Parameter estimation from multinomial trees to jump diffusions with k means clustering

Lee, Kiseop and Xu, Mingxin (2007): Parameter estimation from multinomial trees to jump diffusions with k means clustering.

Abstract

Ever 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.

• Item Type: MPRA Paper
• Institution: University of North Carolina at Charlotte
• Language: English
• Keywords: parameter estimation; multinomial tree; jump model; weak convergence; K means clustering
• Subjects: G - Financial Economics > G1 - General Financial Markets > G10 - General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General

References

Ait-Sahalia, Y.: Maximum likelihood estimation of discretely sampled diffusions: A closed-form approximation approach, Econometrica, 70, 223-262 (2002)

Ait-Sahalia, Y., Kimmel, R.: Maximum likelihood estimation of stochastic volatility models, Journal of Financial Economics, 83, 413-452 (2007)

Albanese, C., Kuznetsov, A.: Discretization schemes for subordinated processes, working paper (2007)

Bhar, R., Chiarella, C., To, T.: A maxium likelihood approach to estimation of Heath-Jarrow-Morton model, preprint

Chang, L. B., Palmer, K.: Smooth convergence in the binomial model, Finance and Stochastics, 11, 91--105 (2007)

Clewlow, L., Strickland, C.: Implementing Derivatives Models, Wiley Financial Engineering, (1999)

Ramezani, C., Zeng, Y.: An Empirical Assessment of Double Exponential Jump-Diffusion Process, Forthcoming in Annals of Finance

Cox, J. C., Ross, S. A., Rubinstein, M.: Option pricing: a simple approach, The Journal of Financial Economics, 7, 229--263 (1979)

Durham, G., Gallant, R.: Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes, preprint

Florescu, I., Viens, F.: Stochastic volatility: option pricing using a multinomial recombining tree, preprint (2006)

Hastie, T., Tibshirani, R., Freidman, J.: The Elements of Statistical Learning, Springer Series in Statistics (2001)

Heston, S., Zhou, G.: On the rate of convergence of discrete-time contingent claims, Mathematical Finance, 10, 53--75 (2000)

Li, M., pearson, N., Posteshman, A.: Conditional estimation of diffusion processes, Journal of Financial Economics, 74, 31-66 (2004)

Nieuwenhuis, J. W., Vellekoop, M. H.: Weak convergence of tree methods, to price options on defaultable assets, Decisions in Economics and Finance, 27, 87--107 (2004)

Prigent, J-L.: Weak Convergence of Financial Markets, Springer Finance, (2003)