Μια προσέγγιση πλέγματος για την αποτίμηση δικαιωμάτων με δύο μεταβλητές κατάστασης
A lattice approach for option pricing with two state variables
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Keywords
Μοντέλο Kamrad & Ritchken ; Μοντέλο Stulz ; Δικαίωμα προαίρεσης ; Μία μεταβλητή κατάστασης ; Μοντέλο Boyle ; Αλγόριθμος Levenberg - Marquardt ; Δύο μεταβλητές κατάστασης ; Εκτίμηση παραμέτρων ; Προβλεπτική ικανότητα ; Αριθμητική ανάλυσηAbstract
This thesis refers to the valuation of options via a lattice approach when there are two underlying state variables. More specifically, the case where the payoff of the option is a function (maximum & minimum) of two underlying state variables is examined. Initially, the options and their characteristics are described in general and we also provide a historical review of options’ valuation with two state variables. Then the lattice models of Cox-Ross-Rubinstein (1979), Boyle (1988) and Kamrad & Ritchken (1991) for valuation of options with one state variable are presented, followed by the extension of the Black & Scholes (1973) model as well as of the aforementioned lattice models (Boyle, Kamrad & Ritchken) for valuation of options with two state variables.
Empirical study and numerical analysis is also performed using the MATLAB programming language for the lattice models of Boyle (1988) and Kamrad & Ritchken (1991) for one and two state variables, respectively. After evaluating the parameters of the models with the Levenberg - Marquardt iterative algorithm and checking their predictive ability, we conclude that the Kamrad & Ritchken (1991) lattice model is a reliable model for valuation of options with two state variables.
Postgraduate Studies Programme
Χρηματοοικονομική και Τραπεζική με κατεύθυνση στην Χρηματοοικονομική και Τραπεζική ΔιοικητικήDepartment
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Χρηματοοικονομικής και Τραπεζικής ΔιοικητικήςNumber of pages
119Language
Greek
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Attribution-NonCommercial-NoDerivatives 4.0 Διεθνές
Attribution-NonCommercial-NoDerivatives 4.0 Διεθνές