Question

You would like to be holding a protective put position on the stock of XYZ Co. to lock in a guaranteed minimum value of $105 at year-end. XYZ currently sells for $105. Over the next year the stock price will increase by 8% or decrease by 8%. The T-bill rate is 5%. Unfortunately, no put options are traded on XYZ Co. a. Suppose the desired put option were traded. How much would it cost to purchase? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

$1.5

Step-by-step explanation:

If the stock price increases by 8% then the stock value would be $113 given by

($105*(1+0.08) = $113.4

with "0" Value of put payoff.

if, however, the stock price declines by 8% then the stock value would be $97 given by

$105 × (1 - 0.08) = $96.6

resulting to a put payoff of $8 that is ($105 - $97).

Thus, here in this case to guarantee a value of $105, two puts would have to be purchased.

Hence the present value of stock at $105 would be

PVpo = P/1.05 (at T-bill rate of 5% (1 + 0.05)

PVpo = 113/1.05

PVpo = 108

The general formula to evaluate the cost of purchase, if the option were traded is,

S+2P = 10

8

where S = stock price, $105

105+2P = 10

8

2P = 3

P = $1.50