Why Option Pricing Models are Wrong for Tax-exempt Issuers (Part 1)

Posted by Peter Orr on Feb 03, 2015

"It's not how we make mistakes, but how we correct them, that defines us."  - Anonymous

The other day I was asked in the Tax-Exempt Debt Structuring (TEDS) group on LinkedIn to provide some "scholarly" references (outside of our own) that support my comment that “option pricing models are inappropriate for issuer’s use in looking at option value or refundings.” To put a finer point on it, there are two main types of option models: pricing models or more accurately, relative pricing models (some regrettably call these “standard” models as if anything else is non-standard) and real-world models. The question at hand is which type of model is the right one for tax-exempt issuers, or any bond issuer for that matter, to use when analyzing their optional redemption features.   We’ve been dancing around this topic for a while now and think it’s time the matter was set definitively straight.1

The original LinkedIn question to me was odd as it stipulated the reference(s) should be from the narrowWhoops realm of municipal finance alone, a notoriously sparsely researched area (no offense, MFJ). Let me analogize briefly to explain why this is silly. Let’s say we live in a world with only engineless go-karts. Then someone comes along and says, “Hey we have these great things called ‘lawnmower engines’ and they’ll really make these go-karts go!” The LinkedIn question is akin to saying, “Show me some literature from the engine-less go-kart community that says these lawnmower engines are inappropriate for us.”  Doesn’t make much sense, right? Why would anyone from the engineless go-kart community publish such a thing in the first place? In order to properly answer the question we’d need to comb the annals of the Journal of Lawnmower Engines to study up on details of the engines, the conditions under which they work properly, their weight, the torque they deliver, etc. Only with that information in hand, coupled with our knowledge of engineless go-karts, could we ascertain whether small engines and unpowered go-karts would indeed be a winning combination.

All that’s to say we better learn something about bond option pricing models generally if we’re going to determine whether they make any sense for municipal and tax-exempt issuers. And so we have. The fact that option pricing models are the wrong ones for issuers is obvious if you look at three simple questions. The applicability and suitability of option pricing models to any situation rests on a "Yes" answer to all of these basic questions:

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

In the remainder of this article we’ll address 1) and 2) as these speak to the foundational assumptions for any option pricing model to be valid. Question 3) we’ll save for tomorrow’s second and final installment.

  1) Is the market for all components of the option complete?

For standard option pricing models to apply the market must be complete. This means in essence that there are non-call bonds of the issuer in question trading across all relevant parts of the non-call yield curve and without “friction.” What are the relevant parts? The parts that cover the term of the option being modeled. Now some could argue that we can write a non-call yield scale for an issuer, which is true. But writing some best-guess, non-call tax-exempt scale is a far cry from having the full complement of non-call bonds across the curve to trade, both to buy and sell short. Andrew Ang et al discuss the difficulty of selling munis short in their paper, Taxes on Tax-exempt Bonds (more below). And we won’t even mention the “frictions” involved in trading munis. So the answer to 1) is probably a “Not really” but let’s just be charitable and call it a “Maybe...sort of”.  

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

So with the answer to 1) wobbly at best, let’s look at Question 2). Are muni markets free of arbitrage profits? Pose this question to any muni salesperson, trader, investment banker or professional investor and wait for the belly laugh. This is a non-starter. You can’t short munis due to the tax-treatment. And the one flavor of research you could call plentiful in the muni market is the type that concludes with some variety of, “It’s inefficient”, “It’s fragmented”, “It’s unhedgeable”, “It’s expensive” or “It’s broken” You could imagine someone trying to mistakenly argue that it’s arbitrage free, by virtue of the simple fact that you can’t implement an arbitrage trading strategy that captures a bond’s mispricing to begin with. But that’s not arbitrage free, that’s just prohibitively expensive and insufficiently tradable. To quote Ang et al, in Taxes on Tax-exempt Bonds,

"Unlike Treasury bonds, shorting municipal bonds is very hard because only tax-exempt authorities and institutions can pay tax-exempt interest. An investor lending a municipal bond to a dealer would receive a taxable dividend because that dividend is paid by the dealer, not a tax-exempt institution. Even if an active repo municipal market existed, it may be hard to locate a suitable municipal bond as a hedge because of the sheer number of municipal securities. Shorting related interest rate securities, like Treasuries and corporate bonds, opens up potentially large basis risk. Another reason arbitrage may be limited is because the trading costs are much higher than Treasury markets."

Well, there it is. Let’s review the bidding. The answer to 1) is an iffy “Maybe”, the answer to 2) is an unqualified “No.” The foundational assumptions on which bond option pricing models rest simply do not get there in the municipal market. And it's not just a foundational crack, this foundation's built on sand. Can we just sweep these facts under the rug, hold our nose, and blithely hit the Calc button? To what end? So we can generate some winged-horse numbers using sexy models that work nicely in other markets? Where's the benefit?

We could stop here because all 3 questions need a Yes for standard option pricing models to apply. But wait, there’s more! Question 3) is probably the most important of all.  And we’ll cover it fully in our next article. Spoiler alert – muni issuers aren’t options dealers. 

1We tried to set the matter straight with The Right and Wrong Models for Callable Municipal Bonds published back in 2013. But we understand. It took the Royal Navy fifty years after James Lind definitively showed citrus fights scurvy in 1753 to keep fresh oranges on British ships. These things take time.