Parameter estimation with k-means clustering

Ever since the pioneering work of Cox, Ross & Rubinstein (1979), tree models have been popular as an asset pricing method. However, statistical estimation of the parameters of tree models has been less studied. In this article, Kiseop Lee and Mingxin Xu use the k-means clustering method to estimate the parameters of multinomial trees. Using the weak convergence property of such trees to continuous-time models, they show that this method can in turn be used to estimate parameters in continuous-time models, illustrated by an example of the jump-diffusion model

Since the seminal work by Black, Scholes and Merton on the geometrical Brownian motion model, various continuous-time models have been introduced as alternatives to the Black-Scholes model, such as Levy pure-jump, stochastic volatility and jump-diffusion models. These were introduced to fix some unrealistic properties of the Black-Scholes model, and have been successful to various degrees when applied to derivatives pricing and hedging. On the other hand, an important practical problem about the