Why Option Pricing Models are Wrong for Tax-exempt Issuers (Part 2)

Posted by Peter Orr on Feb 06, 2015

In Part 1 (a suggested read if you’re getting to this article first) we proposed 3 questions that determine whether bond option pricing models, in contrast to real-world option models, are appropriate for tax-exempt issuers analyzing their callable bonds:

1) Is the market for all components of the option complete (defined in context below)?

2) Are markets for the items in 1) free of arbitrage profit due to trading activity sufficient to drive such profits to zero?

3) Is the purpose for using the model one of pricing and/or hedging?

Reviewing the bidding for our beloved tax-exempt/muni  market, we have a “Maybe” on 1) and a solid “Absolutely Not” on 2).1 This brings us to question 3), one of the least discussed but critically important questions for understanding suitability. Is the purpose for using the model by issuers one of option pricing and hedging? Or is it more aptly described as risk and/or performance management? Are munis simply figuring out the right hedging strategy to implement so they can make an arbitrage-free option price? That doesn’t sound like a muni or tax-exempt borrower to me; that sounds like an options dealer.2

Aren’t munis taking real risk in managing these call features? Of course they are. TheySee the light aren’t running some sort of matched options book (which in munis, doesn’t exist anywhere anyway). Issuers own a bunch of options through the sale of callable bonds, and in trader parlance, they are naked long. Refund too early and the opportunity for greater budgetary benefit may be precluded; refund too late and an attractive interest rate market may never return. It is decidedly not a simple engineering exercise of coming up with an option price based on highly liquid underlying instruments, predicated on conditions that, in muniland, just do not exist. So the answer to 3) is also an unmistakable, “Not remotely.”3 

But here let me circle back to the original LinkedIn question and provide a nice piece of research germane to the topic of fixed-income option model suitability. It is by two of the world’s foremost authorities on yield curve models, Riccardo Rebonato and Sanjay Nawalkha. The article is both free and meaningfully titled, “The Right Interest Rate Models to Use: Buy Side vs Sell Side” published in the Journal of Investment Management, 2011.   

The points made in the paper apply more broadly than to just tax-exempt entities. But as I explained in the first article on this topic, this is where we need to go to learn about lawnmower engines and how they might work in a go-kart. Though the paper focuses on one particular type of option pricing model, the popular LMM-SABR model, the points made about option pricing models being “useless at best and dangerous at worst for the buy-side institutions” are completely general and unnequivocally apply to tax-exempt borrowers.

The Cliff’s Notes: tax-exempt borrowers clearly fit into the paper’s “Buy-side.” Unlike dealers, buy-siders “are not in the business of making money by ’trading’ interest rate derivatives while maintaining zero interest rate exposures. This is the major difference between sell-side dealer banks and the buy-side borrowers and investors.” The authors further go on to describe “less sophisticated buyers such as, cities, counties, foundations, charities,…etc.” So tax-exempt issuers are clearly in the “buy-side.” Easy enough.

Cutting to the chase, the authors then say “…buyside practitioners and sellside banks need different types of interest rate models.” The buy-side institution “is interested in knowing whether the derivative is priced too cheaply or too expensively by a realistic model that can simulate the risk and return trade off under the physical measure.” Translation: issuers need a real-world (synonymous with “physical measure”) model  to provide an estimate of value to compare to what the market might provide. As an aside, we think the best practice version of this uses the issuer’s actual refunding criteria, something that is accomplished naturally with a suitable real-world model.   

To be clear, these models that buyers (tax-exempt issuers) should use are not arbitrage-free pricing models such as Black-Derman-Toy, Black-Karacinski, or Hull-White. Buyers need a real-world (physical measure) interest rate options model like Bernadell, Coche, Nyholm (2005), Rebonato (2002, ppt file), or the more powerful one we use to calculate Refunding Adjusted Yield (RAY), Deguillaume-Rebonato-Pogudin, 2013. 

But most municipal market practitioners know this, even if they don’t have the technical background to explain exactly why. If decades-old option pricing models really applied so neatly to tax-exempts than bankers, financial advisors, salespeople, traders and issuers would’ve been using them successfully for years. But the vast majority of them have not, and rightly so. Now with truly appropriate and far more powerful alternatives available, why should they?


1In the words of MMA's Matt Fabian at today's Municipal Analyst Group of NY lunch, "There's only one way to short munis; and that's don't own munis."

2But of course there can be no real option dealers in the muni market because the answers to questions 1) and 2) are a joint “No” to begin with. 

3The fact is, even if the answer to 1) and 2) had been a resounding “Yes”, if the answer to 3) is a “No”, then option pricing models would still not be appropriate. The answer to all 3 must be “Yes” for option pricing models to be appropriate.