1. Risk Management: An Introduction to Financial Engineering23
Risk Management: An Introduction to Financial Engineering

2. Chapter 23 – Index of Sample Problems
Slide # Futures price
Slide # Contract value
Slide # Contract profit or loss
Slide # Lifetime values
Slide # Futures hedge
Slide # Futures options
Slide # Interest rate swap

3. 2: Futures price
Given the following table, what is the price per troy ounce that will
be used for today’s marking-to-market for the September contract?
Silver – 5,000 troy oz.; cnts per troy oz.
Open
High
Low
Settle
Chg
Lifetime
Interest
Jul
598.1
614.1
598.0
611.0
14.4
849.3
435.6
1,269
Sep
598.3
615.2
597.9
612.7
14.3
831.1
476.8
21,268
Dec
601.9
621.3
601.8
616.6
848.7
439.8
18,276

4. 3: Futures price
The price per troy ounce that will be used for today’s marking-to-
market for the September contract is cents per troy ounce.
Silver – 5,000 troy oz.; cnts per troy oz.
Open
High
Low
Settle
Chg
Lifetime
Interest
Jul
598.1
614.1
598.0
611.0
14.4
849.3
435.6
1,269
Sep
598.3
615.2
597.9
612.7
14.3
831.1
476.8
21,268
Dec
601.9
621.3
601.8
616.6
848.7
439.8
18,276

5. 4: Contract value
Given the following table, what is this day’s closing contract price for
one December futures contract?
Silver – 5,000 troy oz.; cnts per troy oz.
Open
High
Low
Settle
Chg
Lifetime
Interest
Jul
598.1
614.1
598.0
611.0
14.4
849.3
435.6
1,269
Sep
598.3
615.2
597.9
612.7
14.3
831.1
476.8
21,268
Dec
601.9
621.3
601.8
616.6
848.7
439.8
18,276

6. 5: Contract value
Today’s closing contract price for one December futures contract:
Contract price = 5,000   .01 = $30,830
Silver – 5,000 troy oz.; cnts per troy oz.
Open
High
Low
Settle
Chg
Lifetime
Interest
Jul
598.1
614.1
598.0
611.0
14.4
849.3
435.6
1,269
Sep
598.3
615.2
597.9
612.7
14.3
831.1
476.8
21,268
Dec
601.9
621.3
601.8
616.6
848.7
439.8
18,276

7. 6: Contract profit or loss
Assume that you originally bought one July futures contract at a
quoted price of What is your total profit or loss as of today’s
close?
Silver – 5,000 troy oz.; cnts per troy oz.
Open
High
Low
Settle
Chg
Lifetime
Interest
Jul
598.1
614.1
598.0
611.0
14.4
849.3
435.6
1,269
Sep
598.3
615.2
597.9
612.7
14.3
831.1
476.8
21,268
Dec
601.9
621.3
601.8
616.6
848.7
439.8
18,276 fs

8. 7: Contract profit or loss
Total profit = 5,000  (611.0 – 586.7)  .01 = $1,215
Silver – 5,000 troy oz.; cnts per troy oz.
Open
High
Low
Settle
Chg
Lifetime
Interest
Jul
598.1
614.1
598.0
611.0
14.4
849.3
435.6
1,269
Sep
598.3
615.2
597.9
612.7
14.3
831.1
476.8
21,268
Dec
601.9
621.3
601.8
616.6
848.7
439.8
18,276

9. 8: Lifetime values
You purchased 5 September futures contracts as soon as they were
available. What is the total dollar difference between the highest and
the lowest values for your account?
Silver – 5,000 troy oz.; cnts per troy oz.
Open
High
Low
Settle
Chg
Lifetime
Interest
Jul
598.1
614.1
598.0
611.0
14.4
849.3
435.6
1,269
Sep
598.3
615.2
597.9
612.7
14.3
831.1
476.8
21,268
Dec
601.9
621.3
601.8
616.6
848.7
439.8
18,276

10. 9: Lifetime values
Total dollar difference = 5  5,000  (831.1 – 476.8)  .01 = $88,575
Silver – 5,000 troy oz.; cnts per troy oz.
Open
High
Low
Settle
Chg
Lifetime
Interest
Jul
598.1
614.1
598.0
611.0
14.4
849.3
435.6
1,269
Sep
598.3
615.2
597.9
612.7
14.3
831.1
476.8
21,268
Dec
601.9
621.3
601.8
616.6
848.7
439.8
18,276

11. 10: Futures hedge
You are a dairy farmer. You expect to have 600,000 pounds of milk for
January delivery. You hedge your position at a time when the futures
prices are as quoted below. In January, the actual market price is
How much more would you have made or lost in total had you
not taken the hedge position?
Milk– 200,000 lbs.; cents per lb.
Open
High
Low
Settle
Chg
Lifetime
Interest
Jan
12.41
12.72
12.02
.01
12.46
11.99
489

12. 11: Futures hedge Milk– 200,000 lbs.; cents per lb. Open High Low
Settle
Chg
Lifetime
Interest
Jan
12.41
12.72
12.02
.01
12.46
11.99
489

13. 12: Futures options
You buy one May 415 call on gold. What is the total price per troy
ounce that you will spend to acquire one troy ounce of gold?
Ignore trading costs.
Gold – 100 troy ounces; $ per troy ounce
Price
Call
Apr
May
Jun
Put
415
7.80
12.10
15.40
4.30
7.30
11.20
420
5.30
9.80
12.70
7.60
10.80
13.70

14. 13: Futures options
Total cost per troy ounce = $415 + $12.10 = $427.10
Gold – 100 troy ounces; $ per troy ounce
Price
Call
Apr
May
Jun
Put
415
7.80
12.10
15.40
4.30
7.30
11.20
420
5.30
9.80
12.70
7.60
10.80
13.70

15. 14: Futures options
You sell one April 420 put on gold. What is the total amount
of the option premium you will receive? Ignore trading costs.
Gold – 100 troy ounces; $ per troy ounce
Price
Call
Apr
May
Jun
Put
415
7.80
12.10
15.40
4.30
7.30
11.20
420
5.30
9.80
12.70
7.60
10.80
13.70

16. 15: Futures options Option premium = $7.60  100 = $760
Gold – 100 troy ounces; $ per troy ounce
Price
Call
Apr
May
Jun
Put
415
7.80
12.10
15.40
4.30
7.30
11.20
420
5.30
9.80
12.70
7.60
10.80
13.70

17. 16: Interest rate swap
Company X can borrow at prime + 2 or at a fixed rate of 8.5%.
Company Y can borrow at prime + 3 or at a fixed rate of 8%.
Company X wants a fixed rate loan. Company Y wants a variable rate loan.
Can you arrange an interest rate swap that is beneficial to Company A, to Company B and to the dealer?

18. 17: Interest rate swap Company X: Company Y:
borrows at prime borrows at 8%
pays 8.25% fixed pays prime + 2.5
Dealer:
pays prime + 2
receives prime + 2.5
pays 8%
receives 8.25%

19. 23
End of Chapter 23