greater of zero or strike minus futures price. Any remaining premium is time value.

Example: Futures are $6.40. A $6.10 call trades at $0.42. The call has $0.30 intrinsic value and $0.12 time value. A $6.70 put trading at $0.38 has $0.30 intrinsic value and $0.08 time value. Out-of-the-money options have zero intrinsic value but can have time value before expiration. At expiration, time value is zero.

Time value is influenced by time remaining, expected volatility, the option's relationship to the strike, and market conditions. More volatility generally increases both call and put premiums because the range of possible favorable outcomes expands, all else equal. Time decay is not linear and generally accelerates near expiration, but an increase in volatility can temporarily offset decay.

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Delta

Delta estimates how much an option premium changes for a small change in the underlying futures price:

$\Delta \text{Premium} \approx \text{Delta} \times \Delta \text{Futures Price}$

• Call delta ranges from about 0 to +1. An at-the-money call often has a delta near +0.50, but the actual market value varies.
• Put delta ranges from about -1 to 0. An at-the-money put often has a delta near -0.50.
• Deep in-the-money options have larger absolute deltas; far out-of-the-money options have smaller absolute deltas.

If a corn call has delta +0.40 and corn futures rise $0.10 per bushel, the option premium is estimated to rise about $0.04 per bushel. For 5,000 bushels, that is an estimated $200 contract gain:

$0.40 \times \$0.10 \times 5{,}000 = \$200$

If a put has delta -0.35 and futures rise $0.10, its premium is estimated to fall $0.035 per unit. The minus sign indicates direction.

Delta is a local estimate, not a guarantee. As futures move, delta itself changes. Time and volatility also affect the premium. A large price move should not be calculated by applying the original delta as though it never changed.

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Delta-Equivalent Exposure and Hedging

One option with delta +0.60 has approximately the price exposure of +0.60 futures contract for a small move. Ten such calls have about +6 futures equivalents. A trader seeking a short-term delta hedge could sell roughly six futures. The position is only temporarily delta-neutral because the calls' deltas change.

For a commercial hedge, delta can estimate how many options are needed. If 20 futures contracts would fully hedge a cash exposure and the selected puts have an absolute delta of 0.50, approximately 40 puts provide 20 initial futures equivalents:

$20 / 0.50 = 40$

That approach costs more premium than buying 20 options, and the effective hedge ratio evolves. Exam questions will normally supply the delta and ask for the initial approximation.

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Return on Equity and Writer Risk

A long option's maximum loss is premium plus transaction costs. If a trader buys an option for $1,000 and later sells it for $1,600, the pre-commission profit is $600 and return on premium is 60%:

$\text{ROE} = \$600 / \$1{,}000 = 60\%$

If it expires worthless, the pre-commission return is -100%.

A writer's analysis is different. The premium received is the maximum gain for an uncovered short option, but it is not the capital at risk and not necessarily the margin deposit. A short call can face theoretically unlimited loss as futures rise. A short put can face a large loss as futures fall; traditional exam questions often assume a zero floor, while a stated negative-price scenario can extend the loss. Never describe premium received as the writer’s maximum loss.