Math 425
Solutions to Exam 3
April 23, 2001
1. (15) The formula V (s, t) = 10e-r(T -t) N (d2 ) gives the price of a cash or nothing option, which expires at time T , where the strike price is $40, and d2 = ln (s/40) + r - 2 /2 (T - t) . T -t
(a) What is t
Math 425
1.
Exam 3
April 25, 2002
(30) Assume a stock pays a continuous dividend at a yield of D y . That is, if during the time interval dt the stock has value S, then the amount of the dividend is D y S dt.
a.
b.
Let VS, t denote the value of an option
Math 425
Exam 2 Solutions
March 26, 2002
1. (20) Let C denote the price of an American call option on a share of non-dividend paying stock.
Let X denote the strike price, er the annual interest, and the time to expiration.
(a) Justify the inequality:
C S
Math 425
Solutions Exam 2,
March 1, 2012
1. (30) Let S0 = 100, r = 0.02, t = one week , u = 1.2, and d = 0.98.
(a) Find the value of a call with strike price 99 that expires in two weeks.
(b) Find the value of a European put with strike price 101 that als
Math 425 - 500
Solutions Exam 2
March , 2013
1. (50) The table below gives end-of-week stock prices. Assume the Geometric Brownian Motion model of stock prices for this problem, and that the annual risk free rate r = 0.02. Feb. 22 March 1 March 8 March 15
Math 425
1.
Solutions Exam 2
April 27, 2006
(50) The table below represents the possible prices of a share of stock, and the possible values of an
option whose value at t 1 depends on the stock price at t 1.
105
Stock:
5
, Option:
100
?
90
3
Assume A 0 50
Math 425
Solutions Exam 2
March 22, 2001
1. (15) The put call parity formula relates the prices of a European call to a European put option on the same stock with each option having the same strike price and expiration date. What is this formula, and expl
Math 425
Solutions to Exam 1
February 14, 2002
1. (30) Suppose that M-Corp stock is currently selling for $20 a share. That, Su = 22,
Sd = 19, and er = 1.01. A broker decides to oer a European call option with expiration
in one year, and a strike price of
Math 425 - 500
Solutions Exam 1
February 19, 2013
1. (30) Let X denote the strike price of a forward contract, which expires at time T . If the cost
of the asset is S0 , and the risk free continuously compounded interest rate is r, then we have
X = S0 erT
Math 425
1.
Solutions Exam 1
March 9, 2006
(30) Let F represent the forward price of a commodity at time n. Suppose 100r% is the interest rate per time period. Let S 0 represent the price of the commodity right now. Show, by use of the no arbitrage princi
Math 425
Solutions Exam 1
Feb. 9, 2012
1. (20) You buy one put with a strike price of $50 and sell another put with a strike price of
$45. Both puts have the same expiration date. Graph the value of this portfolio at expiration
as a function of the stock
Math 425
Solutions Exam 3,
April 26, 2012
1. (25) Use Itos lemma to show that the geometric Brownian motion model of stock prices,
St = S0 e(
2 /2)t
eBt satises the equation
dS = Sdt + SdBt .
Itos lemma states that df =
dS =
f
t
S 1 2S
+
2
t
2 Bt
+
1 2f
2