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
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
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
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
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
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
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
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 the
The Greek Letters
Explain how a stop-loss trading rule can be implemented for the writer of an out-of-themoney call option. Why does it provide a relatively poor hedge?
Suppose the strike price is 10.00. The opt
Estimating Volatilities and Correlations
Explain the exponentially weighted moving average (EWMA) model for estimating volatility
from historical data.
Define ui as ( Si Si 1 ) / Si 1 , where Si is value of a mar
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