Will highly appreciate if anybody can provide logical financial proof why the Black-Scholes option pricing model overestimates the value for long-term options as described in this paper "Warren Buffett, Black-Scholes and the Valuation of Long-dated Options" by Bradford Cornell.
Instead of a logical proof, would you accept a little bit of hand waving?
Think about these two constants in Black-Scholes:
Also think about a long-term option, say, one whose expiration date is a year from now. Will $r$ and $\sigma$ be the same over the year? Probably not. And yet a constant interest rate and volatility are two assumptions. That's the source of the mispricing.
---EDIT--- Here is a salient portion of Buffet's strawman argument:
Here, I believe, is the assumption that makes Buffet think that B-S pricing would produce "absurd results." Buffet is attacking "geeks bearing formulas" (which means you, dear reader of this thread). On what basis is he taking issue with Black-Scholes? Cornell explains.
Cornell dispenses of the first horn of the dilemma: "The culprit is unlikely to be the drift." He points his finger at volatility:
In short, Cornell is citing Siegel to say that the reason Buffet is getting "absurd results" is because his estimation of volatility is too high for the long run.