Question

Suppose you want to establish a bullish spread strategy. The are two call options. The first one has X1=$50 and C1=$5. The second one has X2=$40 and C2=$6.

When the underlying asset price is S(t)=$45, what is the profit from the strategy?

What is the maximum profit of the strategy?

What is the minimum payoff of the strategy?

Answer 1

A bull call spread is constructed by

• Buying a call option with a lower strike price (X2), and
• selling another call option with a higher strike price (X1)

Profit / (Loss) from the strategy = Payoff from long position + payoff from short position = max (S - X2, 0) - C2 + C1 - max (S - X1, 0)

When the underlying asset price is S(t)=$45, what is the profit from the strategy?

Profit = max (S - X2, 0) - C2 + C1 - max (S - X1, 0) = max (45 - 40, 0) - 6 + 5 - max (45 - 50, 0) = 5 - 6 + 5 - 0 = $ 4

What is the maximum profit of the strategy?

Maximum profit occurs when S(t) ≥ X1 = 50

In that case the short position is not exercised.

Hence, maximum profit = max (S - X2, 0) - C2 + C1 - max (S - X1, 0) = max (50 - 40, 0) - 6 + 5 - max (50 - 50, 0) = 10 - 6 + 5 - 0 = $ 9

What is the minimum payoff of the strategy?

Minimum profit occurs when S(t) ≤ X2 = 40. At this none of the two options are exercized.

Hence, minimum profit = max (S - X2, 0) - C2 + C1 - max (S - X1, 0) = max (40 - 40, 0) - 6 + 5 - max (40 - 50, 0) = 0 - 6 + 5 - 0 = - $ 1