Related papers: On Financial Markets Based on Telegraph Processes
Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or…
In this paper, we provide a model-independent extension of the paradigm of dynamic hedging of derivative claims. We relate model-independent replication strategies to local martingales having a closed form which we can characterise via…
We start with the idea that open quantum systems can be used to represent financial markets by modelling events from the external environment and their impact on the market price. We show how to characterize distinct orbits of the time…
The dynamics of market prices is described as the evolution of opinions in the trading community regarding future market behavior. The price then is a function of the voting process of the market players in favor to raise or reduce the…
We analyze the empirical performance of several non-parametric estimators of the pricing functional for European options, using historical put and call prices on the S&P500 during the year 2012. Two main families of estimators are…
We propose a financial market model that comprises a savings account and a stock. The stock price process is modeled as a one-dimensional diffusion, in which two types of agents exist: an ordinary investor and a fundraiser who buys or sells…
A new model for stocks markets using integer values for each stock price is presented. In contrast with previously reported models, the variables used in the model are not of binary type, but of more general integer type. It is shown how…
In this dissertation two simple models of stock exchange are developed and simulated numerically. The first is characterized by centralized trading with a market maker. Unfortunately, this model is unable to generate realistic market…
It is well-known that the Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by financial markets. This paper…
This paper studies pricing derivatives in an age-dependent semi-Markov modulated market. We consider a financial market where the asset price dynamics follow a regime switching geometric Brownian motion model in which the coefficients…
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the…
Price movements of stock market are not totally random. In fact, what drives the financial market and what pattern financial time series follows have long been the interest that attracts economists, mathematicians and most recently computer…
Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate…
Classical technical analysis methods of stock evolution are recalled, i.e. the notion of moving averages and momentum indicators. The moving averages lead to define death and gold crosses, resistance and support lines. Momentum indicators…
Measuring model risk is required by regulators on financial and insurance markets. We separate model risk into parameter estimation risk and model specification risk, and we propose expected shortfall type model risk measures applied to…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
In financial mathematics, it is a typical approach to approximate financial markets operating in discrete time by continuous-time models such as the Black Scholes model. Fitting this model gives rise to difficulties due to the discrete…
In this paper we study coupled fully non-local equations, where a linear non-local operator jointly acts on the time and space variables. We establish existence and uniqueness of the solution. A maximum principle is proved and used to…
In an observed generalized semi-Markov regime, estimation of transition rate of regime switching leads towards calculation of locally risk minimizing option price. Despite the uniform convergence of estimated step function of transition…
We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday return are described by a discrete time homogeneous semi-Markov process and the…