6533b828fe1ef96bd128861d
RESEARCH PRODUCT
The Random-Time Binomial Model
Dietmar Leisensubject
Economics and EconometricsMathematical optimizationControl and OptimizationWeak convergenceApplied MathematicsExtrapolationStructure (category theory)jel:G13Binomial distributionRate of convergenceValuation of optionsConvergence (routing)JumpApplied mathematicsConvergence testsBinomial options pricing modelMathematicsbinomial model order of convergence smoothing extrapolation jump-diffusiondescription
In this paper we study Binomial Models with random time steps. We explain, how calculating values for European and American Call and Put options is straightforward for the Random-Time Binomial Model. We present the conditions to ensure weak-convergence to the Black-Scholes setup and convergence of the values for European and American put options. Differently to the CRR-model the convergence behaviour is extremely smooth in our model. By using extrapolation we therefore achieve order of convergence two. This way it is an efficient tool for pricing purposes in the Black-Scholes setup, since the CRR model and its extrapolations typically achieve order one. Moreover our model allows in a straightforward manner to construct approximations to jump-diffusions. The simple valuation approaches and the convergence properties carry immediately over from the Black-Scholes case.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1999-09-01 |