problem set 2 derivatives. problem 1 c(s,x,t) + b(x,t) = s + p(s,x,t) $12 + $89$95 + $2.50 $101...

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!