Value at Risk
Consider a position consisting of a $100,000 investment in asset A and a $100,000
investment in asset B. Assume that the daily volatilities of both assets are 1% and that the
coefficient of correla
Convexity, Timing, and Quanto Adjustments
Explain how you would value a derivative that pays off 100R in five years where R is
the one-year interest rate (annually compounded) observed in four years. What differ
MATBUS 470 Winter 2015 assignment 1.
Due: February 6th before noon in M3-2001.
1. On May 8, 2013, as indicated in Table 1.3 the spot bid price of Google stock is 871.23
and the offer price of a put option with a strike price of $860 and maturity date of
Martingales and Measures
How is the market price of risk defined for a variable that is not the price of an investment
The market price of risk for a variable that is not the price of an investment asset
OIS Discounting, Credit Issues, and Funding Costs
Explain what is meant by (a) the 3-month LIBOR rate and (b) the 3-month OIS rate.
Which is higher? Why?
The 3-month LIBOR rate is the rate at which a AA-rated bank
Suppose you own 5,000 shares that are worth $25 each. How can put options be used to
provide you with insurance against a decline in the value of your holding over the next four
You should buy
What is the difference between a long forward position and a short forward position?
When a trader enters into a long forward contract, she is agreeing to buy the underlying asset
for a certain price
A stock price is currently $40. It is known that at the end of one month it will be either $42 or
$38. The risk-free interest rate is 8% per annum with continuous compounding. What is the
Determination of Forward and Futures Prices
Explain what happens when an investor shorts a certain share.
The investors broker borrows the shares from another clients account and sells them in the
usual way. To cl
Companies A and B have been offered the following rates per annum on a $20 million fiveyear loan:
Company A requires a floating-ra
Properties of Stock Options
List the six factors affecting stock option prices.
The six factors affecting stock option prices are the stock price, strike price, risk-free interest
rate, volatility, time to matur
Securitization and the Credit Crisis of 2007
What was the role of GNMA (Ginnie Mae) in the mortgage-backed securities market of the
GNMA guaranteed qualifying mortgages against default and created securitie
Mechanics of Futures Markets
Distinguish between the terms open interest and trading volume.
The open interest of a futures contract at a particular time is the total number of long positions
Hedging Strategies Using Futures
Under what circumstances are (a) a short hedge and (b) a long hedge appropriate?
A short hedge is appropriate when a company owns an asset and expects to sell that asset in the
Trading Strategies Involving Options
What is meant by a protective put? What position in call options is equivalent to a protective
A protective put consists of a long position in a put option combined with
European Put Option on 1000 shares with strike of 50 and same parameter as 19.3
100,000 put options are sold
Week Stock price Delta of Call Delta of Put Shares purchased Cost ($000) Cumulative Cost ($000) Interest Cost ($000)
Basic Numerical Procedures
Which of the following can be estimated for an American option by constructing a single
binomial tree: delta, gamma, vega, theta, rho?
Delta, gamma, and theta can be determined from a
Explain the difference between a forward start option and a chooser option.
A forward start option is an option that is paid for now but will start at some time in the
future. The strike price is
Interest Rate Derivatives: The Standard Market Models
A company caps three-month LIBOR at 10% per annum. The principal amount is $20
million. On a reset date, three-month LIBOR is 12% per annum. What payment wou
More on Models and Numerical Procedures
Confirm that the CEV model formulas satisfy putcall parity.
It follows immediately from the equations in Section 27.1 that
p - c =Ke - rT - S 0e - qT
in all cases.
Mechanics of Options Markets
An investor buys a European put on a share for $3. The stock price is $42 and the strike
price is $40. Under what circumstances does the investor make a profit? Under what
HJM, LMM, and Multiple Zero Curves
Explain the difference between a Markov and a non-Markov model of the short rate.
In a Markov model the expected change and volatility of the short rate at time t depend only
Interest Rate Derivatives: Models of the Short Rate
What is the difference between an equilibrium model and a no-arbitrage model?
Equilibrium models usually start with assumptions about economic variables and de
Calculate all the fixed cash flows and their exact timing for the swap in Business Snapshot
33.1. Assume that the day count conventions are applied using target payment dates rather
than actual p
MATBUS 470 Fall 2014 Test 2 1.  A stock index is currently 810 and has a volatility of 20% and a dividend yield of 2%. The risk-free
rate is 5%. Consider a 6month European put option with a strike price of 800. Value the option using a
2step binomial m