A simple and efficient numerical method for pricing discretely monitored early-exercise options. (English) Zbl 1510.91187
Summary: We present a simple, fast, and accurate method for pricing a variety of discretely monitored options in the Black-Scholes framework, including autocallable structured products, single and double barrier options, and Bermudan options. The method is based on a quadrature technique, and it employs only elementary calculations and a fixed one-dimensional uniform grid. The convergence rate is \(O ( 1 / N^4 )\) and the complexity is \(O ( M N \log N )\), where \(N\) is the number of grid points and \(M\) is the number of observation dates. Besides Black-Scholes, our method is also applicable to more general frameworks such as Merton’s jump diffusion model.
MSC:
| 91G60 | Numerical methods (including Monte Carlo methods) |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
Keywords:
discrete option pricing; quadrature method; autocallable structured product; single and double barrier option; Bermudan optionReferences:
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