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 hasn’t don’t worry. You will get enough help from EduPristine! A few important concepts have been given right here so don’t panic. Keep reading and you will feel your fears gradually diminishing.
What is Credit Risk?
“The 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.”
What is Credit Derivative?
“Privately 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).”
The Merton model evaluates the various components of firm value. The assumptions of Merton value are as follows:-
The construction of model is as follows:-
ST = Max(VT - F,0)
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)
The value of equity at time t is given by the formula:-
V = Value of the firm
F = Face value of the zero coupon bond
σ = 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:-
T-t = remaining maturity
D = current value of debt
F = face value of debt
Rf = Risk free rate
A vulnerable option is an option with a default risk.
Without default holder of the option receives:
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:
C = value of the option without default
PD = probability of default
RR = Recovery rate
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Disclaimer: Definitions have been cited from Investopedia.
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