A stock has a historical volatility of 39%. The data shows significantly increased volatility in recent
data and significantly lower volatility in older data. The implied estimate of the unconditional
Introduction to Derivatives . 1
An Introduction to Forwards and Options . 5
Insurance, Collars, and Other Strategies. 9
Introduction to Risk Management . 13
Financial Forwards and Futures. 17
Interest Rate Models
Bonds maturing in 1, 2, and 3 years have prices of 0.9345, 0.8766, and 0.8212, respectively. In
year 1, what is the price of a two-year bond?
The Black-Scholes Equation
What term is sometimes used to describe the price at a particular point in time, say maturity, that is
necessary to calculate todays price?
(a) Face value
(b) Par value
(c) Boundary condition
Monte Carlo Valuation
T Multiple Choice
Given X1 = N (0, 1) and X2 = N (0.5, 8), what is the mean of e ?
Monte Carlo simulation assumes all assets earn:
(a) Risk-free rate
(b) Market Index
Brownian Motion and Itos Lemma
Assume a stock price of S(0) = $62.00, r = 0.05, = 0.30, and dividend = 0. What is the price of
a claim that pays S ? Use formula 20.29.
We will assume that Nathans, Inc. has 3-year zero-coupon debt outstanding, which will pay $200
at maturity. The assets are valued at $175, = 0.20, r = 0.04, and the company does not pay a
Financial Engineering and Security Design
Mel, Inc. stock is $135.00 per share. The companys semi-annual dividend is forecasted as $2.10 per
share, indefinitely. What is the price of a zero-coupon equity-linked bond, promisin
The Lognormal Distribution
What is the area under the standard normal distribution curve and is less than 0.654?
What is the probability that a number drawn from the st
Mead, Inc. may invest $20 million in a new fiber optic project. Due to market conditions, annual
production costs and revenues are forecasted at $10 million and $8 million, respectively, starting
next year. Reven
Binomial Option Pricing: II
Consider a two-period binomial model, where each period is 6 months. Assume the stock price is
$46.00, = 0.28, r = 0.06 and the dividend yield is 2.0%. What is the maximum approximate strike
Market-Making and Delta-Hedging
Assume that a $50 strike call pays a 2.0% continuous dividend, r = 0.07, = 0.25, and the stock
price is $48.00. What is the profit or loss, per share, for a short call position if the option ex
The Black-Scholes Formula
What is the price of a $35 strike call? Assume S = $38.50, = 0.25, r = 0.06, the stock pays no
dividend and the option expires in 45 days?
Binomial Option Pricing: I
A stock is currently selling for $22.00 per share. Ignoring interest, determine the intrinsic value of
a call option should there exist equally probable stock prices of $25.00 and $23.00.
Parity and Other Option Relationships
Jafee Corp. common stock is priced at $36.50 per share. The company just paid its $0.50 quarterly
dividend. Interest rates are 6.0%. A $35.00 strike European call, maturing in 6 months, se
Interest Rate Forwards and Futures
The price of a 3-year zero coupon government bond is 85.16. The price of a similar 4-year bond is
79.81. What is the yield to maturity (effective annual yield) on the 4-year bond?
Commodity Forwards and Futures
When answering questions 1 thru 6 refer to the following table of commodity forward and spot prices.
The annual risk free interest rate is 4.0%.
Today = spot
Financial Forwards and Futures
KMW, Inc. plans to pay a dividend of $0.50 per share both 3 and 6 months from today. KMWs
share price today is $36.00 and the continuously compounded quarterly interest rate is 1.5%. What is
An Introduction to Forwards and Options
The spot price of the market index is $900. A 3-month forward contract on this index is priced at
$930. What is the profit or loss to a short position if the spot price of the market ind
Introduction to Derivatives
T Multiple Choice
Which of the following is not a derivative instrument?
(a) Contract to sell corn
(b) Option agreement to buy land
(c) Installment sales agreement
(d) Mortgage backed security