Thursday, September 25, 2008

When a warrant is not a warrant

Many commentators appraised the Berkshire-Goldman deal using black scholes for the warrants, then stood up, cheered and applauded Buffet's outstanding eye for a deal. Bubblevision anchors practically slavered with admiration.

Black scholes valuation assumes arbitrage. Goldman Sachs cannot be shorted so no one can extract realised volatility gains from the position. Look at the recent destruction in convertible arbitrage hedge funds. That Berkshire had no intention of realising volatility in this way is moot. A massive haircut is required on whatever volatility assumptions were used to come up with the warrant valuation. In fact, intrinsic may be the most appropriate measure of value. It may well still be a good deal given the advertising content embedded in Berkshire's endorsement of Goldman, but let's rein in the obsequience. Who does it benefit the most?

5 Comments:

Jake said...

you can delta hedge with other options (buy/sell calls or puts)

Andrew Clavell said...

Accepted for limited size, but this does not explain why convertible arb fund were shattered last week after the shorting ban was put into place.

Jeff Norman said...

The value of an option does not depend on your ability to delta hedge. The ability to delta hedge makes it possible to CALCULATE the value of an option in the Black-Scholes model by continuously taking an equivalent position in the underlying. Delta-hedging in and of itself does not add value.

Andrew Clavell said...

Jeff I disagree. Delta hedging allows you to capture the gamma related (ie positive convexity) gains in the volatility of the underlying. Without delta hedging (or selling options against your position), whether the underlying traverses a massively volatile path or a non volatile path, all you can say is that you will receive intrinsic on expiry.

With delta hedging, you will make a lot more money if the underlying traverses a hugely volatile path than a non volatile path.

jeff norman said...

If what you are saying is true, Andrew, then there is a riskless arbitrage as follows:
1) Short the option, hold the short to maturity and lose the intrinsic value of the option at maturity.
2) Delta hedge as if you owned the option and capture the gamma-related gains in the volatility of the underlying.
3) Pocket the difference.

You are correct that by delta hedging you will make a lot more money if the underlying traverses a hugely volatile path. In general, you will make less than the final intrinsic value by delta hedging when the path is less volatile than the implied volatility at which you bought it.