This blog is an extension of our blog on Credit and Counter Party Risk.

Greetings to all FRM I and FRM II aspirants! As you might be aware, the FRM exam is only two days away now. We hope that your FRM prep has gone according to plan. If it hasnâ€™t donâ€™t worry. You will get enough help from EduPristine! A few important concepts have been given right here so donâ€™t panic. Keep reading and you will feel your fears gradually diminishing.

What is Credit Risk?

â€œThe risk of loss of principal or loss of a financial reward stemming from a borrower’s failure to repay a loan or otherwise meet a contractual obligation. Credit risk arises whenever a borrower is expecting to use future cash flows to pay a current debt. Investors are compensated for assuming credit risk by way of interest payments from the borrower or issuer of a debt obligation.â€

What is Credit Derivative?

â€œPrivately held negotiable bilateral contracts that allow users to manage their exposure to credit risk. Credit derivatives are financial assets like forward contracts, swaps, and options for which the price is driven by the credit risk of economic agents (private investors or governments).â€

### Merton Model

The Merton model evaluates the various components of firm value. The assumptions of Merton value are as follows:-

• The firm has only one liability claim and it does not pay any dividends.
• The financial markets are perfect i.e. there are no taxes and no transaction costs.

The construction of model is as follows:-

• The firm has only one debt issue which is a zero coupon bond with face value F and time to maturity T.
• If the firm is unable to pay the principal at time T, then it is bankrupt and equity holders will not get anything.
• If the value of the firm at time T is VT which is large enough to pay the principal, then the equity holders will get the balance i.e. VT – F

ST = Max(VT – F,0)

### Equity and Debt Payoff in Merton Model

In Merton model, the payoff for equity holders is same as the payoff for a long call option.

The payoff for the debt holder is same as that of the risk free bond and short position in put option.

At the time of maturity, if the VT > F, then the debt holders will receive F.

At the time of maturity, if the VT < F, then the debt holders will receive VT and their payoff will be reduced by F- VT.

DT = F – Max(F – VT ,0)

DT = VT – Max(VT – F,0)

### Value of Equity at Time t

The value of equity at time t is given by the formula:-

Where

V = Value of the firm

F = Face value of the zero coupon bond

Ïƒ = volatility of the firm value

r = annual interest rate

N(d) = cumulative normal distribution function

Credit spread is defined as the difference between the yield on a risky bond and the yield on a treasury bond.

Both the bonds should have same maturity to calculate the credit spread.

Credit spread is calculated by the formula:-

Where:-

T-t = remaining maturity

D = current value of debt

F = face value of debt

Rf = Risk free rate

### Vulnerable Option

A vulnerable option is an option with a default risk.

Without default holder of the option receives:Â

The vulnerable option holder received the promised payment only if the value of the counterparty firm, V, is greater than the required payment.

Payoff from a vulnerable option is:

Value of the vulnerable option can be calculated with the formula:

Where

C = value of the option without default

PD = probability of default

RR = Recovery rate

All the best for your FRM Exam! Do share your experiences with us after the exam.

Disclaimer: Definitions have been cited from Investopedia.