07
Aug
Importance of d2 in Black-Scholes to Merton Model in Credit Risk – 10 min screencast
by David Harper, CFA, FRM, CIPM
Based on a forum conversation yesterday, I explain N(d2) in the Black-Scholes and its relation to the Merton Model in credit risk. Highlights:
- In Black-Scholes, N(d2) is the probability that the option will be struck (S > K) in the risk-neutral world.
- The Merton model for credit risk uses the Black-Scholes by treating equity as a call option on firm assets. In Merton, d2 becomes the “distance to default.” The d2 is the same as in the Black-Scholes given the correspondences (i.e., firm asset value = stock price, default threshold = strike price), except the riskless rate is replaced by the expected growth (return) in firm’s assets.
- By this translation, d2 becomes the distance to default (DD), N(d2) becomes the probability that the firm’s asset value will exceed the default threshold at period’s end, such that N(-d2) becomes the probability of default.
- KMV uses the Merton model that I review here, basically, with two key differences: first, the development of the option pricing inputs (i.e., firm asset value and asset volatility) are non-trivial. Second, as I note at the end, KMV does not get EDF by assuming normality; i.e., Moody’s KMV EDF is not N(-d2). Rather, they use d2 (i.e., distance to default) and map it to an EDF based on their proprietary database.
Screencast:
Comments
Thank you for this perfectly understandable explanation about the Merton model for credit risk. As a Dutch student following my master in Financial Economics, this explanation really helped me a lot in understanding how to calculate and understand credit risk according to Merton’s model, which I need to know for the course Financial Risk Management!
Great work!
Robert
Hello David, in the above video you said d2 is the distance to default and “N(d2) is the probability of default”. I’m not sure about this because I thought N(d2) is the probability that the option will expire in the money, whereas N(-d2) is the probability of default. Thanks!
Hi Jack,
Yes, I did mispeak later in the video. As I blogged above and say at the beginning “In Black-Scholes, N(d2) is the probability that the option will be struck (S > K) in the risk-neutral world.” Thanks, David
please be advised that I would like to download screencaset, so please tell me how.
best regardes
Nice movie!
Could you explane the meaning of the following case to me?
I take: Exp return (mu) = 0% and Firm Value (V) = FV Debt (F) = $100.000
Now from the picture you draw I would excpect in this case : d2 = 0
However this is not the case, when I use the formula I get d2 = -1/2 σ√T
What is my misunderstanding????
Love your posts! But I was trying to add your RSS feed and your posts were coming up cut off. Know how I can fix that?
-Bruno
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