The current price of a stock is $33, and the annual risk-free rate is 6%. A call option with a strike price of $32 and with 1 year until expiration has a current value of $6.56. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option?
V ¨C P + X exp(-rRF t) = $6.56 - $33 + $32 e-0.06(1) = $6.56 - $33 + $30.136 = $3.696 ¡Ö $3.70.
To determine the value of a put option written on the stock with the same exercise price and expiration date as the call option, we can use the put-call parity formula. The put-call parity formula is given as:
Call Price - Put Price = (Stock Price - Strike Price) / (1 + Risk-free Rate) ^ Time to Expiration
Given:
Call Price = $6.56
Stock Price = $33
Strike Price = $32
Risk-free Rate = 6% or 0.06
Time to Expiration = 1 year
Let's substitute these values into the formula and solve for the Put Price:
$6.56 - Put Price = ($33 - $32) / (1 + 0.06) ^ 1
Simplifying the right side of the equation gives:
$6.56 - Put Price = $1 / 1.06
Now, let's calculate the right side:
$6.56 - Put Price = $0.9434
To find the value of the put option (Put Price), we can subtract $0.9434 from both sides of the equation:
Put Price = $6.56 - $0.9434
Put Price = $5.6166
Therefore, the value of the put option written on the stock with the same exercise price and expiration date as the call option is approximately $5.6166.
To determine the value of a put option, you can make use of the Put-Call Parity formula, which states that the price of a call option minus the price of a put option is equal to the difference between the current stock price and the strike price, discounted at the risk-free rate.
Put-Call Parity formula:
C - P = S - X / (1 + R)^T
Where:
C = Price of the call option
P = Price of the put option
S = Current stock price
X = Strike price
R = Risk-free rate
T = Time until expiration
In this case, you have the following information:
C = $6.56 (Price of the call option)
S = $33 (Current stock price)
X = $32 (Strike price)
R = 6% (Risk-free rate)
T = 1 year (Time until expiration)
We want to find the value of the put option (P). Rearranging the Put-Call Parity formula, we get:
P = C - S + X / (1 + R)^T
Substituting the given values into the formula:
P = $6.56 - $33 + $32 / (1 + 0.06)^1
P = $6.56 - $33 + $32 / 1.06
Calculating, we have:
P = $6.56 - $1.89 + $30.19
P ≈ $35.86
Therefore, the value of the put option written on the stock with the same exercise price and expiration date as the given call option is approximately $35.86.