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
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
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
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
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
A bank quotes you an interest rate of 14% per annum with quarterly compounding. What is
the equivalent rate with (a) continuous compounding and (b) annual compounding?
(a) The rate with continuous c
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
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
Interest Rate Futures
A U.S. Treasury bond pays a 7% coupon on January 7 and July 7. How much interest
accrues per $100 of principal to the bond holder between July 7, 2014 and August 8, 2014?
How would your answe
Martingales and Measures
How is the market price of risk defined for a variable that is not the price of an investment asset?
The market price of risk for a variable that is not the price of an investment asset
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
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
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
The Black-Scholes-Merton Model
What does the BlackScholesMerton stock option pricing model assume about the
probability distribution of the stock price in one year? What does it assume about the
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
Energy and Commodity Derivatives
What is meant by HDD and CDD?
A days HDD is max(0 65 A) and a days CDD is max(0 A 65) where A is the
average of the highest and lowest temperature during the day at a specified w
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
The spread between the yield on a three-year corporate bond and the yield on a similar
risk-free bond is 50 basis points. The recovery rate is 30%. Estimate the average hazard rate
per year over the
Explain the difference between a regular credit default swap and a binary credit default swap.
Both provide insurance against a particular company defaulting during a period of time. In a
Explain the difference between the net present value approach and the risk-neutral valuation
approach for valuing a new capital investment opportunity. What are the advantages of the
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 S0e qT
in all cases.
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
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
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
Companies A and B have been offered the following rates per annum on a $20 million
Company A requires a floating-r
Employee Stock Options
Why was it attractive for companies to grant at-the-money stock options prior to 2005? What
changed in 2005?
Prior to 2005 companies did not have to expense at-the-money options on the inc
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
Wiener Processes and Its Lemma
What would it mean to assert that the temperature at a certain place follows a Markov
process? Do you think that temperatures do, in fact, follow a Markov process?
Imagine that you
Options on Stock Indices and Currencies
A portfolio is currently worth $10 million and has a beta of 1.0. An index is currently
standing at 800. Explain how a put option on the index with a strike of 700 can be
Explain the difference between a call option on yen and a call option on yen futures.
A call option on yen gives the holder the right to buy yen in the spot market at an exchange
rate equal to th