Constructing vertical debit spreads around implied volatility

What the two-leg pair specifies

A vertical option spread is one long option paired with one short option of the same type and the same expiration, differing only by strike. As an option spread, the two-leg construction replaces an open-ended single-contract stance so direction, bounded payoff, and net delta can be specified before entry.

A bull vertical buys the lower strike and sells the higher strike. A bear vertical buys the higher strike and sells the lower strike. In the 0.56/0.58 worked examples, both the bull-call pair and the bull-put pair have a net delta of +0.13. The matching bear constructions have a net delta of -0.13.

Debit and credit payoff bounds

A vertical debit spread is a same-type, same-expiry long and short option pair entered at a net premium paid. The debit is the position’s maximum loss, and the strike gap minus that debit is the maximum gain. In the 0.56/0.58 example, the bull call pays 0.0080 and can make at most 0.0120.

A credit vertical uses the same two-strike construction entered at a net premium received. Maximum gain equals the credit, and maximum loss equals the strike gap minus that credit. In the 0.56/0.58 example, the bull put receives 0.0114 and can lose at most 0.0086.

Strike spacing and the net-delta budget

Net delta is the sum of the long-leg and short-leg deltas. Its sign is the directional bias, and its size scales with strike distance and the number of spreads.

Strike spacing is the gap between the two strikes. With other construction choices held fixed, a wider strike gap raises the vertical’s net delta and therefore its sensitivity to the underlying. A wider gap also changes the maximum profit and loss bounds.

Total directional exposure equals net delta times the number of spreads. Thirty spreads at +0.13 produce +3.90 total delta. Two hundred produce +26.00.

Implied volatility and the at-the-money strike

Implied volatility is the volatility already priced into option premiums. It is used to revalue each candidate vertical under a higher or lower volatility assumption and to decide which strike should be the purchased or sold at-the-money leg.

Option premiums rise when implied volatility is expected to increase and fall when it is expected to decrease. A vertical should be ranked by expected value versus market price rather than by the lowest initial debit or largest credit.

If implied volatility is expected to rise, the construction that buys the at-the-money strike is favored. If implied volatility is expected to fall, the construction that sells the at-the-money strike is favored. The at-the-money option is more sensitive to volatility changes than in-the-money or out-of-the-money options.

With volatility assumed at 30 percent, a rise to 35 percent makes the 0.56/0.60 call vertical the preferred call construction in the comparison, with expected value 0.0147 versus a market price of 0.0139. A fall to 25 percent makes the 0.52/0.56 call vertical the preferred call construction, with expected value 0.0248 versus a market price of 0.0238.