Calculate 3 month future of Oil
$begingroup$
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.
finance economics actuarial-science
asked Jan 21 at 9:55
ʎpoqouʎpoqou
3471211
$endgroup$
add a comment |
$begingroup$
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.
finance economics actuarial-science
asked Jan 21 at 9:55
ʎpoqouʎpoqou
3471211
$endgroup$
add a comment |
$begingroup$
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.
finance economics actuarial-science
asked Jan 21 at 9:55
ʎpoqouʎpoqou
3471211
$endgroup$
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.
finance economics actuarial-science
finance economics actuarial-science
asked Jan 21 at 9:55
ʎpoqouʎpoqou
3471211
asked Jan 21 at 9:55
ʎpoqouʎpoqou
3471211
asked Jan 21 at 9:55
ʎpoqouʎpoqou
3471211
asked Jan 21 at 9:55
ʎpoqouʎpoqou
3471211
asked Jan 21 at 9:55
ʎpoqouʎpoqou
3471211
3471211
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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.
answered Jan 21 at 11:11
gandalf61gandalf61
8,801725
$endgroup$
$begingroup$
$90+frac{1.8}{4}$ does not $= 94.5$USD
$endgroup$
– ʎpoqou
Jan 21 at 12:10
1
$begingroup$
@ʎpoqou Good spot ! I have corrected to $90.45$.
$endgroup$
– gandalf61
Jan 21 at 12:13
add a comment |
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1 Answer
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1 Answer
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$begingroup$
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.
answered Jan 21 at 11:11
gandalf61gandalf61
8,801725
$endgroup$
$begingroup$
$90+frac{1.8}{4}$ does not $= 94.5$USD
$endgroup$
– ʎpoqou
Jan 21 at 12:10
1
$begingroup$
@ʎpoqou Good spot ! I have corrected to $90.45$.
$endgroup$
– gandalf61
Jan 21 at 12:13
add a comment |
$begingroup$
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.
answered Jan 21 at 11:11
gandalf61gandalf61
8,801725
$endgroup$
$begingroup$
$90+frac{1.8}{4}$ does not $= 94.5$USD
$endgroup$
– ʎpoqou
Jan 21 at 12:10
1
$begingroup$
@ʎpoqou Good spot ! I have corrected to $90.45$.
$endgroup$
– gandalf61
Jan 21 at 12:13
add a comment |
$begingroup$
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.
answered Jan 21 at 11:11
gandalf61gandalf61
8,801725
$endgroup$
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.
answered Jan 21 at 11:11
gandalf61gandalf61
8,801725
edited Jan 21 at 12:12
answered Jan 21 at 11:11
gandalf61gandalf61
8,801725
answered Jan 21 at 11:11
gandalf61gandalf61
8,801725
answered Jan 21 at 11:11
gandalf61gandalf61
8,801725
8,801725
$begingroup$
$90+frac{1.8}{4}$ does not $= 94.5$USD
$endgroup$
– ʎpoqou
Jan 21 at 12:10
1
$begingroup$
@ʎpoqou Good spot ! I have corrected to $90.45$.
$endgroup$
– gandalf61
Jan 21 at 12:13
add a comment |
$begingroup$
$90+frac{1.8}{4}$ does not $= 94.5$USD
$endgroup$
– ʎpoqou
Jan 21 at 12:10
1
$begingroup$
@ʎpoqou Good spot ! I have corrected to $90.45$.
$endgroup$
– gandalf61
Jan 21 at 12:13
$begingroup$
$90+frac{1.8}{4}$ does not $= 94.5$USD
$endgroup$
– ʎpoqou
Jan 21 at 12:10
$begingroup$
$90+frac{1.8}{4}$ does not $= 94.5$USD
$endgroup$
– ʎpoqou
Jan 21 at 12:10
1
1
$begingroup$
@ʎpoqou Good spot ! I have corrected to $90.45$.
$endgroup$
– gandalf61
Jan 21 at 12:13
$begingroup$
@ʎpoqou Good spot ! I have corrected to $90.45$.
$endgroup$
– gandalf61
Jan 21 at 12:13
add a comment |
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