# Vertical Spreads : Long/Bull Call vs. and Short/Bull Put?

I modified Kevin Ott's Call Debit Spread and Put Credit Spread payoff graphs that appear similar.

1. Doubtless I can see that the former debits you, and the latter credits you. But how else do these two spreads differ?

2. When ought you use the former, but not the latter?

3. When ought you use the latter, but not the former? Here's a simple retail answer that doesn't involve an option pricing model or a bunch or theory.

• If it's a credit spread, the maximum gain is the credit received and the maximum loss is the difference in strikes less the credit received.

• If it's a debit spread, the maximum gain is the difference in strikes less the debit cost and the maximum risk is the debit.

If the spreads are priced fairly, in terms of P&L, it won't make a difference which spread you do. However, positions are not always priced equally because all legs do not move in tandem and the B/A spread can be wider on one or more legs, slightly affecting P&L. In such cases, choose the spread that has the higher potential profit.

AFAIC, the primary consideration would be that if the spreads are fairly priced and you're bullish, sell the put vertical because if the spread succeeds, both legs will expire worthless and you'll incur no closing costs. For the call spread, one or both legs will be ITM and to close, you'll have B/A slippage and additional commissions if you're still paying them.

It's no big deal to compare the P&L of two verticals since it involves the difference in strikes and either the debit or the credit. For more complex positions, put them in opposition in some simple modeling software and look at the graphic output. Using these two spreads as an example, chart the long call vertical against the long put vertical. If they are fairly priced, the graph will a horizontal line reflecting the cost of money. If they are not, the graph will slope slightly upward to one side.

I just had a play-around with some numbers. Suppose the underlying price today is at point (A), which happens to be 100. Suppose point (B) is 108. We're talking 1-year expiry, with rates zero and implied volatility = 25% for all strikes.

For the call-spread: Suppose you bought ATM call at strike $$K1=100$$ and sold OTM call at strike $$K2=108$$. Your net cashflow is negative, because the ATM call is more expensive than the OTM call (=> so this is a "credit call spread", not a "debit call spread".)

Suppose that the price of the ATM call is 8.4 units, and the price of the OTM call is 5.3 units. Your net cash outflow is -3.1 units. Your pay-off diagram at maturity will be: (i) -3.1 units between underlying price being zero and underlying price being $$K1=100$$, then linearly to zero until underlying price being $$103.1$$, then linearly positive until underlying price $$108$$, at which the pay-off becomes constant positive +4.9 until underlying price infinity: For the put spread: Suppose you bought ATM put at strike $$K1=100$$ and sold ITM put at strike $$K2=108$$. Your net cashflow is positive, because the ITM put is more expensive that the ATM put (=> so this is a "debit put spread", not a "credit put spread".)

Suppose that the price of the ATM put is 8.4 units, and the price of the ITM put is 13.1 units. Your net cash outflow is +4.7 units. Your pay-off diagram at maturity will be: (i) +4.7 units between underlying price being infinity and underlying price being $$108$$, then linearly to zero until underlying price $$103.3$$, then linearly negative until underlying price $$100$$, at which the pay-off becomes constant negative -3.3 until underlying price zero: Whilst both spreads look very similar, effectively, the credit call spread has a lower downside and a higher upside: that's why it should be "more expensive" than the debit put spread: but the numbers look way out of proportion. I actually used Black-Scholes pricer, rather than guessing the option prices: but obviously in real life, the Imp Vols would most definitely be different on the different strikes, and would cause the structure to be more proportionally priced.

When I have more time, I'll try to edit the answer to include a structure with a symmetrical pay-off at maturity.

I know this hasn't addressed the points you specifically asked for, but at least it's a start.