Bull Spread with Put Options

The Bull Spread with Put Options involved buy in a low underlying strike price K1 put option and writing a higher  underlying strike price K2 put option.

The assumed current underlying asset price is lower than K1.

Bull Spread with Put Options

Bull Spread with Put Options with Lower Underlying Asset Price

 Bull Spread with Put Options

Bull Spread with Put Options K1 << K2

The purpose is to profit as long as stock price is above K1 after compensating for initial cash outlay represented by cost of long put option and income generated by writing put option.

Given that time to expiry is the same for both options, the higher strike price put option will be price higher than the lower strike price put option.

Let us assume P1 be buy-in price of put option with underlying strike price K1 and P2 be writing price of put options with underlying strike price K2.

Bull Spread with Put Options

Profit Table

Initial Cash Outlay = – P1 + P2 (P1 << P2)

Underlying Price Range Payoff from Long Put Option at K1 strike Payoff from short Put Option at K2 strike Total Payoffs
ST ≤ K1 K1 – ST -(K2 – ST) K1– K2 – P1 + P2
K1 < ST < k2 0 -(K2 – ST) ST – K2 – P1 + P2
ST ≥ K2 0 0 – P1 + P2

 

In the model of Bull Spread with Put Options, there will be a loss resulting from initial cash outlay if underlying asset prices comes in below K1 after expiry of options. There will be profit if price of underlying ends above K2. This profit comes entirely from cash inflow from writing put options after deducting cost of buying put options.

Three types of Bull Spreads with Put Options can be distinguished

  1. Both puts are initially out of the money
  2. One put is initially in the money; the other put is initially out of money
  3. Both puts are initially in the money

The highest risk and reward Bull Spread with Put Options comes from type 1. They cost very little to set up because they are out of the money but have small probability of giving high payoffs K2 – K1 + P1 – P2 (where P1 << P2 and P1 and P2 => 0)

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