640:495 Mathematical Finance;
PROBLEMS
Fall, 2006
I. Problems on interest and compounding. Consider an investment of V0 today that pays back V1 at the end of one year. We make two denitions. The total annual return of this investment is R= V1 V0
(Note: th
640:495 Mathematical Finance;
PROBLEMS
Fall, 2006
16-19. Problems 1,2,3,4 on page 29 of Stami and Goodman. 20,21. Problems 1,2 on page 38 of Stampi and Goodman. 22. In class, we show geometrically that in the one-period model there is no arbitrage if and
640:495 Mathematical Finance;
PROBLEMS
Fall, 2006
16-19. Problems 1,2,3,4 on page 29 of Stami and Goodman. 20,21. Problems 1,2 on page 38 of Stampi and Goodman. 22. In class, we show geometrically that in the one-period model there is no arbitrage if and
640:495 Mathematical Finance;
PROBLEMS, III
Fall, 2006
31. In each case, data are given for a one-period binomial model with a stock, a risk free interest rate, and a derivative. Determine whether there is a risk-neutral measure. If there is not, explain
640:495 Mathematical Finance, Problem Solutions and Hints. 45. In class we stated the following special case of a fundamental fact about expectations and conditional expectations. Consider the binomial tree model with N periods and some (arbitrary) assign
640:495 Mathematical Finance, Problems. In class we discussed the fact that if (Y1 , . . . , Yn ) and (Y1 , . . . , Yn ) are functions of Y1 , . . . , Yn , then, abbreviating them by and , we have the identity E [ + X | Y1 , . . . , Yn ] = + E [X | Y1 , .
640:495 Mathematical Finance, Problems. 58. Show that if X N (m, 2 ), then aX +b N (am+b, a2 2 ). (See, online notes on Normal random variables and the Central Limit Theorem, http:/www.math.rutgers.edu/courses/495/lect18notes.pdf, page 2.) 59. Show that i
640:495 Mathematical Finance, Problems Itos rule. In class we gave a prescription called Itos rule for nding d[f (Xt , t)] if dXt = t dt + t dBt , where B is a standard Brownian motion. This rule had to do with using Taylor polynomial approximations, and
640:495 Mathematical Finance, Problems 88. Consider an option that pays $1 if ST > X and 0 otherwise, where S is the price of an underlying stock. This is the cash or nothing option. For notation, let 1(X,) (x) = 1, if x > X; 0, otherwise,
denote its payo
Financial Mathematics 640:495
Lecture 1 Slides
I. SCOPE OF COURSE Financial Mathematics, broadly dened, is the application of mathematics to modeling and analysis of nancial markets and to aiding management of nancial resources. In this course, We will fo
Financial Mathematics, 640:495: Lecture 2
Sample Problems 1. Alice is short a European put on XYZ stock at strike $30. The selling price is $4. Under what circumstance does Alice gain? The net payo of a put to the short position is c maxcfw_X ST , 0 where