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zpablo24
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Joined: April 4th, 2019, 12:45 pm

Callable debt

April 17th, 2019, 4:13 pm

Any good models out there for pricing callable debt ? I tried using Hull-White with a yield curve based on credit spreads for noncallable issues, but my callable prices look too low. It has been suggested to me that the credit risk needs to be modeled more explicitly.
 
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Jhammer
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Joined: February 24th, 2014, 8:05 pm

Re: Callable debt

April 18th, 2019, 7:51 pm

Your question is not clear enough, neither is your proposed approach! callable bonds are usually priced by an IR pricing tree. It may also be possible to price the callable bond synthetically.
 
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bearish
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Re: Callable debt

April 19th, 2019, 12:18 pm

The ingredients of a good model for callable corporate bonds are yield curve dynamics, credit dynamics, and a model of call behavior as a function of the refinancing benefit. To start with the last one, you could use the classic textbook approach of setting the bond value equal to the minimum of the continuation value and the call price, but this will tend to overvalue the call option and assign the bond a bit too much duration. A better approach is to build in some refinancing costs or to borrow an empirical prepayment function from the mortgage world. You can model the credit dynamics via a stochastic hazard rate or by some asset value driven default process like Black & Cox or (more ambitiously) Duffie & Lando. Since most callable bonds are found in the HY space, the interest rate model choice is less important than what you assume about the credit behavior, so it would make sense to keep it fairly simple. Also, importantly, regardless of details of your credit and prepayment modeling choices, you will at best get a rough estimate of the value of the embedded call option, since you will be relying on several parameters that are impossible to estimate precisely. Ignoring the problem, e.g. by assuming a constant credit spread, will give you an imprecise estimate that is furthermore biased...
 
zpablo24
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Joined: April 4th, 2019, 12:45 pm

Re: Callable debt

April 19th, 2019, 5:05 pm

Thanks bearish thats really helpful. I started with the fixed credit spread model, which seemed to be overpricing the callables by 10-15 bp (these are better credits but some longer dated). I found some papers by Acharya and Carpenter and also Berndt which use structural and reduced credit models, but so far all I have implemented is HW IR with stochastic credit (i was using Numerix hybrid pricers). With enough negative correlation i can get to market prices but I am not sure if that means much. The derivatives guys I work with think I am making this too complicated but the issue arose because we were looking at 30y zero coupon callables and valuations on the static credit curve were Imconsistent with where these issues seem to swap. It is sort of funny how the guys trading callables just accept whatever OAS things seem to trade at, without wondering about any analytical explanation.
 
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Pat
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Re: Callable debt

April 19th, 2019, 11:21 pm

1. The key question is how to price a European option on the bond. If you can price the European option, then expanding this to a Bermudan pricing model is reasonably straight forward. The key pricing step is usually calibrating the Bermudan model so that it matches the European prices exactly.

2. The pricing model really depends on the objective. Are you trying to determine the price from first priinciples? Or match a model's price to the market price to get the hedges? Or to compare bonds against one another?.Each one requires a different type of model
 
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Pat
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Re: Callable debt

April 20th, 2019, 2:39 am

For example, a common use of models is to compare bonds against each other. Would I prefer the Las Vegas Water Authority Bonds, or the Mesa Ariz School District Bonds? Not only do the borrowers have different credit spreads, but the bonds usually have different callability features. One model is just to tack a constant spread to Libor, and price the bond using the firm's Bermudan pricer, finding the spread which yields the market price. This effectively prices out the financial features (callability etc.), and by comparing the spreads against each other one is effectively comparing like to like. I.e., the the Las Vegas bonds might be prices at 165bps and 225 bps over Libor, but once the callability of the bonds priced out, the "true" spread of the bonds might be 165 and 175 ... After considering the credit quality of both issuers, one might make a different preference using the "true" spreads instead of the raw spreads
 
 
zpablo24
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Joined: April 4th, 2019, 12:45 pm

Re: Callable debt

April 20th, 2019, 1:44 pm

Thanks Pat. I am really trying to get my arms around why those implied libor spreads are what they are for callables. For example my callable agency traders explained to me that using bloomberg oas functionality with the LGM pricer doesnt really work so they switch to a european exercise and then override the volatility with an unrealistically low number. I have heard similar approaches used for convertibles. So i was wondering if there was any theoretical justification for why these embedded options are cheap. I think bearish is saying that more sophisticated credit modeling and attention to the early exercise decision can get you there, but there will always be some parameters that you are basically calibrating to the specific bond. Jarrow 2008 reduced form approach is just to model the credit and call empirically and that is what is built into kamakura risk manager. Maybe that is just as good.
 
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bearish
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Re: Callable debt

April 20th, 2019, 9:14 pm

By curious coincidence, pat wrote that Bloomberg LGM pricer... My main points were really just that the call options embedded in a typical US corporate bond are more driven by credit spread changes than by default free interest rate changes, and that assuming “ruthlessly efficient” exercise of the options is not well supported by empirical observations.
 
zpablo24
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Posts: 5
Joined: April 4th, 2019, 12:45 pm

Re: Callable debt

April 23rd, 2019, 1:26 pm

So the superficially intuitive application of the usual berm pricer to a static credit curve results in off-market prices for corporate debt probably because of unrealistic embedded assumptions regarding the interaction between call decisions and credit, and there doesn’t seem to be a market standard way to address this deficiency. On the other hand, the more empirical OAS approach is widely used for relative-value analysis and hedging, the major drawback being that the spreads seem somewhat arbitrary, and can be difficult to determine before hand. Although the poor liquidity/transparency of this market has probably enabled this situation to persist, isn’t it likely that more sophisticated RV investors and also potential electronic market makers will bring in better models ?
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