The Random-Time Binomial Model
AbstractIn 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.
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Bibliographic InfoPaper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 399.
Date of creation: Feb 1997
Date of revision:
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binomial model; order of convergence; smoothing; extrapolation; jump-diffusion;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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