hw3sol

# hw3sol - Introduction to derivatives Fall 2011 BUSI 588...

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Introduction to derivatives, Fall 2011 BUSI 588, Homework 3 solutions Homework 3 solutions 1. (*) The up and down movements in the tree are u = 1 . 35 and d = 0 . 8. Moreover, r = 1 . 05 1 / 6 = 1 . 00816. From these are the risk-free rate one can back out the risk-neutral probabilities ˆ p u = r- d u- d = 1 . 00816- . 8 1 . 35- . 8 = 0 . 3785; ˆ p d = 0 . 6215; as well as the binomial evolution of the S&P500 over the next four months. 100 135 182.25 80 108 64 Using these, one can work backwards through the tree and backout the value of the call option with a strike of \$100. 15.30 35.81 82.25 3.00 8.00 0.00 (a) A good estimate of the call value seems \$15.30. (b) If the S&P 500 went up in value of the first two months I would value the call at \$35.81; whereas if the S&P 500 went down in value the estimate would be \$3.00. (c) The replicating portfolio at date t = 0 is comprised of Δ units of the S&P500 and B dollars in cash, such that Δ135 + B 1 . 00816 = 35 . 81; Δ80 + B 1 . 00816 = 3 . 00; so that Δ = 0 . 596 and B =- 44 . 35. If we were long the call and wanted to hedge (i.e. eliminate all exposure to the S&P500), then we would like to take a short position in the S&P500 (for 0 . 596 shares), and lend 44 . 35. This portfolio would have to be rebalanced in two months time depending on whether the S&P 500 went up in value or not: • If the S&P 500 went up in value in the first two months, then in order to replicate the payoffs at maturity of the call option we would need to invest in Δ u units of the S&P500 and B u dollars in cash, such that Δ u 182 . 25 + B u 1 . 00816 = 82 . 25; Δ u 108 + B u 1 . 00816 = 8 . 00; so that Δ u = 1 and B u =- 99 . 19. • If the S&P 500 went down in value in the first two months, then in order to replicate the payoffs at maturity of the call option we would need to invest in Δ d units of the S&P500 and B d dollars in cash, such that Δ d 108 + B d 1 . 00816 = 8; Δ d 64 + B d 1 . 00816 = 0; so that Δ d = 0 . 18 and B d =- 11 . 5....
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

hw3sol - Introduction to derivatives Fall 2011 BUSI 588...

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

View Full Document
Ask a homework question - tutors are online