sheet01 - J. Wissel Financial Engineering with Stochastic...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
J. Wissel Financial Engineering with Stochastic Calculus I Fall 2010 Assignment Sheet 1 1. Consider a one-period ( N = 1) binomial model for one bond and one stock with 0 < d < u and 0 < p < 1. At t = 0 we set up a portfolio of η 0 bonds and Δ 0 stocks and hold these positions until t = 1. We allow η 0 , Δ 0 R , i.e. we allow long and short positions in bond and stock. a) Show that if 1+ r u , we can choose η 0 , Δ 0 such that our initial portfolio value is X 0 = 0, and the value X 1 at time 1 is nonnegative with probability 1 and positive with positive probability. b) Show that if 1+ r d , we can choose η 0 , Δ 0 such that our initial portfolio value is X 0 = 0, and the value X 1 at time 1 is nonnegative with probability 1 and positive with positive probability. c) Now suppose d < 1 + r < u . Show that if our initial portfolio value is X 0 = 0, then either X 1 = 0 with probability 1, or X 1 is negative with positive probability. Remark:
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/25/2011 for the course ORIE 5600 at Cornell University (Engineering School).

Page1 / 2

sheet01 - J. Wissel Financial Engineering with Stochastic...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online