# SS17 - question 7 -> price of call?

Reading 46, SS17, Question 17 from the CFAI text: How do you find the price of calls (for strike 1.55 and 1.60)? I keep getting different numbers than the answer. The follow is provided in the question: Portfolio value = \$15 million Spot now = \$1.5 / pound Option pricing: \$1.55 strike ---------> \$0.015 per call \$1.60 strike ---------> \$0.005 per call my calculations are as follows for the \$1.55 strike: (\$15,000,000 / 1.55 ) x 0.015 / \$1.5 = pounds 96,774

if spot goes to 1.3 usd per 1 gbp: a. 15 usd mio will become 15 / 1.3 = 11,538,461 gbp b. you receive usd, you want gbp = you want to hedge the price at which you will sell usd = put on usd = call on gbp c. initially you have 15 usd mio = 15 / 1.5 = 10 gbp mio. You buy one call for each gbp, paying 0.015 usd for each = 10 mio x 0.015 = 150,000 usd d. those 150,000 usd are equivalent to 150,000/1.5 = 100,000 gbp e. gbp goes down from 1.5 to 1.3, so the call on gbp is out of the money = 0 Your total position = a + e - d = 11,538,461 gbp - 100,000 gbp = 11,438,461 gbp I think the problem with this question is the way gbp is quoted: it would be easier if the exchange rate is quoted as how many gbp per each usd, instead of how they did it (how many usd per gbp). It is usually easier is the quote is in terms of how many of your local currency for each unit of the foreign currency you want to hedge Hope I didn´t sound confusing at the end…

hala_madrid Wrote: ------------------------------------------------------- > if spot goes to 1.3 usd per 1 gbp: > > a. 15 usd mio will become 15 / 1.3 = 11,538,461 > gbp > > b. you receive usd, you want gbp = you want to > hedge the price at which you will sell usd = put > on usd = call on gbp > > c. initially you have 15 usd mio = 15 / 1.5 = 10 > gbp mio. You buy one call for each gbp, paying > 0.015 usd for each = 10 mio x 0.015 = 150,000 usd This problem here is you decided to buy 10 milllion calls. But, when time is due, if your contract happens to be in the money (say the rate at time T is \$2/GBP), do you have 15.5 mil USD to exercise your call option? no, you don’t. you only have 15 million USD in your pocket. i.e. you are overhedging your position!

Not sure about what you say randOm… I think this is a separate thing: I mean, if you buy the options in a ratio of 1 to 1 with the underlying (like in the example), you buy the option to convert those usd to gbp at the rate you want (strike). So you will decide which strike you want. Of course you will always have 15 usd mio, so you can not “face” physical settlement… But the option seems to settle in cash. Another thing is that, regarless of the above, to hedge current spot buying itm options, I guess you will have to buy the options in a ratio of less than 1 to 1 Is this what you mean?

Rand0m you are all about overhedging, haha.

correct me if i am wrong, buying call option is like buying insurance. if someone has 15 mil on-the-line, would he buy an insurance against 15.5 mil to play safe? he may but that will introduce some extra cost. if one can use your “settle in cash” as argument, why dont they buy options good for 30 mil? he would gain more if options end up in the money. bottom line, it’s hedging not speculating, right?

yes, don´t misunderstand me, I agree 100% with you, but I think that, in this examples / questions (and perhaps the exam), they don´t try to hedge with options, but rather “get the strike you want” (regardless of it being more expensive as you said). Actually, I have not done many exercises yet, but in the ones I have seen, they never change the number of options you buy even when different strikes are available

so, the difference between your calculation and billwest is that he was running a tighter budget than yours, i.e. he was trying to squeeze 226 pounds out of his insurance budget, which made him a good cfo but failed on cfa test …

hala_madrid Wrote: ------------------------------------------------------- > but I think that, in this examples / > questions (and perhaps the exam), they don´t try > to hedge with options, but rather “get the strike > you want” First off, I believe you Are trying to hedge with options here instead of with futures/forwards. Secondly, the number of options depends on the options Delta. If delta was -0.5, you would have to buy 2x the # of options. For instance, for the \$15M portfolio, if the option contract was based on say \$20,000, that’s 1,500 options or (750 x 2) that would be purchased to hedge. Doest that make sense? p.s. I didnt read the whole thread so if I’m off on what is being discussed please ignore.

makes sense with dynamic hedging. Without dynamic hedging (as I guess applies to end investors in these problems) they just buy at the begining the number of options necessary to be hedged at maturity (when the related transaction with fx risk takes place) again, perhaps this is not the best or what a cfo who failed cfa would do… is just what (I guess) we will need for the exam ¿realistic or not? right now I don´t care. I more or less understand how CFA wants the question to be answered, and I also understand that, in the real world, perhaps that is not be best alternative… But this june we will be tested according to CFA, not the real world… regards