RMS4007_HW1

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

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

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