Fast and accurate pricing of discretely monitored barrier options by numerical path integration
- 85 Downloads
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.
KeywordsBarrier options Discrete monitoring Numerical path integration
Unable to display preview. Download preview PDF.
- Hull, J. (2003). Options, futures and other derivatives, (5th ed.). Prentice Hall International Editions.Google Scholar
- Kloeden P., Platen E. (1992). Numerical solutions of stochastic differential equations. New York, Springer-VerlagGoogle Scholar
- Kou S. (2003). On pricing of discrete barrier options. Statistica Sinica 13, 955–964Google Scholar
- Øksendal B. (2003). Stochastic differential equations (6th ed.). Berlin, Springer-VerlagGoogle Scholar