SEMINARIESCHEMA FÖR MATEMATISK STATISTIK 

Fredag    10/5  15.15         Paul Glasserman
          1996                Columbia University:

                              A Continuity Correction for Discrete
                              Barrier Options


Abstract:

The payoff of a barrier option depends on whether or not a
specified asset price, index, or rate reaches a specified level during
the life of the option.  Most models for pricing barrier options
assume continuous monitoring of the barrier; under this condition
(and the standard Black-Scholes assumptions), the option can often be
priced in closed form.  Most real contracts with barrier provisions
specify discrete monitoring instants; there are essentially no formulas
for pricing these options, and even numerical pricing is difficult.
We show, however, that discrete barrier options can be priced with
remarkable accuracy using continuous-barrier formulas by applying a
simple continuity correction to the barrier.  The correction shifts
the barrier away from the underlying by a factor of
exp(beta sigma sqrt(Delta t)), where beta approx 0.5826, \sigma is the
underlying volatility, and Delta t is the time between monitoring instants.
This correction builds on results of Siegmund and Yuh (1981) for
approximating first passage probabilities in random walks.
A related correction for lookback options builds on results of Asmussen,
Glynn, and Pitman (1995) on discrete approximations to reflected Brownian
motion.


This is joint work with Mark Broadie and Steve Kou.




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