Weather, Energy, and Insurance Derivatives
HDD and CDD can be regarded as payoffs from options on temperature. Explain this
HDD is max(65 A 0) where A is the average of the maximum and minimum tempera
The Greek Letters
What does it mean to assert that the theta of an option position is 0.1 when time is measured
in years? If a trader feels that neither a stock price nor its implied volatility will change,
Valuing Stock Options: The Black-Scholes-Merton Model
A stock price is currently $40. Assume that the expected return from the stock is 15% and its
volatility is 25%. What is the probability distribution for the
Introduction to Binomial Trees
Consider the situation in which stock price movements during the life of a European option
are governed by a two-step binomial tree. Explain why it is not possible to set up a posi
Exotic Options and Other Nonstandard Products
Describe the payoff from a portfolio consisting of a floating lookback call and a floating
lookback put with the same maturity.
A floating lookback call provides a p
Value at Risk
A company uses an EWMA model for forecasting volatility. It decides to change the
parameter from 0.95 to 0.85. Explain the likely impact on the forecasts.
Reducing from 0.95 to 0.85 means that mo
Suppose that the risk-free zero curve is flat at 7% per annum with continuous compounding
and that defaults can occur half way through each year in a new five-year credit default
Properties of Stock Options
Explain why the arguments leading to putcall parity for European options cannot be used to
give a similar result for American options.
When early exercise is not possible, we can argu
Trading Strategies Involving Options
Use putcall parity to relate the initial investment for a bull spread created using calls to the
initial investment for a bull spread created using puts.
A bull spread using
Explain why a bank is subject to credit risk when it enters into two offsetting swap contracts.
At the start of the swap, both contracts have a value of approximately zero. As time passes, it
is likely that
Mechanics of Options Markets
A corporate treasurer is designing a hedging program involving foreign currency options.
What are the pros and cons of using (a) the NASDAQ OMX and (b) the over-the-counter
Determination of Forward and Futures Prices
Is the futures price of a stock index greater than or less than the expected future value of the
index? Explain your answer.
The futures price of a stock index is always
The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0. A 1.5-year bond
that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond that
will pay cou
Hedging Strategies Using Futures
In the Chicago Board of Trades corn futures contract, the following delivery months are
available: March, May, July, September, and December. State the contract that should be
Interest Rate Futures
The price of a 90-day Treasury bill is quoted as 10.00. What continuously compounded
return (on an actual/365 basis) does an investor earn on the Treasury bill for the 90-day
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
Mechanics of Futures Markets
The party with a short position in a futures contract sometimes has options as to the precise
asset that will be delivered, where delivery will take place, when delivery will take plac