Bewertung Amerikanischer Optionen mit Hilfe von regressionsbasierten Monte-Carlo-Verfahren

Abstract

Pricing of American options in discrete time by means of regression-based Monte Carlo methods is considered in this thesis. Thereby, the options are allowed to be based on several underlyings (so-called basket options). It is assumed that the underlyings price processes satisfy the Markov property and consequently are Markov processes. In this dissertation, Monte Carlo methods are used to generate artificial sample paths of these price processes, and subsequently adaptive nonparametric least squares regression estimates are used to estimate the so-called continuation values from these data. The continuation values describe the mean values of the American options for given values of the underlyings at time t, subject to the constraint that the options are not exercised at time t, but optimally exercised in the future. Adaptive least squares neural networks as well as adaptive least squares spline estimates are used as nonparametric regression estimates. In conjunction with the pricing of American options, these estimates are theoretically analysed, and results with respect to consistency and rate of convergence are derived. Finally, the pricing of American options on simulated data by means of the estimates is illustrated.