Stochastic modelling of financial processes with memory and semiheavy tails
This PhD thesis aims to study financial processes which have semiheavytailed marginal distributions and may exhibit memory. The traditional BlackScholes model is expanded to incorporate memory via an integral operator, resulting in a class of market models which still preserve the completeness and arbitragefree conditions needed for replication of contingent claims. This approach is used to estimate the implied volatility of the resulting model. The first part of the thesis investigates the semiheavytailed behaviour of financial processes. We treat these processes as continuoustime random walks characterised by a transition probability density governed by a fractional Riesz Bessel equation. This equation extends the Feller fractional heat equation which generates astable processes. These latter processes have heavy tails, while those processes generated by the fractional RieszBessel equation have semiheavy tails, which are more suitable to model financial data. We propose a quasilikelihood method to estimate the parameters of the fractional Riesz Bessel equation based on the empirical characteristic function. The second part considers a dynamic model of complete financial markets in which the prices of European calls and puts are given by the BlackScholes formula. The model has memory and can distinguish between historical volatility and implied volatility. A new method is then provided to estimate the implied volatility from the model. The third part of the thesis considers the problem of classification of financial markets using highfrequency data. The classification is based on the measure representation of highfrequency data, which is then modelled as a recurrent iterated function system. The new methodology developed is applied to some stock prices, stock indices, foreign exchange rates and other financial time series of some major markets. In particular, the models and techniques are used to analyse the SET index, the SET50 index and the MAI index of the Stock Exchange of Thailand.
Year of publication: 
2005


Authors:  Pesee, Chatchai 
Publisher: 
Queensland University of Technology 
Subject:  Alpha stable distribution  L´evy distribution  the Feller fractional heat equation  the RieszBessel distribution  volatility  the AnhInoue model  the tick test  recurrent iterated function systems  memory  semiheavy tails  longrange dependence  fractional Brownian motion 
Type of publication:  Book / Working Paper 

Type of publication (narrower categories):  Thesis 
Notes:  Pesee, Chatchai (2005) Stochastic modelling of financial processes with memory and semiheavy tails. PhD thesis, Queensland University of Technology. Faculty of Science and Technology; Mathematical Sciences 
Source:  BASE 
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