problem set 2 derivatives. problem 1 c(s,x,t) + b(x,t) = s + p(s,x,t) $12 + $89$95 + $2.50 $101...
TRANSCRIPT
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
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
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
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
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
Problems 4, 5, 6, 7
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
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
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
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?
PENsSCPERS
BT
Counterpary
PEFCO
$5 mm
$5mm + Appreciat
ion
1% Coupon Fixed Undisclosed Flow
AppreciationAppreciation
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
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%
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%
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!
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
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
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!