1 / 67

The pricing of forward and futures contracts

The pricing of forward and futures contracts. Outline. Spot and futures prices for non-dividend paying investment assets Spot and futures prices for investment assets paying a known income Spot and futures prices for investment assets paying a known yield/return

palmer-luna
Download Presentation

The pricing of forward and futures contracts

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. The pricing of forward and futures contracts

  2. Outline • Spot and futures prices for non-dividend paying investment assets • Spot and futures prices for investment assets paying a known income • Spot and futures prices for investment assets paying a known yield/return • Spot and futures prices for commodities with storage costs • Spot and futures prices for consumption commodities with storage costs • The cost of carry • The valuation of forward contracts

  3. Case 1a: Non-dividend paying investment asset The forward price of a contract expiring in three months is $43. The three-month annualized interest rate is 5%, and the current price of the underlying asset is $40/share.No dividend is expected

  4. Case 1a: Non-dividend paying investment asset The forward price of a contract expiring in three months is $43. The three-month annualized interest rate is 5%, and the current price of the underlying asset is $40/share.No dividend is expected

  5. Case 1a: Non-dividend paying investment asset The forward price of a contract expiring in three months is $43. The three-month annualized interest rate is 5%, and the current price of the underlying asset is $40/share.No dividend is expected

  6. Case 1a: Non-dividend paying investment asset The forward price of a contract expiring in three months is $43. The three-month annualized interest rate is 5%, and the current price of the underlying asset is $40/share.No dividend is expected

  7. Case 1a: Non-dividend paying investment asset The forward price of a contract expiring in three months is $43. The three-month annualized interest rate is 5%, and the current price of the underlying asset is $40/share.No dividend is expected

  8. Case 1a: Non-dividend paying investment asset The forward price of a contract expiring in three months is $43. The three-month annualized interest rate is 5%, and the current price of the underlying asset is $40/share.No dividend is expected Arbitrage profit at expiration : $2.50

  9. Case 1a: Implications Eventually, investors would bid up the stock price, and drive down the forward price

  10. Case 1b: Non-dividend paying investment asset The forward price of a contract expiring in three months is $39. The three-month annualized interest rate is 5%, and the current price of the underlying asset is $40/share.No dividend is expected

  11. Case 1b: Non-dividend paying investment asset The forward price of a contract expiring in three months is $39. The three-month annualized interest rate is 5%, and the current price of the underlying asset is $40/share.No dividend is expected

  12. Case 1b: Non-dividend paying investment asset The forward price of a contract expiring in three months is $39. The three-month annualized interest rate is 5%, and the current price of the underlying asset is $40/share.No dividend is expected

  13. Case 1b: Non-dividend paying investment asset The forward price of a contract expiring in three months is $39. The three-month annualized interest rate is 5%, and the current price of the underlying asset is $40/share.No dividend is expected Arbitrage profit at expiration : $1.50

  14. Case 1b: Implications Eventually, investors would drive down the stock price, and bid up the forward price

  15. Relationship between spot and forward/futures prices for a non-dividend paying investment asset F0 = S0erT F0 = forward/futures price today S0 = underlying asset spot price today r = risk-free rate T = time to expiration

  16. Case 2a: Asset with a known income A bond has the one-year forward price of $930. The current spot price of the bond is $900. Coupon payments are $40 every six months. The six-month risk-free rate is 9%/year and the one-year risk-free rate is 10%.

  17. Case 2a: Asset with a known income A bond has the one-year forward price of $930. The current spot price of the bond is $900. Coupon payments are $40 every six months. The six-month risk-free rate is 9%/year and the one-year risk-free rate is 10%.

  18. Case 2a: Asset with a known income A bond has the one-year forward price of $930. The current spot price of the bond is $900. Coupon payments are $40 every six months. The six-month risk-free rate is 9%/year and the one-year risk-free rate is 10%.

  19. Case 2a: Asset with a known income A bond has the one-year forward price of $930. The current spot price of the bond is $900. Coupon payments are $40 every six months. The six-month risk-free rate is 9%/year and the one-year risk-free rate is 10%.

  20. Case 2a: Asset with a known income A bond has the one-year forward price of $930. The current spot price of the bond is $900. Coupon payments are $40 every six months. The six-month risk-free rate is 9%/year and the one-year risk-free rate is 10%.

  21. Case 2a: Asset with a known income A bond has the one-year forward price of $930. The current spot price of the bond is $900. Coupon payments are $40 every six months. The six-month risk-free rate is 9%/year and the one-year risk-free rate is 10%.

  22. Case 2a: Asset with a known income A bond has the one-year forward price of $930. The current spot price of the bond is $900. Coupon payments are $40 every six months. The six-month risk-free rate is 9%/year and the one-year risk-free rate is 10%. Arbitrage profit at expiration : $17.61

  23. Case 2a: Implication Eventually, investors would drive down the forward price, and bid up the spot price of the bond

  24. Case 2b: Asset with a known income A bond has the one-year forward price of $905. The current spot price of the bond is $900. Coupon payments are $40 every six months. The six-month risk-free rate is 9%/year and the one-year risk-free rate is 10%.

  25. Case 2b: Asset with a known income A bond has the one-year forward price of $905. The current spot price of the bond is $900. Coupon payments are $40 every six months. The six-month risk-free rate is 9%/year and the one-year risk-free rate is 10%.

  26. Case 2b: Asset with a known income A bond has the one-year forward price of $905. The current spot price of the bond is $900. Coupon payments are $40 every six months. The six-month risk-free rate is 9%/year and the one-year risk-free rate is 10%.

  27. Case 2b: Asset with a known income A bond has the one-year forward price of $905. The current spot price of the bond is $900. Coupon payments are $40 every six months. The six-month risk-free rate is 9%/year and the one-year risk-free rate is 10%.

  28. Case 2b: Asset with a known income A bond has the one-year forward price of $905. The current spot price of the bond is $900. Coupon payments are $40 every six months. The six-month risk-free rate is 9%/year and the one-year risk-free rate is 10%.

  29. Case 2b: Asset with a known income A bond has the one-year forward price of $905. The current spot price of the bond is $900. Coupon payments are $40 every six months. The six-month risk-free rate is 9%/year and the one-year risk-free rate is 10%. Arbitrage profit at expiration : $952.39 - $40 - $905 = $7.39

  30. Case 2b: Implication Eventually, investors would drive down the spot price, and bid up the forward price of the bond

  31. Relationship between spot and forward/futures prices for an investment asset providing a known income F0 = (S0 - PVincome)erT In our example: PVincome = $40e-(0.09)(0.5) + $40e-(0.1)

  32. Case 2c: Asset providing a known yield/return Assume two-year rates in the US and Canada are 7% and 5% respectively. The spot rate of the C$ is US$0.62. The two-year forward rate US$0.63.

  33. Case 2c: Asset providing a known yield/return Assume two-year rates in the US and Canada are 7% and 5% respectively. The spot rate of the C$ is US$0.62. The two-year forward rate US$0.63.

  34. Case 2c: Asset providing a known yield/return Assume two-year rates in the US and Canada are 7% and 5% respectively. The spot rate of the C$ is US$0.62. The two-year forward rate US$0.63.

  35. Case 2c: Asset providing a known yield/return Assume two-year rates in the US and Canada are 7% and 5% respectively. The spot rate of the C$ is US$0.62. The two-year forward rate US$0.63.

  36. Case 2c: Asset providing a known yield/return Assume two-year rates in the US and Canada are 7% and 5% respectively. The spot rate of the C$ is US$0.62. The two-year forward rate US$0.63.

  37. Case 2c: Asset providing a known yield/return Assume two-year rates in the US and Canada are 7% and 5% respectively. The spot rate of the C$ is US$0.62. The two-year forward rate US$0.63.

  38. Case 2c: Asset providing a known yield/return Assume two-year rates in the US and Canada are 7% and 5% respectively. The spot rate of the C$ is US$0.62. The two-year forward rate US$0.63. Arbitrage profit = US$16.91

  39. Case 2c: Implication Eventually, investors would drive down the forward price and bid up the spot price of the US$

  40. Relationship between spot and forward/futures prices for an investment asset providing a known yield/return F0 = S0e(r-q)T Where q is the known yield/return provided by the investment asset In case 2c, q is the interest rate on the foreign currency.

  41. Case 3a: Commodities The one-year futures price of gold is $500 per troy once. The spot price is $450 per troy once and the risk-free rate is 7%/year. The storage cost of gold is $2 per troy once per year.

  42. Case 3a: Commodities The one-year futures price of gold is $500 per troy once. The spot price is $450 per troy once and the risk-free rate is 7%/year. The storage cost of gold is $2 per troy once per year.

  43. Case 3a: Commodities The one-year futures price of gold is $500 per troy once. The spot price is $450 per troy once and the risk-free rate is 7%/year. The storage cost of gold is $2 per troy once per year.

  44. Case 3a: Commodities The one-year futures price of gold is $500 per troy once. The spot price is $450 per troy once and the risk-free rate is 7%/year. The storage cost of gold is $2 per troy once per year.

  45. Case 3a: Commodities The one-year futures price of gold is $500 per troy once. The spot price is $450 per troy once and the risk-free rate is 7%/year. The storage cost of gold is $2 per troy once per year.

  46. Case 3a: Commodities The one-year futures price of gold is $500 per troy once. The spot price is $450 per troy once and the risk-free rate is 7%/year. The storage cost of gold is $2 per troy once per year. Arbitrage profit = $1,537

  47. Case 3a: Implications In the long run, investors would bid up the spot price of gold and drive down its futures price.

  48. Example 3b: Commodities The one-year futures price of gold is $470 per troy once. The spot price is $450 per troy once and the risk-free rate is 7%/year. The storage cost of gold is $2 per troy once per year, payable in arrears.

  49. Example 3b: Commodities The one-year futures price of gold is $470 per troy once. The spot price is $450 per troy once and the risk-free rate is 7%/year. The storage cost of gold is $2 per troy once per year, payable in arrears.

  50. Example 3b: Commodities The one-year futures price of gold is $470 per troy once. The spot price is $450 per troy once and the risk-free rate is 7%/year. The storage cost of gold is $2 per troy once per year, payable in arrears.

More Related