I am trying to compare bull call spread and bull put spread for equity index option. For the options where the put call parity holds, I am getting a different payoff for bull call spread and bull put spread, where bull call spread is giving higher payoff? What can be the reason for this and if the put-call parity holds, shouldn't the payoff of bull call spread and bull put spread match?
2
-
$\begingroup$ Could you show us your calculation? $\endgroup$– vonjdJul 2, 2021 at 11:08
-
$\begingroup$ They don't have to be equal. $\endgroup$– amdoptJul 2, 2021 at 19:18
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
How do you define higher payoff? Could you show what you compute? Do you look at what the options cost at the moment?
If you want the same payoff (graphically and expiry), you can do the two things:
- buy call (say ATM) and sell call (OTM)
- buy put (ATM) & sell Put (ITM with same strike as OTM call)
Now, it is intuitive that (although same strike and tenor, hence same IVOL), that OTM is cheaper than ITM. Put call parity also does not state that calls and pulls cost the same, just that there is a relation. With a bull call spread, you have costs upfront, a bull put spread is actually an inflow of money up front as the ITM put that you sell is more expensive as the ATM you buy.
Profit is in both cases maximum when the underlying closes above the short strike on expiration. Breakeven however differs in calculation:
- bull call spread: Break even point = Lower strike price + Net premium paid
- bull put spread: Break even point = upper strike price - net premium received
In other words, if below lower strike, and calls, you simply have the costs that are lost. With puts, you have your inflow from selling ITM put minus the loss in the the put you sold ($notional*(K_{High}-K_{Low})$). Therefore, below lowest strike, you should have upfront cost bull call spread = "income" bull put spread - loss of strategy.
Similar arguments hold for in between and above higher strike.
