On Monday last week, Old National Bancorp bought back the warrants it had granted Treasury as part of its participation in TARP, after buying back its preferred stock on March 31. Today, the New York Times ran a story saying that Treasury only paid $1.2 million to buy back the warrants, while the warrants were almost certainly worth more.

The main authority cited by the Times was Linus Wilson, a finance professor at the University of Louisiana, Lafayette and a sometime commeter on this blog, so let’s go straight to the source.

Linus’s blog post is here (from May 14, I’m embarrassed to say) and his paper is here. Basically, he runs three different valuation models on the warrants (pages 14-16 in the paper), each with three different sets of assumptions. The assumptions have to do with volatility, dividend yield, and probability that half the warrants would be canceled.

- Volatility matters because the value of an option depends on its volatility, and volatility has increased recently, so you will get a different estimate depending on the length of time you estimate volatility over.
- Dividend yield matters because higher future dividends reduce the value of warrants (since when you exercise the warrant, you only get the share, not the share plus the dividends paid while you were holding the warrant), and again the dividend yield depends on whether you look at historical data or at current dividends.
- Finally, the warrant terms include a provision that half the warrants will be canceled if the bank makes a qualifying stock offering before the end of 2009. So the assumptions include subjective estimates of the likelihood of the bank making such a stock offering.

You can look at the paper to see how Wilson came up with these assumptions. My guesses would be that the most likely assumptions are the volatility assumption of the middle valuation, the divided yield assumption of the high valuation, and the warrant cancellation probability assumption of the low valuation.

Wilson’s preferred model (page 14) produces the lowest estimates of warrant values – from $1.5 million to $6.9 million. Traditional Black-Scholes (page 16) produces estimates from $4.1 million to $8.5 million.

(For those wondering, warrants have a positive value even though the exercise price of the warrant exceeds the market value of the common share you get by exercising the warrant, because there is a significant chance – given the length of the warrants – that at some point the share price will exceed the exercise price.)

OK, so that’s the calculation. The question is, since Treasury undoubtedly has many smart economists who know all about derivative pricing, why did they end up getting only $1.2 million? That question is left as an exercise for the reader.

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