This question is from an exercise sheet for financial mathematics.
Calculate the $3$-month future on Oil given the following information:
- Spot Oil is trading at $90$ USD per barrel.
- USD interest rates are at $2$%.
- Storage charges for Oil are $1$ USD per barrel per month.
- Insurance against Oil disasters costs $0.20$c per barrel.
- A spike in demand is likely to push Oil prices up by $5$ USD per barrel.
Last point seems to be a trick but I am not sure if I can include it somehow using a random variable that is 1 or 0 depending on whether there is a spike or not.
The formula I have for a forward is
$Fwd = S + (\text{gains from holding currency}) - (\text{losses from not holding asset})$
$S$ is the value of the underlying asset. I think I have to do something with this to adapt is to the question but I am not quite sure what.
An arbitrage-free pricing model tells us that the economic value of buying one barrel of oil now and selling one barrel's worth of 3-month futures must be the same as placing the price of the barrel of oil on deposit for 3 months.
If we buy one barrel at spot this costs $90$ USD. Over 3 months we have to pay $3$ USD storage costs and $0.20$ USD insurance. If the 3-moth futures price is $F$ USD per barrel then the value of the barrel in 3 months time is $F - 3.2$ USD.
If we place $90$ USD on deposit for 3 months at $2$% interest per annum, in 3 months time this is worth $90 + \frac{1.8}{4} = 90.45$ USD. So we have
$F - 3.2 = 90.45$
The "likely" rise in oil prices is irrelevant in arbitrage-free pricing.