midterm review fall 2014
TRANSCRIPT
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15.437 Midterm Review
Michael Abrahams
MIT Sloan School of Management
Fall 2014
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Agenda
1) Some Tips for the Midterm
2) Bonds
3) Swaps
4) Forwards
5) Options
Key Concepts + Exercises
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Some Tips for the Midterm
Read each question very carefully!
Since this is an open book exam, dont expect simple
plug and chug type problems
Attempt to understand the intuition before focusing onthe equations
Expect to draw information from the whole course
It is important to explain your answers and show
intermediate steps for full (or partial) credit
Remember your calculator - laptops are not allowed
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Bonds Key Concepts
Replication can allow you to price, hedge, or
build an arbitrage portfolio if it is mispriced
know how to do all of these!
Know the standard terminology and how the
different terms relate to each other:a.Coupon bond
b.Zero coupon bond and zero coupon yield curve
c.Par bond and par bond yield curve
d.Forward rates
e.Floating-rate bond
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Know how to: replicate and price both sides of a swap
find the fair value swap rate
value a swap with changing notional value an existing swap position
Key result: value of individual floating
payment at time t is (Zt-1 Zt) per unit of
notional amount
Swaps Key Concepts
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Exercise (Swap)
Consider a newly-issued 2-year swap with the following characteristics:
Notional values: $1M at period 1, $1.5M at 2, $2.0M at 3, and $2.5M at 4.
The fixed side pays every six months (i.e., at the end of 1,2,3, and 4).
The floating side makes a single payment at the end of period 4 (based on
the given notional).
What is the swap rate in this contract?
Exercise 4.1
t (6-mth) 1 2 3 4
Zt 0.970 0.941 0.912 0.883
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Forwards Key Concepts
Know how to: find the forward price
replicate a forward contract
exploit arbitrage opportunities value an existing forward position
Key result:F = FVT[spot price] FVT [forgone cash flows]
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Options Key Concepts
Learn the standard terminology (puts, calls, option
premium, strike price, American vs. European, etc.)
Put-Call Parity for European options: S = C P + PV(K) if no intermediate cash flows on S
S = C P + PV(K) + PV(D) if there are dividends or other
intermediate cash flows
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Options Key Concepts
Know how options relate to forward contractsa. A call and put with strike equal to the forward price must
have the same premium
b. Rewrite put-call parity as S PV(D) = C P + PV(K). What
does S PV(D) look like? The present value of the forward
price (spot minus PV of forgone cash flows)! Thus, we also
have PV(F) = C P + PV(K), for any K.
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Exercise 4.2
Exercise (Previous Exam Question)A year ago your firm took a long position in a three-year forward contract on
100,000 pounds of copper. The forward price when the contract was initiated
was $3.20 per pound. The forward price for that delivery date has since risen to
$4.00 per pound.
Two-year European options, each covering 100 pounds of copper, are availableon the following terms:
Striking Price Call Put
350 80 35
400 52 52
450 30 75The current price of a zero coupon bond maturing in two years is $.90. Your
counterparty on the forward contract has just offered your firm $70,000
to cancel the contract. Should your firm take this offer?
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Exercise (Previous Exam Question)
A firm has created a ten-year trust that holds one thousand shares of ABC stock.
This stock serves as collateral for three securities that the firm has issued. These
securities represent different claims on the stock.
The first security receives all of the dividends paid by the stock during the ten-
year period. The residual value of the trust on the termination date is then
divided between the remaining securities. The second security receives anycapital appreciation the stock has experienced over the ten-year period. If the
stock has declined in value, the second security receives nothing. The third
security receives the full value left in the trust after the second security has been
paid.
The price of the stock when the trust was created was $100 per share. Show how
you could express the current value of each of the three securities in terms of the
current value of ABC stock, the current value of a zero coupon bond maturing
on the termination date of the trust, and the current value of European options
on ABC stock that expire on the termination date.
Exercise 4.3
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Exercise (Forward on a Swap)
Consider a forward on a swap (distinct from a forward swap), that is, a
forward contract that requires you to buy an existing swap contract at a given
price in the future.
Specifically, determine the appropriate forward price on a 1-year forward ona newly-issued, 2-year plain vanilla floating-for-fixed swap with notional of
$100. The forward matures just after the 1-year swap payment date. The
prices of 0.5, 1.0, 1.5, and 2.0 year zeros are 0.95, 0.90, 0.85, and 0.80
respectively. Assume that you will receive floating payments.
Exercise 4.4