The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation) has been developed that gives the general formalism for determining the option price and the optimal trading strategy (optimal control policy) that reduces t...

As a generic model for transport of interacting fermions through a barrier or interstitials in a lattice, quantum Brownian motion in a periodic potential is studied. There is a duality transformation between the continuous coordinate or phase representation and the discrete momentum or charge representation for general frequencydependent damping. Sub-Ohmic friction is mapped on super-Ohmic fric...

The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation) has been developed that gives the general formalism for determining the option price and the optimal trading strategy (optimal control policy) that reduces t...

A Dissertation submitted for the Degree of Doctor of Philosophy To the memory of my mother Contents Preface iii 1 Introduction 1 1.1 Option pricing in discrete time 1 1.2 Option pricing in continuous time 4 1.3 The Black-Scholes model 8 1.4 Interest-rate models 9

Modeling the conditions for the emergence of extremism is a very important problem, with clear applications for describing the interaction among individuals. Traditional models either are not suited for the task, as in the case of discrete models, or, like Bounded Confidence models, are built with rules that make opinions tend to a common ground between agents or not change at all. Continuous O...

This paper examines how noise in observed option prices arising from discrete prices and other microstructural frictions affects empirical tests of option pricing models and risk-neutral density estimation. The discrete tick size alone introduces enough noise to make model comparisons difficult, especially for lower-priced stocks. We demonstrate that microstructural noise can lead to incorrect ...

In the context of a Black-Scholes economy and with a no-arbitrage argument, we derive arbitrarily accurate lower and upper bounds for the value of European options on a stock paying a discrete dividend. Setting the option price error below the smallest monetary unity, both bounds coincide, and we obtain the exact value of the option.

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Our model nests Duan’s GARCH option models where conditional returns are constrained to being normal, as well as extends Merton’s jump-diffusion model by allowing return volatility to exhibit GARCH-like behavior. Empirical analysis on the S&P 500 index r...