The Buffett critique: volatility and long-dated options

Abstract

In his 2008 letter to shareholders, Warren Buffett, Chairman and CEO of Berkshire Hathaway, criticizes the ability of the Black-Scholes model to accurately price long-dated options. Buffet discusses how the model leads to over-pricing of put options with long maturities using examples of Berkshire’s investments in derivatives contracts. We confirm that traditional implied volatility estimates do indeed overstate long-term volatility. As an alternative, we propose a maturity-matching technique for estimating long-term volatility using historical holding period returns. We focus on three large asset classes, large cap stocks, long-term bonds, and treasury bills, to demonstrate how volatility evolves over different holding periods. We apply this rolling-period simulation method to estimate volatility for annual maturities ranging from 1 to 30-years within the Black-Scholes model. This method generates superior long-dated option values, and effectively answers Buffett’s critique. This is of particular importance for firms with significant investment holdings, as the issuance and valuation of these derivatives can have a substantial effect on firm capital.