YOUR KILLER EQUITIES INTERVIEW QUESTIONS: What is the price of a one year call option on a stock, with share price = $100, known interest rates of 5%, volatility of zero and no dividends?

22 July 2011

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YOUR KILLER EQUITIES INTERVIEW QUESTIONS: What is the price of a one year call option on a stock, with share price = $100, known interest rates of 5%, volatility of zero and no dividends?

Here's the latest question sent in by site visitors who have attended equities interviews at investment banks. This question has allegedly been asked in equity derivatives trading interviews. The answer has been suggested by the person who submitted the question (and is not being advocated by us). If you disagree with the answer, or have any superior alternative responses, please express your opinion in the comments box below.

THE QUESTION: What is the price of a one year call option on a stock, with share price = $100, known interest rates of 5%, volatility of zero and no dividends? How would you hedge it?

THE SUGGESTED ANSWER:

Just because the option has no volatility, the price of the option is not zero.

A call option allows you to buy the stock at $100 in one year's time and if the forward price is effectively known with certainty, $105 (100 x [1 +r = 5%]), you can make $5 in one year. Therefore, the option's price is simply the discounted value of this, which is $4.76 ($5 / [1 + r= 5%]).

How would you hedge this? Well in options theory, your call option would have a delta of 1 (and your put option of the same strike, a delta of zero, since the stock will be higher than $100 in one year with absolute certainty), and therefore you should theoretically sell 100% of the stock to make your position delta neutral.

In reality, you would obviously never do this. Moreover why would anyone ever enter into such a trade - there is no value in it for the buyer or seller of the option. This is a question very much based in theory and is testing whether the candidate really understands what an option is and how it works.

AUTHORSarah Butcher

Global Editor

IB
IBD
25 July 2011
Isn't it:
If stock PX is higher in T+1 than 105,
You would:
1) Buy the call
2) Lend at the PV of $105 ($100)
3) Sell a Put
3) In T+1 exercise the call and use the $105 paid back to pocket St(T+1) - Strike
Points:
Your buying of the call is hedged by selling a put at T=0
Your exercise of the call is paid for by returned funds lent out
Arb profit made by St (T+1) being greater than FV of Call Option in T+1
Reply
gr
greekygeeky
25 July 2011
oh dear oh dear oh dear
this question ( or something similar ) has been doing the interview rounds for ever
"Nul Point " to our efinancial readers who have attempted an answer....c'mon fellas its not too hard surely
our desk grads would be beaten if they gave some of these answers
Reply
Bo
BoutiqueBanker
25 July 2011
Isn't it:
If stock PX is higher in T+1 than 105,
You would:
1) Sell the Call
2) Borrow at PV of 105
3) Use the borrowed funds to buy the spot at 100
4) Pocket the arb between points 2 and 3 now
5) T+1 pay back 105 borrowed with proceeds from spot long at T=0
Reply
Ho
HoneyDew
25 July 2011
Right, the answer is definitlly (105-Strike)/(1+5%).
Quickly, if it is higher you shall do:
at T=0 with strike=100:
-sell a call
-borrow SpotPrice to hedge the call
-invest the premium at the one year 5% interest rate
At maturity:
-provide the stock at 100
-get back your premium + interests
Total -100*(1+5%)+strike+Premium*(1+5%) >0
the equation above shall be equal to zero to avoid any arbitrage.
Reply
Fi
FinanceCowboy
25 July 2011
I think Sarah's right here but the question (esp. Strike) and answers are a bit muddly.
The stock in this case is de facto not a stock, but a riskless investment.
However, its not the forward price that's important (that one's anyway known today) but the future spot price of the stock, which will HAVE TO BE 105. Otherwise it would open arbitrage opportunities.This of course means that the value will be (105 - X)/ (1+r).
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