problem set 2 derivatives. problem 1 c(s,x,t) + b(x,t) = s + p(s,x,t) $12 + $89$95 + $2.50 $101...
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![Page 1: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/1.jpg)
Problem Set 2
Derivatives
![Page 2: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/2.jpg)
Problem 1
C(S,X,t) + B(X,t) = S + P(S,X,t)
$12 + $89 $95 + $2.50
$101 $97.50
Profit = $3.50
![Page 3: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/3.jpg)
Problem 2
C(S,X,t) + B(X,t) = S + P(S,X,t)
$11 + $42.70 $50 + $3$53.70
$53Build a Box!
$2 + $47.44 $50 + $5
$49.44$55
![Page 4: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/4.jpg)
So, what comes from building the box?
Problem 2
Initially: $55–$49.44 –$53 + $53.70= $6.26
At expiration you will pay $5 (option portion) and receive $5 (bond portion) so net zero
S5045
$45–$50 = –$5
Profit: $6.26
![Page 5: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/5.jpg)
Problem 3
C(S,X,t) + B(X,t) = S + P(S,X,t)
$14.50 + $80.75
$91.50 + $3.75
$95.25 $95.25
Use a box to borrow
$11.875 + $85.50
$91.50 + $5.875
$97.375 $97.375
![Page 6: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/6.jpg)
So, what comes from building the box?
Problem 3
S9085
Initially: $5.875 – $11.875 + $14.50 – $3.75= $4.75
$85–$90 = –$5
At expiration you will pay $5 no matter what
Borrow at T-bill rate
![Page 7: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/7.jpg)
Problems 4, 5, 6, 7
![Page 8: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/8.jpg)
Keys for using OPT as an analytical tool
C(S,X,t) = S - B(X,t) + P(S,X,t)C(S,X,t) = S - B(X,t) + P(S,X,t)
Stock
Cal
l
B(X,t) Stock
Cal
l
B(X,t)
S C
X C
t C
C
R C
P
P
P
P
P
![Page 9: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/9.jpg)
![Page 10: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/10.jpg)
Problem 8
New York• $10 buys a put to sell
£120 in exchange for $200 (exchange at the forward rate)
London• £5.58 buys a call to buy
$200 in exchange for £120 (exchange at the forward rate)
• Answer:$10 * .62 = £6.20, so buy the
calls in London & sell puts in New York
$1 = £0.62 spot$1 = £0.60 forward
![Page 11: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/11.jpg)
Problem 9
New York• Find equilibrium price
for a call to buy €100 in exchange for $135 (exchange at the forward rate)
• Answer:€5 * 1.32 = $6.60
Frankfurt• €5 buys a put to sell
$135 in exchange for €100 (exchange at the forward rate)
€ 1 = $1.32 spot€ 1 = $1.35 forward
![Page 12: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/12.jpg)
Problems for Discussion
10. Will the premium for a currency option be higher when there is greater uncertainty about the inflation differential in the two countries?
11. Explain the factors that determine the value of currency options such as the ones in problems 8 and 9.
12. Suppose a corporate treasurer complains that currency options are too expensive? Explain the advantages of currency options compared with forward contracts. Why do options command a premium?
![Page 13: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/13.jpg)
PENsSCPERS
BT
Counterpary
PEFCO
$5 mm
$5mm + Appreciat
ion
1% Coupon Fixed Undisclosed Flow
AppreciationAppreciation
![Page 14: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/14.jpg)
![Page 15: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/15.jpg)
Warm-up: Problem 2
NY
LON
ZUR
$1=£0.40
$1=CHF 1.30
£1=CHF 2.60
$1,000,000
£ 500,000
CHF 1,300,000
$1,250,000
Profit = $250,000
![Page 16: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/16.jpg)
Problem 6 (Basis too big)
$1,050,000 500,000 bu
$1,150,000 500,000 bu
Profit = $84,350.92
Moneytoday
Wheattoday
$2.00 per bushel
$2.30 per bushelWheatlater
Storage 10¢
$1,065,649.08 Moneylater
3%
Lend @ 18.45%
![Page 17: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/17.jpg)
Problem 7 (Basis too small)
$1,000,000 500,000 bu
$1,010,000 500,000 bu
Profit = $4,903.88
Moneytoday
Wheattoday
$2.00 per bushel
$2.02 per bushelWheatlater
Storage 10¢
$1,014,903.88 Moneylater
3%
Borrowing @ 2.02%
![Page 18: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/18.jpg)
Problem 9
Net for RRNB: extra 1% each year
This is includes a Floating/Floating Swap
RRNBT-Bill + 1%
CitiCorpLIBOR + 1%
CounterpartyT-Bill
LIBOR
BW Homes
T + 2%
Midland Bank
LIBOR + 1%
$10,000 per year profit!
![Page 19: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/19.jpg)
Problem 10
• Breakup Value$750,000,000 from Shug’s Restaurants
$600,000,000 from Betty’s Boutiques
$200,000,000 from airline liquidation
$1,550,000,000 Total
• Market Value of Package: $1,000,000,000
• Value of airline as going concern:$550,000,000
![Page 20: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/20.jpg)
Problem 12
C(S,X,t) + B(X,t) = S + P(S,X,t)
$10 + $89 $95 + $1.75$99
$96.75Build a Box!
$12 + $84.06 $95 + $1.25
$96.06$96.25
![Page 21: Problem Set 2 Derivatives. Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50](https://reader035.vdocuments.us/reader035/viewer/2022062718/56649e8a5503460f94b8fc95/html5/thumbnails/21.jpg)
So, what comes from building the box?
Problem 12
S9085
Initially: $10 – $1.75– $12 + $1.25= – $2.50
$90 – $85 = $5
At expiration you will receive $5 no matter what
Double your money!