Question

1. Suppose the current price (as of August 31) of WTI crude oil is $44.53 per barrel, and assume oil can be stored costlessly.  

1. What is the forward price of WTI for delivery in 2 months (T=October 31) if the 2-month interest rate is 1.6%?
2. If the forward price of WTI for delivery in 2 months (10/31) were $44.41, is there an arbitrage opportunity?  If so, how would you exploit it and what would your profit be?
3. Go forward 1 month in time (t=9/30), and assume the one month interest rate is 1.6% at that time.  The one-month forward price (T=10/31) of WTI is $46.00.  If you had taken a long position in the original 2-month forward on WTI with F=$44.41 on August 31, how much would that long position be worth one month later (9/30)?
4. If on September 30, the 1-month forward price (T=10/31) of WTI is $46/brl, what is the value on September 30 of a short contract in WTI with T=10/31 and F=$46/brl?

Answer 1

Given,

On August 31st, current price of WTI crude oil is $44.53 per barrel and there is no storage costs of oil.

(a) Forward price of WTI for delivery in 2 months:

Given interest @1.6% for 2 months

Forward Price = Spot price + Interest

= 44.53 + 44.53×1.6%

= 45.24

(b) If forward Price for 2 months is $44.41, then how will you exploit it:

if spot price is $44.53, I will enter into forward cover for 2 month @ $44.41,being afraid of price of oil going up and if after 2 months if the spot price remains to be same, then I will gain from the forward cover and so

Gain from forward cover = $44.53 - $44.41

=$0.12

(c) If on August 31st, I have taken long position on 2 months forward cover @$44.41 and then 1 month later if forward rate for 1 month is equal to $46 and interest for 1 month is @1.6% then after another month the forward price will be

Forward Price = $46 + $46×1.6%

=$46.74

Where as I have taken long position @ $ 44.41

Hence long position worth 1 month later will be a gain of $2.33[$46.74 - $44.41]

(d) If on September 30th, 1 month forward Price is $46 then, on September 30th, value of short contract in WTI shall be as follows

Price on August 31st is $44.53, on September 30th, WTI being afraid of decrease in oil prices, WTI enter into a short contract @ $46 there by gain a profit of $1.47[$46 - $44.53]

Therefore value as on September 30th by entering into short contract will be $47.47[$46 + $1.47].