6.5 Vertical, Calendar, and Arbitrage Option Spreads

6.5 Vertical, Calendar, and Arbitrage Option Spreads

An option spread combines a purchased option and a written option on the same underlying futures contract. The legs alter cost, maximum gain, maximum loss, and sensitivity to price and time. For vertical spreads, the expirations are the same and the strikes differ. Always calculate the net premium first and the strike width second.

---

Bull Call Spread: Debit and Widening

A bull call spread buys a lower-strike call and sells a higher-strike call. The lower-strike call costs more, so the position is normally a debit. The trader expects call values to widen in favor of the lower-strike call as futures rise.

Example: Buy a 70 call for 6 and sell an 80 call for 2.

• Net debit and maximum loss: 6 - 2 = 4.
• Strike width: 80 - 70 = 10.
• Maximum profit: 10 - 4 = 6.
• Lower breakeven: 70 + 4 = 74.

At or below 70, both calls expire worthless and the 4 debit is lost. At 76, the long call is worth 6 and the short call is worthless, producing 2 net profit after the debit. At or above 80, the long and short intrinsic values differ by 10, so profit is capped at 6.

---

Bear Call Spread: Credit and Narrowing

A bear call spread sells the lower-strike call and buys the higher-strike call. It normally receives a credit and benefits when both calls expire worthless or the value relationship narrows.

Example: Sell a 70 call for 6 and buy an 80 call for 2.

• Net credit and maximum gain: 4.
• Maximum loss: width 10 - credit 4 = 6.
• Breakeven: short call strike 70 + credit 4 = 74.

The purchased 80 call caps the otherwise unlimited risk of the short 70 call. Above 80, the 10-point strike difference is the gross loss, reduced by the 4 credit. A credit is cash received at entry, not proof that the position is conservative; loss can exceed the credit.

---

Bear Put Spread: Debit and Widening

A bear put spread buys the higher-strike put and sells the lower-strike put. The higher-strike put is more valuable, so the position normally pays a debit. It benefits when futures fall and the put-value difference widens.

Example: Buy an 80 put for 7 and sell a 70 put for 3.

• Net debit and maximum loss: 4.
• Maximum profit: width 10 - debit 4 = 6.
• Breakeven: long put strike 80 - debit 4 = 76.

At or above 80, both puts expire worthless and the debit is lost. At or below 70, their intrinsic values differ by 10 and profit is capped at 6.

---

Bull Put Spread: Credit and Narrowing

A bull put spread sells the higher-strike put and buys the lower-strike put. It normally receives a credit and benefits if futures remain at or above the higher strike.

Using the same premiums in reverse—sell the 80 put for 7 and buy the 70 put for 3—creates a 4 credit. Maximum gain is 4. Maximum loss is 10 - 4 = 6. Breakeven is 80 - 4 = 76. The long lower-strike put limits the short put's downside.

These four verticals form a compact exam table:

For every vertical, maximum profit plus maximum loss equals the strike width when both are measured per unit before commissions. Multiply the per-unit result by contract size for dollars.

---

Calendar Spreads

A calendar or time spread uses the same option type and usually the same strike but different expirations. A common long calendar buys the longer-dated option and sells the nearer-dated option. The trader expects the near option to lose time value faster, but the result also depends on futures price, implied volatility, and the relationship between the two expirations.

Unlike a simple vertical, a calendar spread may not have one fixed maximum profit that can be calculated solely from strike width. The legs can reference different underlying futures months, and the near option can be exercised or assigned before the long option expires. Traders must manage the resulting futures position and the remaining option.

---

Arbitrage and Synthetic Relationships

At the same strike and expiration, a long call plus a short put has the payoff of a long futures position at expiration. A long put plus a short call has the payoff of a short futures position. If executable option prices depart materially from the corresponding futures relationship, an arbitrageur may buy the cheaper package and sell the richer package.

A paper discrepancy is not automatically a riskless profit. The calculation must include bid-ask spreads, commissions, exercise and assignment, margin financing, timing, and the ability to execute every leg. Series 3 questions usually simplify these costs; in practice they determine whether the apparent arbitrage exists.

Calculation Checklist

1. Put every premium and strike in the same per-unit terms.
2. Label each premium paid or received.
3. Compute debit or credit.
4. Compute strike width.
5. Apply the correct maximum-profit, maximum-loss, and breakeven formula.
6. Multiply by contract size and subtract stated commissions.