Parameter estimation from multinomial trees to jump diffusions with k means clustering
AbstractEver since the pioneering work of Cox, Ross and Rubinstein, tree models have been popular among asset pricing methods. On the other hand, statistical estimation of parameters of tree models has not been studied as much. In this paper, we use K Means Clustering method to estimate the parameters of multinomial trees. By the weak convergence property of multinomial trees to continuous-time models, we show that this method can be in turn used to estimate parameters in continuous time models, illustrated by an example of jump-diffusion model.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 3307.
Date of creation: 26 Apr 2007
Date of revision: 26 Apr 2007
parameter estimation; multinomial tree; jump model; weak convergence; K means clustering;
Find related papers by JEL classification:
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
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- Li, Minqiang & Pearson, Neil D. & Poteshman, Allen M., 2004. "Conditional estimation of diffusion processes," Journal of Financial Economics, Elsevier, vol. 74(1), pages 31-66, October.
- Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
- Steve Heston & Guofu Zhou, 2000. "On the Rate of Convergence of Discrete-Time Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 53-75.
- Ram Bhar & Carl Chiarella & Thuy Duong To, 2002. "A Maximum Likelihood Approach to Estimation of Heath-Jarrow-Morton Models," Research Paper Series 80, Quantitative Finance Research Centre, University of Technology, Sydney.
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