midterm review fall 2014

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    15.437 Midterm Review

    Michael Abrahams

    MIT Sloan School of Management

    [email protected]

    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