RMS4007_HW1

RMS4007_HW1 - (1976 introduce the default barrier H...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
RMS 4007 Risk Mangement with Derivatives Concepts Assignment 1 Due date: 27 September, 2010 1. When a firm has only one future promised payment, D , at time T , the Merton model of default risk derives that the market value of equity, S t , is a standard call option on the firm’s value, V t , while the market value of debt, B t is the risk-free bond less a put option on the firm. Answer the following questions based on the Merton model. (a) Show that S t V t S t + De - r ( T - t ) . (b) Merton (1974) argued that the Black-Scholes option pricing for- mula can be used to calculate the market value of equity and the market value of debt. What are the weaknesses of using the Black-Scholes formula? (c) Suppose that the market value of the firm follows a geometric Brownian motion. Show that the credit spread will be widen when the default probability increases. (d) Under the model setting of Merton (1974), explain why sharehold- ers are encouraged to run a risky business and it is a disadvantage to debtholders. 2. The shortcomings of the Merton (1974) model makes Black and Cox
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (1976) introduce the default barrier, H . Whenever the firm value hits the downside default barrier, a default event is triggered, and debt holders will own the firm upon default. Under the Black-Cox model, the market value of equity becomes a down-and-out (DOC) call option on the firm with strike price D and barrier level H . Answer the following questions based on the Black-Cox model. (a) The debtholders’ position can be fully replicated by a long position of a default-free bond, a short position of a put option and a long position of a barrier option. What is that barrier option? (b) Other things being fixed, show that the DOC option price in-creases from 0 to the standard call option price when the barrier level H decreases from V t to 0. (Hint: You may use no-arbitrage arguments.) (c) Show that, if V t = S t + D , then H > D . What is the problem with this consequence? 1...
View Full Document

This note was uploaded on 04/22/2011 for the course RMSC 4007 taught by Professor Wonghoiying during the Spring '11 term at CUHK.

Ask a homework question - tutors are online