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
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
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 a
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
informa
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. Fur
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 doe
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
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
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 e
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 dividen
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.
(
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 compounde
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Math 454
March 31, 2015
Test 1.5
1. In the following problem, the call options discussed are European options, all on the same non-dividendpaying stock, all with the same time to expiry.
(a) (10 point
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 compounde
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 op
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 vol
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 doe
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
informa
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 pay
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
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
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