文档介绍：Chapter 12 On the Pricing of Corporate Debt
Chapter 12: On the Pricing of Corporate Debt
XingluanHuang
Department of Finance, XMU
123>.1 Introduction
The value of corporate debt depends on essentially on
The required rate of return of riskless debt;
The various provisions and restrictions contained in the indenture;
The probability of default.
The purpose of this chapter is to present a theory of the risk structure of interest rates.
On the pricing of corporate liabilities
Some assumptions:
There are no transactions costs, taxes, or problems with indivisibilities of assets.
There are sufficiently many investors parable wealth levels.
There exists an exchange market for borrowing and lending at a same rate of interest.
Short-sales of all assets, with full use of the proceeds is allowed.
Assumptions (con.)
Trading in assets takes place continuously in time.
The MM theorem obtains.
The term structure is “flat” and known with certainty.
The dynamics for the value of the firm, V, can be describer as:
Where is the instantaneous expected rate of return on the firm per unit time;C is the total dollar payouts by the firm per unit time to either its shareholders or liabilities-holders if positive, and it is dollars received by the firm from new financing if negative; is the instantaneous variance of the return on the firm per unit time;and dz is a standard Gauss-Wiener process.
Suppose there exists a security whose market value Y =F(V, t).
Comparing terms in () and ()
Forming a three-security portfolio
Let:
W1 be the number of dollars of the portfolio invested in the firm;
W2 be the number of dollars invested in the particular security;
W3 (= -W1+W2) be the number of dollars invested in riskless debt.
If dx is the instantaneous dollar return to the portfolio ,then
Choosing W*
Substituting for
Remark on ()
Equation () must be satisfied by any security whose value can be written as a function of the value of the firm a