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### 1. True and False (10 points). Answer each of the following questions with True or False. You do not need to provide any explanation. Each question is worth 2 points. (a) The most common form of swaps

Question Preview:

1. True and False (10 points).

Answer each of the following questions with True or False. You do not need to provide any

explanation. Each question is worth 2 points.

(a) The most common form of swaps is a plain vanilla _fixed-for-floating interest rate swap

where the notional values are exchanged at the beginning and at the end of the contract.

(b) Options and Futures are designed to enable the transfer of market risk, while swaps are

designed to enable the transfer of credit risk.

(c) A margin call will be issued only i...

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Question Preview:

1. True and False (10 points).

Answer each of the following questions with True or False. You do not need to provide any

explanation. Each question is worth 2 points.

(a) The most common form of swaps is a plain vanilla _fixed-for-floating interest rate swap

where the notional values are exchanged at the beginning and at the end of the contract.

(b) Options and Futures are designed to enable the transfer of market risk, while swaps are

designed to enable the transfer of credit risk.

(c) A margin call will be issued only if the investor's margin account balance becomes neg-

ative.

(d) Options market makers who are delta-hedging a long call position would most likely sell

the underlying when markets are rising.

(e) A rise in the convenience yield decreases the futures price while a rise in storage costs

increases the futures price.

2. Futures Market Arbitrage (18 points)

You are the analyst for Safeway Food Stores (SWY). The company is currently quoted at

$21.19. The stock is a high dividend paying stock and is expected to pay a dividend of$0.75

at the end of the year (exactly 3 months from now), a $1 dividend in June 2011 (9 months from now), and a$1.25 dividend in December 2011 (15 months from now). The 12 month

futures prices for SWY is \$20.12, the continuously compounded risk-free rate is 2%, and it is

possible to borrow and lend at this rate.

(a) (2 points) Notice that the 12 months futures price is below the spot price of SWY. Does

this imply that an arbitrage opportunity exists? Explain!

(b) (2 points) Is this market said to be in contango or in backwardation? Explain!

(c) (4 points) What is the fair price of a 12 month SWY futures?

(d) (8 points) Is there an arbitrage opportunity? If yes, explain how you could exploit it,

and illustrate all transactions!

(e) (2 points) Also, if an arbitrage opportunity exists, you can synthetically earn interest

on an investment at a rate different from the risk-free rate, _and that rate and explain,

if applicable.

3. Decomposing Option Value (20 points)

Using common industry lingo, a typical trader often decomposes the value of an option (OP,

option price) into its \time value" and its \intrinsic value". The intrinsic value (IV) of an

option is the value of the option if you exercise it now. The time value (TV) of an option

is the price of the option (OP) minus its intrinsic value (IV). For this question, assume that

there are no dividend payments and ignore insurance value.

(a) (2 points) Given a call option on a stock trading at S with a strike of K, write an ex-

pression for the intrinsic value (IV) of the stock trading at S.

(b) (14 points) Given an in-the-money American call option, _fill in how the value changes

with increase, decrease, no change, or it depends, if the following characteristics experi-

(c) (2 points) Show mathematically that the time value (TV) of an option is strictly less

than or equal to the option price (OP).

(d) (2 points) If an American call option were out-of-the-money, what would this imply for

its time value (TV), intrinsic value (IV) and option price (OP)?

4. Option Payout Diagrams (22 points)

Use the information in Table 1 to draw the NET and GROSS payout_ diagrams for the follow-

ing strategies, given that the stock price of Microsoft (MSFT) is 49.06 on April 29, 2015. Use

the bid and ask prices, when you are short and long respectively, in your calculations.

(a) (4 points) Buy a share of MSFT stock and buy an October put at 47.

(b) (4 points) Invest into a zero-coupon bond worth 47 USD and buy an October call at 47.

(c) (2 points) Compare the last two option payout_ diagrams. What do you observe?

(d) (4 points) Buy a 47-52.50 October bullish call spread (i.e. buy the lower strike call and

sell the higher strike call).

(e) (4 points) Buy a 47-52.50 October bearish put spread (i.e. buy the higher strike put and

sell the lower strike put).

and write two calls at 50)

5. Black-Scholes-Merton and the Merton Model (30 points).

Company XYZ has issued equity S and 1 year zero-coupon debt D with a face value of 90.

Assume that the value of the assets of the firm V are initially at 100. According to the Merton

model (Merton JF 1974), debt and equity are contingent claims on the assets of the _firm.

(a) (5 points) Draw the payout_ diagram for both the equity and debt of the _firm as a function

of the _firm's value one year from now. Draw the individual payoffs of debt and equity,

without the _financing costs.

(b) (5 points) What is the value of Company XYZ's equity at t = 0. Assume an annual

continuously compounding interest rate of 0% (zero), a time horizon of T = 1 year and

asset volatility of _V = 20%?

3

(c) (5 points) What is the value of Company XYZ's debt at t = 0, assuming an annual

continuously compounded interest rate of 0%, a time horizon of T = 1 year and asset

volatility of _V = 20%? Indicate two ways how you can calculate the value of debt!

(d) (4 points) What is the risk-neutral probability of default?

(e) (5 points) What is the delta, gamma and vega of XYZ's equity?

(f) (6 points) You, as a shareholder, would like to hedge yourself against market risk by

making your holdings delta-, gamma- and vega-neutral. How can you do this by using

only the company's stock and the two options indicated in the Table 2? Hint: Assume

that each call (put) option contract gives the right to buy (sell) 1 unit of the underlying

asset.

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### Solution preview

(a) The most common form of swaps is a plain vanilla _fixed-for- floating interest rate swap
where the notional values are exchanged at the beginning and at the end of the contract.

Solution (a) False

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