Forums > Pricing & Modelling > Default probabilities from equity/equity vol

 Page 1 of 1
Display using:
 Rookie_Quant Total Posts: 757 Joined: Jun 2004
 Posted: 2017-07-20 17:16 Suppose I wanted to obtain the default probability of a firm in two ways, and plot the difference in the two. It's straightforward to pull default probabilities (in a loose sense) from CDS spreads, but is there a way to do this with equity and/or equity option data?Merton gives some framework for this, assuming zero recovery for equity and i've seen a few extensions to account for non-zero equity recovery.Bottom line question is: can I find an equation or estimation of default probability using only equity market data in the same way I can "translate" cash bond spreads into a CDS-equivalent for purposes of calculating a basis?**EDIT**I have a Carr and Wu (2011) method that is easy to replicate for turning put option data into default probabilities. My more technical question is how does mis-estimation of the recovery rate on the CDS side of the trade impact the equity side of things? What are some of the biases relating to recovery rate that I'm introducing by calculating a measure of, say, CDS_p(default) - Put_p(default)? "These metaphors and similes aint similar to them, not at all." -Eminem
 ronin Total Posts: 435 Joined: May 2006
 Posted: 2017-07-21 12:57 The short answer is no.Merton says that a company defaults when its equity is worthless. So if you go by Merton, you are estimating when the share price will hit 0.Carr and Wu have replaced that with share price hitting some crash put strikes above zero. That is all OK in theory.In reality, crash puts are a mug's game. Nobody makes money buying crash puts, and in the long run nobody makes money selling them either. Plus, liquidity in crash strikes is non-existent and information content in prices is zero. "There is a SIX am?" -- Arthur
 baghead Total Posts: 865 Joined: Sep 2004
 Posted: 2017-07-21 13:39 one would need to observe three implied vols from the skew and iteratively solve for Merton's asset vol, leverage and implied time to expiry to derive an implied credit spread from Equity vol data.Basically, you assume that an Equity option is a compound option in the Merton world (because the underlying Equity is an option on the assets)https://pdfs.semanticscholar.org/ea63/ddf598935b40f5f6e520a896f84997e7fdb7.pdfI looked at 30 European high yield companies around 2004 but the relationship between implied credit spreads from Equity vol data and CDS was very weak.
 ronin Total Posts: 435 Joined: May 2006
 Posted: 2017-07-21 14:49 Just to add to that.Lots of people have tried trading CDS v puts in the past. It was called Capital Structure Arbitrage. It was big in 2006. By 2009, pretty much every desk that was doing it was dead, buried and forgotten. When it came to the crunch, real world turned out to be a bit more complex than a simple one factor model. "There is a SIX am?" -- Arthur
 Cheng Total Posts: 2864 Joined: Feb 2005
 Posted: 2017-07-21 15:42 I guess the Merton model is the canonical way to go. But... you have to estimate the default barrier (how do you account for short term debt? Moody's KMV used all long term debt + 50% short term debt iirc) and what would happen if the default barrier is crossed between two coupon dates (if you can't pay but you don't have to there is no default, no? Almost Zen like...)? Finally I would guess that there are some pricing differences between the two markets and that prices don't always fit exactly. Ages ago there was a product called Equity Default Swap, which was basically a one-touch put in disguise, that should mimic CDS in equity land but it never gained any traction afaik. "He's man, he's a kid / Wanna bang with you / Headbanging man" (Grave Digger, Headbanging Man)
 Cheng Total Posts: 2864 Joined: Feb 2005
 Posted: 2017-07-21 15:43 Lesson for today: press F5 before answering. I second Ronin on capital structure arbitrage... *coughcough*big bs*cough* "He's man, he's a kid / Wanna bang with you / Headbanging man" (Grave Digger, Headbanging Man)
 baghead Total Posts: 865 Joined: Sep 2004
 Posted: 2017-07-21 17:34 Equity vs Credit used to be (still is?) very popular in indices on an intra-day basis picking off itrx/cdx market makers and for distressed companies.
 NIP247 Total Posts: 545 Joined: Feb 2005
 Posted: 2017-08-07 16:22 Old paper from JPM ( 2010 ) requested here and provided here.Have great deal of respect for Einchcomb, although I'm always skeptical of big "arbitrage" models; market disruptions tend to overshadow any collection of pennies. The article can serve as a framework at least. NP Practitioners can probably give a more informed feedback...[ EDIT: saw that Baghead had already commented on the article at the time and found it not to be useful... ] On your straddle, done on the puts, working the calls...
 ronin Total Posts: 435 Joined: May 2006
 Posted: 2017-08-18 22:07 The basic principle is actually pretty sound. If you price all the cash flows in an entity accurately, you can value its equity and debt. If you can do that, then surely you can judge when they are relatively cheap or expensive.But it all goes sharply downhill from there.The problem is that the practical challenges are enormous. At one point we did that sort of modelling for some simple project SPVs. The thing is, even for simplest project SPVs imaginable - say a commercial office building funded with a single floating rate loan - you would have to model a minimum of 10-20 correlated factors. Some of the factors can be calibrated to some market parameters, but most can't.For any type of non-trivial corporate, the number of factors would go into millions. Good luck with that sort of model. "There is a SIX am?" -- Arthur
 Rookie_Quant Total Posts: 757 Joined: Jun 2004
 Posted: 2017-08-29 04:08 thanks to all who weighed in. Gave me plenty to think about for sure. "These metaphors and similes aint similar to them, not at all." -Eminem
 nikol Total Posts: 639 Joined: Jun 2005
 Posted: 2017-09-08 16:57 Finkelstein / CreditGrades extends Merton with use of threshold. Feature of this model that its credit spread gets into singularity at t->0. Can be fixed, but also don't forget about ivol structure etc etc (I never tried though)
 Page 1 of 1