Math 454 - March 25, 2015 - Quiz 12
Name:
1. For a European call option on a dividend-paying stock, how can we interpret the expression eT N (d1 )?
(a)
(b)
(c)
(d)
This
This
This
This
is
is
is
is
the
the
the
the
of the option.
risk-neutral probability th
Math 454 - February 20, 2015 - Quiz 3
Name:
1. For an at-the-money 3-month European call option on a stock you are given the following
information.
(a) The current stock price is 30.
(b) The stock does not pay dividends.
(c) The continuously compounded an
Math 454 - March 16, 2015 - Quiz 8
Name:
1. Suppose two European options on a non-dividend paying stock are identical, except for
their time-to-expiry. That is, the options are on the same stock, have the same strike, are
both calls, or both puts, etc. Le
Math 454 - March 9, 2015 - Quiz 6
Name:
1. The price of a stock is 40, and it pays continuous dividends at a 4% annual rate. The
risk-free rate is 6%. Determine the lowest possible no-arbitrage price for a 1-year American
put option with a strike price of
Math 454 - February 16, 2013 - Quiz 2
Name:
1. The model for a stocks price is geometric Brownian motion with the following parameters:
(a)
(b)
(c)
(d)
The
The
The
The
annual continuously compounded expected return on the stock is 15%.
volatility of the s
Math 454 - February 10, 2013 - Quiz 1 Solution
Name:
1. A stocks price follows a lognormal model. You are given:
(a) The annual continuously compounded expected return on the stock is 10%.
(b) The volatility of the stock is 20%.
(c) The continuous dividen
Math 454 - February 20, 2015 - Quiz 3
Name:
1. For an at-the-money 3-month European call option on a stock you are given the following
information.
(a) The current stock price is 30.
(b) The stock does not pay dividends.
(c) The continuously compounded an
Math 454 - February 23, 2015 - Quiz 4
Name:
1. A stock follows the Ito process
dS = 0.15Sdt + 2SdZ
You are to value a put option with strike 30 and time to expiry 10 years, given the following
information.
(a) The current stock price is 40.
(b) The stock
Math 454 - February 16, 2013 - Quiz 2
Name:
1. The model for a stocks price is geometric Brownian motion with the following parameters:
(a)
(b)
(c)
(d)
The
The
The
The
annual continuously compounded expected return on the stock is 15%.
volatility of the s
Math 454 - March 10, 2015 - Quiz 7
Name:
1. Graph the payo of (the long side of) a (non-prepaid) forward contract at the end date
as a function of the strike price K. Assume S, r, , and T are xed. Further, assume r > 0,
= 0, T = 1 and graph the value pri
Math 454 - February 23, 2015 - Quiz 4
Name:
1. A stock follows the Ito process
dS = 0.15Sdt + 2SdZ
You are to value a put option with strike 30 and time to expiry 10 years, given the following
information.
(a) The current stock price is 40.
(b) The stock
Math 454 - March 3, 2015 - Test 1
Name:
1. (10 points) You are given the following information:
1. The continuously compounded interest rate on the US Dollar (USD) is 0%.
2. The continuously compounded interest rate on the Russian Ruble (RUB) is 15%.
3. T
Math 454
March 31, 2015
Name:
Question Points Score
1
14
2
15
3
28
4
20
5
10
6
10
7
5
8
10
9
10
10
22
11
8
Total:
152
1
Test 1.5
1. In the following problem, the call options discussed are European options, all on the same non-dividendpaying stock, all wi
Math 454 - March 3, 2015 - Test 1
Name:
1. (10 points) You are given the following information:
1. The continuously compounded interest rate on the US Dollar (USD) is 0%.
2. The continuously compounded interest rate on the Russian Ruble (RUB) is 15%.
3. T
Math 454 - March 20, 2015 - Quiz 10
Name:
1. Indicate whether each of the following statements about European options priced using
the Black-Scholes formula is true or false.
(a) is always positive.
(b) The of a call option is always negative.
(c) is the
Math 454 - March 23, 2015 - Quiz 11
Name:
Throughout this quiz, the underlying stock will be a company called XYZ whose current
stock price is 100. The volatility is 20% and interest rates and dividends are zero. In your
computations, make sure to keep at
Math 454 - February 27, 2015 - Quiz 5
Name:
1. The exchange rate of Brutopian Pesos (BRP) to U.S. Dollars (USD) is 10 to 1. Assume,
for purposes of this problem, that the annualized volatility of this exchange rate is 10%.
You are the derivatives analyst
Math 454 - February 27, 2015 - Quiz 5
Name:
1. The exchange rate of Brutopian Pesos (BRP) to U.S. Dollars (USD) is 10 to 1. Assume,
for purposes of this problem, that the annualized volatility of this exchange rate is 10%.
You are the derivatives analyst
Math 454 - March 23, 2015 - Quiz 11 Solutions
Name:
Throughout this quiz, the underlying stock will be a company called XYZ whose current
stock price is 100. The volatility is 20% and interest rates and dividends are zero. In your
computations, make sure
Math 454 - February 10, 2013 - Quiz 1
Name:
1. A stocks price follows a lognormal model. You are given:
(a) The annual continuously compounded expected return on the stock is 10%.
(b) The volatility of the stock is 20%.
(c) The continuous dividend rate is
Math 454 - March 20, 2015 - Quiz 10
Name:
1. Indicate whether each of the following statements about European options priced using
the Black-Scholes formula is true or false.
(a) is always positive.
(b) The of a call option is always negative.
(c) is the
Math 454 - May 1, 2015 - Quiz 17
Name:
1. Suppose that Z(t) is standard Brownian motion, and nd the stochastic integral:
t
eZ(s) dZ(s)
0
Hint: Guess and check.
1
Math 454 - March 18, 2015 - Quiz 9
Name:
1. If N (x) is the cumulative normal distribution function, nd N (x).
Solution. By the Fundamental Theorem of Calculus, and the denition of N (x), N (x) is
the standard normal pdf.
1 x2
N (x) = e 2
2
2. Suppose C i
Math 454 - March 16, 2015 - Quiz 8
Name:
1. Suppose two European options on a non-dividend paying stock are identical, except for
their time-to-expiry. That is, the options are on the same stock, have the same strike, are
both calls, or both puts, etc. Le
Math 454 - March 9, 2015 - Quiz 6
Name:
1. The price of a stock is 35, and it pays continuous dividends at a 4% annual rate. The
risk-free rate is 6%. Determine the lowest possible no-arbitrage price for a 1-year American
put option with a strike price of
Math 454 - March 25, 2015 - Quiz 12
Name:
Suppose a stock S has current price 100. We buy a portfolio which is long two options
on S: an at-the-money call C and an at-the-money put P .
1. Draw the payo diagram for our option portfolio, i.e. the total payo
Math 454 - April 20, 2015 - Quiz 14
Name:
1. Let X(t) be an Ito process which is a function of t and a standard Brownian motion Z(t).
State Itos Lemma: give the equation for dX(t).
2. Give the table of multiplication rules for dt and dZ.
3. Suppose Y (t)
Math 454 - April 22, 2015 - Quiz 15
Name:
1. Give the table of multiplication rules for dt and dZ.
2. Suppose Y (t) = log X(t) and that dX(t)/X(t) = dt + dZ(t). Use Itos Lemma to
calculate dY (t).
3. Suppose X(t) = (tZ(t)2 + 3t2 Z(t). Use Itos Lemma to ca
Math 454 - April 27, 2015 - Quiz 16
Name:
1. Suppose that Z(t) is standard Brownian motion, and dene a process X(t) = Z(t)3
ctZ(t). For what value of c, if any, is X(t) a martingale? Show your work.
2. Suppose that Z(t) is standard Brownian motion, and d
Math 454 - March 25, 2015 - Quiz 12
Name:
Suppose a stock S has current price 100. We buy a portfolio which is long two options
on S: an at-the-money call C and an at-the-money put P .
1. Draw the payo diagram for our option portfolio, i.e. the total payo