Question about valuing call option in derivatives

I got this question from Prepsmarter

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?

Thanks in advance for helping :slight_smile:

Look up Put-Call Parity.

Thanks I knew I was missing something!

You’re welcome, Shaz.

For what it’s worth, I wrote an article on put-call parity:

nb: as of 4/25/16 there’s a charge for reading the articles on my website.

Put Call Parity = Sip Pepsi Be Cool

S + P = B + C

S = Stock Price at time t = $ 110

P = Total Value (Intrinsic Value + Time Value) of the Put Option = $ 5

B = PV of the Bond with a Face Value equal to the strike price = $ 100/(1 + 6%)^0.5

C = Total Value (Intrinsic Value + Time Value) of the Call Option - This is what we are trying to find - Plug and Chug.

Strike Price of the put option = $ 100

Current Market price = $ 110

Put option is ‘out of money’.

Therefore, intrinsic value = 0

Value of the put option is made up of Time Value and Intrinsic value.

Intrinsic value = 0.

Hence, Time Value of the Put option = $ 5.

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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.

Would you guys please help me if i am wrong? In this question, i understand that

  • P0=$100
  • S0=110
  • Risk-free bond: $5

The value of the put is $100?

Seems high.

And the value of the bond ($5) seems low.

Methinks that you’re mixing up your variables.

Yes, i know, But that’s what i thought when i read the question. :frowning:

So . . . what are the correct values?



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Thanks so much. I appreciate your patience.