Calculate 3 month future of Oil












1












$begingroup$


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.










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$endgroup$

















    1












    $begingroup$


    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.










    share|cite|improve this question









    $endgroup$















      1












      1








      1





      $begingroup$


      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.










      share|cite|improve this question









      $endgroup$




      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






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      share|cite|improve this question











      share|cite|improve this question




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      asked Jan 21 at 9:55









      ʎpoqouʎpoqou

      3471211




      3471211






















          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.






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            $90+frac{1.8}{4}$ 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











          Your Answer





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          1 Answer
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          active

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          3












          $begingroup$

          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.






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            $90+frac{1.8}{4}$ 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
















          3












          $begingroup$

          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.






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            $90+frac{1.8}{4}$ 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














          3












          3








          3





          $begingroup$

          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.






          share|cite|improve this answer











          $endgroup$



          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.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Jan 21 at 12:12

























          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


















          • $begingroup$
            $90+frac{1.8}{4}$ 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


















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