Question

You are considering purchasing a put option on a stock with a current price of $26. The exercise price is $28, and the price of the corresponding call option is $2.65. According to the put-call parity theorem, if the risk-free rate of interest is 6% and there are 90 days until expiration, the value of the put should be ____________.

Answer 1

-22.42

Step-by-step explanation:

Given,

Stock = $26, Call = $2.65, Exercise price = $28, Risk-free rate = 6%, Time = 0.24657 (90 / 365)

The put-call parity formula is
`$ C+Ke^(-rT) = P+S_0 $` where:

C = Call Price, K = Exercise Price, r = Risk-Free Rate, T = Time to Expiration,

P = Put Price, and
`$S_0$` = Stock Price

Subtracting
`$S_0$` from both sides, we get

`$ P=C+Ke^(-rT) -S_0 $`

`$P= 2.65 + 28 e^(-(6)(0.24657))-26 $`

`$P= 2.65 + 28 e^(-(1.47942))-26 $`

`$P= 2.65 + (28) (0.033157)-26 $`

= -22.42

Answer 2

Answer: $4.24

Step-by-step explanation:

According to the Put-Call Parity, the value would be expressed by;

Put Price = Call price - Stock price + Exercise price *e^-(risk free rate *T)

T is 90 days out of 365 so = 90/365

= 2.65 - 26 + 28 * 2.71 ^ (-0.06 * 90/365)

= $4.24