Fast and accurate pricing of discretely monitored barrier options by numerical path integration |
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Authors: | Christian Skaug Arvid Naess |
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Affiliation: | (1) Istituto per le Applicazioni del Calcolo, CNR, Bari, Italy;(2) Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway |
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Abstract: | Barrier options are financial derivative contracts that are activated or deactivated according to the crossing of specified
barriers by an underlying asset price. Exact models for pricing barrier options assume continuous monitoring of the underlying
dynamics, usually a stock price. Barrier options in traded markets, however, nearly always assume less frequent observation,
e.g. daily or weekly. These situations require approximate solutions to the pricing problem. We present a new approach to
pricing such discretely monitored barrier options that may be applied in many realistic situations. In particular, we study
daily monitored up-and-out call options of the European type with a single underlying stock. The approach is based on numerical
approximation of the transition probability density associated with the stochastic differential equation describing the stock
price dynamics, and provides accurate results in less than one second whenever a contract expires in a year or less. The flexibility
of the method permits more complex underlying dynamics than the Black and Scholes paradigm, and its relative simplicity renders
it quite easy to implement. |
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Keywords: | Barrier options Discrete monitoring Numerical path integration |
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