I think I figured out the source of my estimation error on the index puts. The assumed interest rate is 4% and I thought 5% would be more realistic. However, the shocker was the assumed dividend rate of 4%. The relatively low interest rate and the relatively high dividend rate significantly increases the delta. I am surprised especially by the use of a dividend rate equal to the interest rate.
Berkshire determines the estimated fair value of equity index put option contracts based on the widely used Black-Scholes option valuation model. Inputs to that model include the current index value, strike price, discount or interest rate, dividend rate and contract expiration date. The weighted averaged discount and dividend rates used as of December 31, 2008 were each approximately 4%. Berkshire believes the most significant economic risks relate to changes in the index value component and to a lesser degree to the foreign currency component. For additional information, see Berkshire’s Market Risk Disclosures.
The Black-Scholes model also incorporates volatility estimates that measure potential price changes over time. The weighted average volatility used as of December 31, 2008 was approximately 22%. The impact on fair value as of December 31, 2008 ($10.0 billion) from changes in volatility is summarized below. The values of contracts in an actual exchange are affected by market conditions and perceptions of the buyers and sellers. Actual values in an exchange may differ significantly from the values produced by any mathematical model. Dollars are in millions.
I suppose there may be conventions regarding what parameters to use in B-S for financial reporting. However, it does seem that the use of fairly stable, fixed parameters based on prior historical data appropriate as an estimate of future volatility, interest, and dividends is appropriate.
This is the first time that the interest and dividend assumptions have been disclosed. I have to wonder if Buffett is trying to throw in the kitchen sink on these. Maybe it was the external auditor's idea.