The Essentials of Risk Management, Second Edition, 2nd Edition

Appendix 11.1

THE BASIC IDEA OF THE REDUCED FORM MODEL

Consider a defaultable zero-coupon debt instrument issued by a corporation with a promised payment at maturity, say one year, of $100.

Notations:

RR: recovery rate as a percentage of the promised payment = 1 – LGD (loss given default)

PD: one-year risk-neutral probability of default¹

i: one-year risk-free interest rate

y: one-year risk-adjusted yield

P: zero-coupon bond price

There are two approaches to value this defaultable zero-coupon bond:

• The risk-neutral valuation where expected cash flows (using risk-neutral probabilities) are discounted at the risk-free rate:

• The risk-adjusted ...