Buffett's Miscalculation on his Long-Dated Put Deals

Abstract

In his 2009 Letter to Investors, Buffett discussed in some details about the problems of the Black-Scholes formula when applied to extremely long-dated put options. This short comment shows that if his arguments are interpreted in the usual way, he probably made several mistakes in his Letter. First, the expected loss computed from a single loss event is not correct, and Buffett might have underestimated his expected loss by at least 10 times. Second, the put was incorrectly thought to be overpriced. Third, his discussions were largely done in real world terms, which is irrelevant to the Black-Scholes no-arbitrage pricing. The Black-Scholes price for a 100-year put turns out to be extremely sensitive to volatility and risk-free rate; without knowing a priori the correct values of these parameters, it is impossible to know whether Black-Scholes over- or under-prices. Obviously, Buffett's writing of a naked put is purely an act of speculation.