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it as outdated and inferior.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
