Assume that the value of a put option with a strike price of $100 and six months remaining to maturity is $5. For a stock price of $110 and an interest rate of 6%, what value is closest to the corresponding call option with the same strike price and same expiration as the put option?
A- $17.87
B- $11.99
C- $12.74
What I did was compute the present value of the exercise price which came to 97.12 and then subtracted it from 110 to get C option as the answer
But the correct answer is
Call value = $110 + $5 – $100 / 1.060.5 = $17.87.
Can anyone please explain why $5 was added too?What does the value of the put option with the value of the call option?
If you don’t know put/call parity and don’t have to show your work, you can guess at the answer.
The put has intrinsic value of $0 but is worth $5. This means the remaining time value is currently priced at $5.
The call’s intrinsic value is $10 ($110-$100) and it has same time to expiration as put. So at the very least, it should be worth about $15, as such, this price is closest to the correct answer A.