# CFAI Reading 40 Q 7 P324

I understand how to calculate the forward stuff and understand the payoff side fo the option. The question I have is how we factor the option premium. I realize at 1.30 for example, the value is 15,000,000/1.30 but if you do for example 15,000,000 - (15,000,000x .03) = 14550000/1.3 = 11192307 How do they arrive at the 11,338,000? It appears the option premium is 200k… where does that come from?

The option premium is 200,000 b/c they give it to quoted in dollars per pound, but the question states you are a Brittish exporter so you would actually buy the option in pounds per dollar. You just have to convert the option price to the same currency as your portfolio It’s not labeled very well, and I just gave this one to the old CFA tricksters.

I still don’t get the math. No premium = 15,000,000/1.30 = 11,538,461pounds //simple… Wrong Solution 1 With premium 15,000,000 initial Option Premium = .03pounds*1.5=.045\$ //aren’t your option premiums at spot at t=o? 15,000,000*.045 = \$675,000 15,000,000-675,000 = 14,325,000/1.3=11,019,231//This happens at t=1(forward) That is just one example, I could do it wrong about 4 other ways…I just don’t get where this 200 grand is coming from…would someone be kind enough to work through it?

Option Premium per pound = \$.03/1.5= pound .020 Total Premium = (\$1.5m/1.5) x pound .20 = pound 200,000.-

I had a hard time with this , still do until I go really slowly thru it : Premium cost is 0.03 \$/pound. Sum insured is \$15m , or 10m pounds. So cost in dollars is \$0.03*10m = \$300,000 . This cost of \$300,000 is paid at the inception of the option contract in british pounds ( being a British exporter , dealing with a UK bank , he pays costs in pounds and receives the payout in pounds) So upfront he pays \$300000/1.5 = 200,000 pounds. Now choose any of rates , say 1.3 . At 1.3 USD/pound , he gets pounds 11538 ( thousand) to convert \$15m , plus pays back his 200,000 pounds loan taken to buy the option leaving 11,338 pounds. The only strike that you have to take care with is the 155 , because there is no 1.55 rate listed. So the 1.6 rate for a 155 strike call is struck at 1.55 . For a cost of \$150000 or pounds 100 ( thousand) we are left with \$10m/1.55 = pounds 9677 and then take out 100 ( thousand) option cost to leave pounds 9577 ( thousands) I’ll never be able to do this problem correctly in the heat of the exam , no way

janakisri Wrote: ------------------------------------------------------- > I had a hard time with this , still do until I go > really slowly thru it : > > Premium cost is 0.03 \$/pound. > > Sum insured is \$15m , or 10m pounds. So cost in > dollars is \$0.03*10m = \$300,000 . > > This cost of \$300,000 is paid at the inception of > the option contract in british pounds ( being a > British exporter , dealing with a UK bank , he > pays costs in pounds and receives the payout in > pounds) > > So upfront he pays \$300000/1.5 = 200,000 pounds. > > Now choose any of rates , say 1.3 . At 1.3 > USD/pound , he gets pounds 11538 ( thousand) to > convert \$15m , plus pays back his 200,000 pounds > loan taken to buy the option leaving 11,338 > pounds. > > The only strike that you have to take care with is > the 155 , because there is no 1.55 rate listed. So > the 1.6 rate for a 155 strike call is struck at > 1.55 . For a cost of \$150000 or pounds 100 ( > thousand) we are left with \$10m/1.55 = pounds > 9677 and then take out 100 ( thousand) option cost > to leave pounds 9577 ( thousands) > > I’ll never be able to do this problem correctly in > the heat of the exam , no way Thanks tons :), you too AMA Ok Great, that makes sense. Looking at the blue section, page 307, are they just rounding in the chart? According to my math, the 110 ecx rate (using puts 100) would be Initial \$1,000,000 - premium (.03/E)=970,000 X 1E/1 = 970,000E 970,000E X 110\$/E = 1,067,000\$ //Chart says 1,070,000 At 1.05 Initial \$1,000,000 - premium (.03/E)=970,000 X 1E/1 = 970,000E 970,000E X 1.05\$/E = 1,018,500\$E //Again Chart says 1,020,000 Are they rounding or is it my math?

I think they are rounding !

It is not rounding , the cost of the premium is calculated in euros using a spot rate at the time the option is purchased , not the rate at the expiry . Look carefully at the first part of the problem , it shows the spot rate is euro 1 per dollar , so 30000 USD = 30000 Euro. So you are left with 1million euro - 30000 euro = 970000 euro

I think the key is, don’t subtract premium at the beginning, subtract it at the end, in the native currency, reconvert the whole notional at the end, then subtract out the premium See the difference Base Currency is dollar, holding Euro. Im going to insure my euro@ .03 per euro To begin with we are holding 1,000,000 Euro, Dollar value 1,000,000 Dollars Then, we insure it 1,000,000E *.03 Dollars = 30 grand Time passes 1,million euros is now worth say 1.05 Dollars per. So now we convert back 1,000,000 * 1.05 = 1,050,000 less premium 30,000 = 1,020,000 its at the end instead of eating the assets down at the beginning.

So, the interest cost of premium is not accounted for !

Both the blue section and the answer from CFAI to problem 7 , expressly say this: “Again, assume that we buy the calls by borrowing pounds at a zero interest rate” So interest cost of premium is not accounted

No option seller will agree to collect the premium cost at the expiry of the option! They always like the money upfront , and they like it in local currency equivalent i.e. British pounds in the UK

janakisri. You are right. I didn’t look into the details of the question. Thanks a lot !

I worked through this problem and the problem in the text on a spreadsheet and was able to work through the calculations. From what i see on the currency exchange option problems, if the strike rate is given in foreign / domestic, the payoff to the call domestic currency option is max ( 0, principal / strike - principal / current rate)