4 ms·

Implied probability of default over a given time-span can be approximated with the equation P = 1 - ( e ^ ( ( -S * t ) / ( 1 - R ) ) where S is the CDS spread a

Implied probability of default over a given time-span can be approximated with the equation P = 1 - ( e ^ ( ( -S * t ) / ( 1 - R ) ) where S is the CDS spread and R is the recovery rate. The spread can be solved using the inverse S = ln ( 1 - P ) * ( ( R - 1 ) / t ) Probabilities and rates are both expressed as percentages not basis points. S is the spread. t is years. R is the recovery rate. Source is my notes from undergrad. Options, Futures, and Other Derivatives (9th Edition) by John C. Hull. Take all this with a grain of salt as I am not a quant. (but I am looking for a job!) Doing some additional reading, there are some more precise approximations but they are less general.[1] Last number I was able to pull up the $CS CDS was trading at 551 BP. Up from 446 yesterday (an all-time high for $CS) Lehman Bros hit 640 BP just days before collapse. [1] https://quant.stackexchange.com/questions/15986/how-to-compute-the-implied-probability-of-default-from-a-cds-spread https://quant.stackexchange.com/questions/15986/how-to-compu...

lordnacho 4y ago
What did you use as the recovery rate? Weird thing about the recovery rate is that everyone I've asked says the same thing, and I've traded CDS: the recovery rate is 40%. It's a bit of a free variable in that equation, and it matters. Trouble is how on earth do you estimate it? But random people I've met in the business will just say 40%, for every issuer, somehow.
- oakwhiz 4y ago
  Sounds like the financial version of dark matter
  - lordnacho 4y ago
    A fudge factor that makes your models agree with observation? Yeah, pretty much. I was never an expert in CDS so I always wondered if other people had better ways of dealing with it. But nobody I've come across has ever offered anything other than 40%.
  - WastingMyTime89 4y ago
    It’s not necessarily. A peculiarity of finance as a field of study is that a lot of the people studying finance only care about direct applications and a lot of the people teaching finance had this mindset when they learnt. It’s easy to end up with some poorly taught material. If you carefully looked at the model which gave rise to the equation you are considering, there probably is a very tangible meaning to the figure everyone is ball parking.
    - itronitron 4y ago
      >> there probably is a very tangible meaning to the figure everyone is ball parking 40 is awfully close to 42
  - curiousgal 4y ago
    Not really. Quants modelled stochastic recovery rates and they saw that it doesn't really add much. Fixed recovery rates work just fine.
- trillic 4y ago
  Yup 40%, it's in the textbook, and as the other commenter nicely put it, it also seems like the financial equivalent of dark matter to me. We are living in times of idiosyncratic risk and my approximations above are likely no better than hearsay. That being said I'm not rushing to buy or sell $CS stock even with my elevated risk tolerance and the seemingly low price.
  - 6stringmerc 4y ago
    I'm very interested in your term "idiosyncratic risk" having worked the Street and particularly fond of synthetics / swaps / GICs / etc. as a platform. My mental picture is a very unsteady hub and spoke like in Wipeout or something where the parties and counter parties are intertwined in ways that the dynamics are, as you put it, idiosyncratic.
  - cuteboy19 4y ago
    What do you mean by idiosyncratic risk here? It seems as though you just read the word in an online forum where it was used in an context free manner. Read through investopedia.com/terms/i/idiosyncraticrisk.asp and tell me how it applies here?
    - jmillikin 4y ago
      It's a bit gutsy to ask someone who casually drops a CDS valuation formula into a conversation to justify themselves against an Investopedia article, as if a retail-oriented content farm is the definitive resource on finance. To answer your question, "idiosyncratic risk" in this context means that an individual company might have problems that don't broadly apply to the rest of its industry. For example Credit Suisse might have management that is bad at running a bank, leading to repeated investment losses and regulatory actions well beyond what's normal for big multinational banks. Look at the CS balance sheets over the past few years, or its stock price and PE ratio, or hell just Google "Credit Suisse books loss" and look at how many times they tried to stick their fingers in the wrong cookie jar. They got hit by the Hwang thing, they got hit by Greensill, and apparently they can't even accurately report how much money they're making (losing). I wouldn't want to have any position on their equity either.
- acchow 4y ago
  The recovery rate is written down in the terms of the swap. You'll have to read the contract.
time_to_smile 4y ago
Thanks for sharing this. Quantitative finance really is a fascinating field, not because it will make you rich, but because you can dive much deeper into understand exactly what the market believes about the probability of different events. Of course what the market believes doesn't have to be correct, but nonetheless very interesting to dive into.
deleted 4y ago
[deleted]
nafey 4y ago
Coincidentally, I am in a class being conducted by John C. Hull right now as I type this comment.
- chasd00 4y ago
  Put your phone down and pay attention! ;)
hd95489 4y ago
They should have another factor for government shenanigans where a entity defaults but the cds isn’t recognized as a default
omgomgomgomg 4y ago
Can you check how that data looked for ubs and CS before they habe been bailed out? I am certain the Swiss government will bail them out, direct democracy be damned.
- slt2021 4y ago
  Switzerland's wealth is tied to the reputation of their banks being top tier. Swiss bankers already lost a lot of customers to US banks, letting CS fail would have very bad consequence on Swiss economy long term

lordnacho 4y ago

What did you use as the recovery rate? Weird thing about the recovery rate is that everyone I've asked says the same thing, and I've traded CDS: the recovery rate is 40%. It's a bit of a free variable in that equation, and it matters. Trouble is how on earth do you estimate it? But random people I've met in the business will just say 40%, for every issuer, somehow.

oakwhiz 4y ago
Sounds like the financial version of dark matter
- lordnacho 4y ago
  A fudge factor that makes your models agree with observation? Yeah, pretty much. I was never an expert in CDS so I always wondered if other people had better ways of dealing with it. But nobody I've come across has ever offered anything other than 40%.
- WastingMyTime89 4y ago
  It’s not necessarily. A peculiarity of finance as a field of study is that a lot of the people studying finance only care about direct applications and a lot of the people teaching finance had this mindset when they learnt. It’s easy to end up with some poorly taught material. If you carefully looked at the model which gave rise to the equation you are considering, there probably is a very tangible meaning to the figure everyone is ball parking.
  - itronitron 4y ago
    >> there probably is a very tangible meaning to the figure everyone is ball parking 40 is awfully close to 42
- curiousgal 4y ago
  Not really. Quants modelled stochastic recovery rates and they saw that it doesn't really add much. Fixed recovery rates work just fine.
trillic 4y ago
Yup 40%, it's in the textbook, and as the other commenter nicely put it, it also seems like the financial equivalent of dark matter to me. We are living in times of idiosyncratic risk and my approximations above are likely no better than hearsay. That being said I'm not rushing to buy or sell $CS stock even with my elevated risk tolerance and the seemingly low price.
- 6stringmerc 4y ago
  I'm very interested in your term "idiosyncratic risk" having worked the Street and particularly fond of synthetics / swaps / GICs / etc. as a platform. My mental picture is a very unsteady hub and spoke like in Wipeout or something where the parties and counter parties are intertwined in ways that the dynamics are, as you put it, idiosyncratic.
- cuteboy19 4y ago
  What do you mean by idiosyncratic risk here? It seems as though you just read the word in an online forum where it was used in an context free manner. Read through investopedia.com/terms/i/idiosyncraticrisk.asp and tell me how it applies here?
  - jmillikin 4y ago
    It's a bit gutsy to ask someone who casually drops a CDS valuation formula into a conversation to justify themselves against an Investopedia article, as if a retail-oriented content farm is the definitive resource on finance. To answer your question, "idiosyncratic risk" in this context means that an individual company might have problems that don't broadly apply to the rest of its industry. For example Credit Suisse might have management that is bad at running a bank, leading to repeated investment losses and regulatory actions well beyond what's normal for big multinational banks. Look at the CS balance sheets over the past few years, or its stock price and PE ratio, or hell just Google "Credit Suisse books loss" and look at how many times they tried to stick their fingers in the wrong cookie jar. They got hit by the Hwang thing, they got hit by Greensill, and apparently they can't even accurately report how much money they're making (losing). I wouldn't want to have any position on their equity either.
acchow 4y ago
The recovery rate is written down in the terms of the swap. You'll have to read the contract.

time_to_smile 4y ago

Thanks for sharing this. Quantitative finance really is a fascinating field, not because it will make you rich, but because you can dive much deeper into understand exactly what the market believes about the probability of different events. Of course what the market believes doesn't have to be correct, but nonetheless very interesting to dive into.

deleted 4y ago

[deleted]

nafey 4y ago

Coincidentally, I am in a class being conducted by John C. Hull right now as I type this comment.

chasd00 4y ago
Put your phone down and pay attention! ;)

hd95489 4y ago

They should have another factor for government shenanigans where a entity defaults but the cds isn’t recognized as a default

omgomgomgomg 4y ago

Can you check how that data looked for ubs and CS before they habe been bailed out? I am certain the Swiss government will bail them out, direct democracy be damned.

slt2021 4y ago
Switzerland's wealth is tied to the reputation of their banks being top tier. Swiss bankers already lost a lot of customers to US banks, letting CS fail would have very bad consequence on Swiss economy long term