Question

EXplain 21, and 22.*(DOUBLE-WEİGHD Suppose a call option on a given stock has premium $4 per share, and the put option at the same exercise price (E-$100) has premium $3 per share. The price of a Treasury security having the same maturity as the option is.9800 (dollars per face). a. What would you expect the price of the underlying security to be? b. Illustrate with a graph the profit or payoff profile that would result from a "covered call" (write call on the security you own) on this stock. Explain. An investor buys a security and writes t Furmn 23.

Answer 1

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:

Payoff (S- 99) +4- max (S - 100, 0) 20 20 40 60 80100 120 140 160 180 200 HL 20 4 -60 -80 Stock Price ($)

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.