Part (a)
Recall the Call Put Parity Equation:
C0 + PV (E) = P0 + S0.
Hence, 4 + 0.9800 x 100 = 3 + S0.
Hence, S0 = 4 + 98 - 3 = 99
Hence, the price of the security = S0 = 99
Part (b)
Payoff from covered call = Payoff from owning the stock + Payoff from writing the call = (S - S0) + C - max (S - E, 0)
= (S - 99) + 4 - max (S - 100, 0)
Hence, payoff table will look like as shown below:
Stock Price, S ($) | Payoff ($) = (S - 99) + 4 - max (S - 100, 0) |
0 | -95 |
20 | -75 |
35 | -60 |
50 | -45 |
65 | -30 |
80 | -15 |
95 | 0 |
110 | 5 |
125 | 5 |
140 | 5 |
155 | 5 |
170 | 5 |
185 | 5 |
And the payoff diagram will be as shown below:
The payoff profile is very similar to short a put option.
This can be further explained by the Call put parity equation
Covered call = S - C - PV(E) = - P (Can be obtained by rearranging the call put parity equation: C + PV (E) = S + P
Thus a covered call is equivalent to short a put position.
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