Derivative Securities, Courant Institute, Fall 2006
Sample Final Exam
Questions added December 15, 4pm.
Question 2 (Feynman Kac) revised and sign corrected December
18, 12:30
Important:
• The final exam is on Wednesday, December 20, from 7:10 to 9 pm in the
usual classroom.
• You only may bring one piece of paper with whatever information you
want to put on it. You must be able to read this without magnifying
lenses or electronics. No other materials or books are allowed.
• You may not use and will not need a calculator.
• The questions below are examples of the kind of questions that will be on
the actual final. The questions on the final will be different, though some
may be similar.
• I will have special office hours from 5 to 7 on Monday and Tuesday, De-
cember 18 and 19.
• Feel free to post and argue over answers on the class bboard .
Part 1, multiple choice
1. I have a formula for Y (t), the effective interest rate for money borrowed
now and repaid at time t. This formula is called the (see Hull, Chapter 28)
(a) Volatility of interest rates (b) Term structure of interest rates
(c) Option price of interest rates (d) Hedge ratio of interest rates
2. In the martingale measure with Y (t) to be a numeraire for a one factor
market with tradable instruments X1 (t), . . ., Xn (t) with no arbitrage op-
portunities, what must be constant in time: (Hull, Chapter 25)
(a) The volatility of Y (t) (b) The expected return of Y (t)
(c) The expected value of Y (t)/X1 (t) (d) The expected value of X1 (t)/Y (t)
3. The term volatility skew refers to the fact that
(a) The implied volatility of an option is an increasing or decreasing
function of the strike price
(b) Different stocks have different volatilities
(c) The volatility is an increasing function of time
(d) The volatility is a convex function of the strike price.
4. The smooth pasting condition for American style options is the fact that
1
Sample Final Exam
Questions added December 15, 4pm.
Question 2 (Feynman Kac) revised and sign corrected December
18, 12:30
Important:
• The final exam is on Wednesday, December 20, from 7:10 to 9 pm in the
usual classroom.
• You only may bring one piece of paper with whatever information you
want to put on it. You must be able to read this without magnifying
lenses or electronics. No other materials or books are allowed.
• You may not use and will not need a calculator.
• The questions below are examples of the kind of questions that will be on
the actual final. The questions on the final will be different, though some
may be similar.
• I will have special office hours from 5 to 7 on Monday and Tuesday, De-
cember 18 and 19.
• Feel free to post and argue over answers on the class bboard .
Part 1, multiple choice
1. I have a formula for Y (t), the effective interest rate for money borrowed
now and repaid at time t. This formula is called the (see Hull, Chapter 28)
(a) Volatility of interest rates (b) Term structure of interest rates
(c) Option price of interest rates (d) Hedge ratio of interest rates
2. In the martingale measure with Y (t) to be a numeraire for a one factor
market with tradable instruments X1 (t), . . ., Xn (t) with no arbitrage op-
portunities, what must be constant in time: (Hull, Chapter 25)
(a) The volatility of Y (t) (b) The expected return of Y (t)
(c) The expected value of Y (t)/X1 (t) (d) The expected value of X1 (t)/Y (t)
3. The term volatility skew refers to the fact that
(a) The implied volatility of an option is an increasing or decreasing
function of the strike price
(b) Different stocks have different volatilities
(c) The volatility is an increasing function of time
(d) The volatility is a convex function of the strike price.
4. The smooth pasting condition for American style options is the fact that
1
