Tuesday, 25 November 2008

Warren's puts

There is a very nice post on Financial Crookery about Warren Buffett's written puts.
Let us assume that BRK sold $40bn notional 20 year puts (over 4 indices) in 2006-2007 at an average equivalent S&P 500 level of 1400. At the prevailing swap rate and dividend yields, and implied volatility of around 24%, this would have realised premia of approximately $4.5bn, close enough to the premia actually received not to worry too much about the exact details of the transactions.

The undiscounted future value of this liability, ie the fair value expectation of payment in 2027, is presently around $19bn. (At the money long dated volatility has expanded to 38%; this option now is well in the money and the skewed volatility for 1400 strike is more like 33%). The present value of this liability, before the impact of credit spreads, is around $10bn using the current swap curve.

So far, so simple. But this valuation does not take account of the credit spread of the writer of the put...
[The writer then goes on to estimate the credit effect and to speculate on whether BRK uses such credit-effected prices for its own mark to market. My reading of FAS 157/159 is not only that it can but that it must.]

The only issue I might take issue with it is that the article uses Black Scholes with vols that seem rather low (33%) to value Warren's 18 year puts. These are far out of the money forward, and I am always a bit nervous about using Black Scholes for long-dated OTM puts - my guess would be that different process-theoretic assumptions would increase the value of the position (i.e. increase Warren's loss). Kudos to Goldman though for buying these options: all that downside vol in size must make hedging their index books fun at the moment.

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