A covered call is a long stock and short call. The pattern of payoffs is given below:

In this problem, you are asked to simulate the payoffs of a covered call over 52 weeks, with weekly updating of the positions. Start by deriving the formula for the covered call: Add together the Black-Scholes price and the stock price:

Thus we see that a covered call is a long position in the stock and a long position in the bond. Now implement the following spreadsheet to test the effectiveness of a simulated covered call strategy.

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A В E G 1 COVERED CALL PROFIT PATTERN 2 Future stock price, ST 3 Call exercise price, X 4 Call price 50 45 6 5 6 Payoffs at T Long stock, +ST 7 50 <-- =B2 Short call payoff, -Max[ST-X,0] -5 <- =-MAX(B2-B3,0) 45 <-- =B7+B8 8 9 Total payoff 10 11 12 Data table of payoffs 13 Future stock price, ST 14 45 50 15 16 17 5 45 - 10 10 40 - 15 15 35 18 19 20 20 20 25 25 30 30 30 25 21 35 35 20 - 22 40 40 23 45 45 15 - 24 50 45 10 25 55 45 5 26 60 45 27 65 45 10 20 30 40 50 60 70 80 28 70 45 29 75 45 Stock price, ST 30