Question

A put option with a strike \(K_{1}=35\), costs \(P_{1}=\$ 4\) and a put with a strike of \(K_{2}=40\) costs \(P_{2}=\$ 8\). How can you construct a bull spread using these puts? What are the payoffs and profits from the strategy, for different values of the stock price at maturity?

Answer 1

To construct a bull spread using the put options with strikes of 35 and 40, you would need to buy the put option with a strike of 35 and sell the put option with a strike of 40. This would result in a net cost of \$4 for the put option with a strike of 35, minus the premium received for the put option with a strike of 40, which is \$8. Therefore, the net cost of the bull spread would be \$4 - \$8 = \$-4.

The payoffs and profits from the bull spread strategy will depend on the underlying asset's price at maturity. If the underlying asset's price is below the strike price of 35, the put option with a strike of 35 will be in the money, and will have a payoff equal to the strike price minus the underlying asset's price. The put option with a strike of 40 will be out of the money, and will have a payoff of 0. Therefore, the net payoff from the bull spread will be the strike price of 35 minus the underlying asset's price.

For example, if the underlying asset's price is 30 at maturity, the put option with a strike of 35 will have a payoff of 35 - 30 = 5, and the put option with a strike of 40 will have a payoff of 0. Therefore, the net payoff from the bull spread will be 5 - 0 = 5. The profit from the bull spread will be the net payoff minus the net cost of the spread, which is 5 - (-4) = $9.

If the underlying asset's price is between the strike prices of 35 and 40 at maturity, both put options will be out of the money, and will have a payoff of 0. Therefore, the net payoff from the bull spread will be 0 - 0 = 0. The profit from the bull spread will be the net payoff minus the net cost of the spread, which is 0 - (-4) = $4.

If the underlying asset's price is above the strike price of 40 at maturity, both put options will be out of the money, and will have a payoff of 0. Therefore, the net payoff from the bull spread will be 0 - 0