Question

Suppose that the temperature for each day in December was 65 degree high and 25 degree low. What is the payoff from a call option on the cumulative HDD during December with a strike 420 and a payment rate of $5,000 per HDD?

Answer 1

1) The option mentioned here is the Call option. It represents the option to buy at a strike of 420 HDD.

Price per HDD is given at $5000.

The higher temperature =65°f and lower=25°f.

Average temperature per day= (higher+lower)/2

= (65+25)/2=45°f.

The december month comprises of 31 days.

The formula for deriving cumulative HDD is,

(No.of days)*(65°f- Average temperature per day)

=31*(65-45)=31*20=620 HDD

Thus, the cumulative HDD for december month is 620 HDD.

In the above formula, 65° is standard for any problem.

Payoff:

The call option holder has an option with strike of 420 HDD.....So, if he exercises the call option, he can get full month supply by just paying for 420 HDD instead of paying for 620 HDD if he goes out. Hence, he exercises the option.

Payoff= (price per HDD)*(620-420)= 5000*200= $1,000,000.

So the answer is, C....$1,000,000.

2) As per the given information in the question, he is holding long at 400 at JFK and short at 480 at LGA.

Given that the high temperature at LGA is 1° higher than in JFK and low temperatures are same.

Hence if we take average temperature per day, which is (high+low)/2, for LGA the high +low is 1° more than JFK ...Hence the average temperature at LGA is 0.5° higher than in JFk per day.

For June month total days are 30. Hence cumulative CDD difference between JFK and LGA is (0.5*30)=15 CDD.

As per question, he will buy(long) at 400 cdd and sell (short) at 480....So, here the difference is (480-400)=80 CDD ....But the difference between JFK and LGA is 15CDD

...So we have to reduce it ....It becomes (80-15)=65 CDD net difference ...What ever be the actual CDD's.....Since he is in swap position, the difference of 65cdd holds good in any situation in future......The payoff is 65 CDD * price per CDD= 65*5000= $325,000.

So, his final p&l position is $325,000....So the answer is B .$325,000.

Hope it helps

Thank u.