Thursday, December 6, 2012

"Why Black-Scholes is Better Than We Think"

From Condor Options:
Every options trader knows about or at least of the Black-Scholes-Merton (BSM) pricing model. Because it is the oldest formalized pricing model and only the first of many, some traders regard it as outdated and inferior. Perhaps it is a victim of the familiarity that breeds contempt. But a recent paper gives some reasons why traders should give BSM a second look.

Delta hedging is an essential component of any volatility trading strategy. When straddle buyers also buy and sell the underlying asset to “scalp” the gamma in the trade, they are hedging the deltas created by that gamma to prevent the position from becoming a simple directional bet.

Any pure volatility trade will require hedging to eliminate directional price exposure, but even traders who want a mixture of volatility and price exposure will need, at times, to alter the delta bias of positions. To hedge the delta exposure of an option position, it is necessary to have a confident estimate of that exposure. But the delta of a given option is not dictated from on high or declared by fiat. It depends upon some pricing model. Now, although many traders do not make active use of multiple complex pricing models when finding and structuring trades, that does not mean understanding the relative merits of different models is not of practical importance.

Carol Alexander, Andreas Kaeck and Leonardo Nogueira note in a 2009 Journal of Futures Markets article that the existing literature is unclear about whether BSM deltas are more cost-effective for hedging than deltas produced by either of the two contemporary types of models for pricing options, local or stochastic volatility models: 
[O]nce stochastic volatility is modeled [e.g., Heston 1993], the inclusion of jumps leads to no discernible improvement in hedging performance. It is conjectured that this is because the likelihood of a jump during the hedging period is too small, at least when the hedge is rebalanced frequently … .Dumas et. al (1998) test several para- metric and semi-parametric forms of the local volatility function, and conclude that BSM deltas appear to be more reliable than any of the local volatility deltas that they tested.

This is already an interesting result, because ambiguity about the effectiveness of contemporary models (relative to BSM) should lead us to reduce whatever bias we might have had in their favor....MORE