Buffett thinks the Black-Scholes formula produces "absurd results" when applied to long-dated options (see page 19).
"Though historical volatility is a useful – but far from foolproof – concept in valuing short-term options,
its utility diminishes rapidly as the duration of the option lengthens."
Berkshire Hathaway has sold equity put options that require payment if various stock market indexes (S&P 500, the FTSE 100, the Euro Stoxx 50, and the Nikkei 225) have gone down after 15 or 20 years from the inception of the contracts.
Buffett think that the likelihood of these indexes going down over such an extended period is extremely unlikely, due to inflation and an increase in corporate retained earnings. But, even if the indexes do decline, he has already received the option premium up front and is able to invest that money for 15-20 years, before having to pay out anything.
"Clearly, either my assumptions are crazy or the formula is inappropriate."
Buffett thinks the Black-Scholes formula produces "absurd results" when applied to long-dated options (see page 19).
"Though historical volatility is a useful – but far from foolproof – concept in valuing short-term options, its utility diminishes rapidly as the duration of the option lengthens."
Berkshire Hathaway has sold equity put options that require payment if various stock market indexes (S&P 500, the FTSE 100, the Euro Stoxx 50, and the Nikkei 225) have gone down after 15 or 20 years from the inception of the contracts.
Buffett think that the likelihood of these indexes going down over such an extended period is extremely unlikely, due to inflation and an increase in corporate retained earnings. But, even if the indexes do decline, he has already received the option premium up front and is able to invest that money for 15-20 years, before having to pay out anything.
"Clearly, either my assumptions are crazy or the formula is inappropriate."