Question

3) Delta utilizes 1,500,000 gallons ofjet fuel every month and wants to hedge its position buy entering into a swap contract to buy its jet fuel monthly starting in one month for the next 6 months. The risk-free rate for all horizons up to 6 months is 1.25% and the forward price of jet fuel per gallon is listed below. What would be the swap price of the 1,500,000 gallons of jet fuel each month for the next 6 months? Month Forward Price 1 $ 1.7900 2 $ 1.7950 3 $ 1.7975 4 $ 1.8010 5 $ 1.8075 6 $ 1.8135

Answer 1

Let S be the swap price. At the time of entering into the contract the PV of all the fixed payments will be same as that of forward payments. If F_i be the forward price in the month i then

$\sum_{i=1}^{n}\frac{S}{(1+r)^i} = \sum_{i=1}^{n}\frac{F_{i}}{(1+r)^i}$

$S\sum_{i=1}^{n}\frac{1}{(1+r)^i} = \sum_{i=1}^{n}\frac{F_{i}}{(1+r)^i}$

$\therefore S= \frac{\sum_{i=1}^{n}\frac{F_{i}}{(1+r)^i}}{\sum_{i=1}^{n}\frac{1}{(1+r)^i} }$

where r = discount rate per month = 1.25% / 12 = 0.10%

i	1 / (1+r)^i	Fi	Fi / (1 + r)^i
1	0.9796	1.7900	1.7535
2	0.9596	1.7950	1.7225
3	0.9400	1.7975	1.6897
4	0.9208	1.8010	1.6584
5	0.9020	1.8075	1.6304
6	0.8836	1.8135	1.6025
Total	5.5857		10.0570

Hence, S = 10.0570 / 5.5857 = $ 1.8004