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Multivariate fluctuation relations are established in three stochastic models of transistors, which are electronic devices with three ports and thus two coupled currents. In the first model, the transistor has no internal state variable and…
In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the…
We introduce a novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process. It contains the Heston model as a limit case. We show that the joint density of any finite sequence of log returns…
We introduce a multi-factor stochastic volatility model based on the CIR/Heston volatility process that incorporates seasonality and the Samuelson effect. First, we give conditions on the seasonal term under which the corresponding…
We introduce stochastic volatility models, in which the volatility is described by a time-dependent nonnegative function of a reflecting diffusion. The idea to use reflecting diffusions as building blocks of the volatility came into being…
In this manuscript we analyse the leading statistical properties of fluctuations of (log) 3-month US Treasury bill quotation in the secondary market, namely: probability density function, autocorrelation, absolute values autocorrelation,…
Stochastic volatility processes with heavy-tailed innovations are a well-known model for financial time series. In these models, the extremes of the log returns are mainly driven by the extremes of the i.i.d. innovation sequence which leads…
The methodology presented provides a quantitative way to characterize investor behavior and price dynamics within a particular asset class and time period. The methodology is applied to a data set consisting of over 250,000 data points of…
This dissertation investigates the ability of the Ising model to replicate statistical characteristics, or stylized facts, commonly observed in financial assets. The study specifically examines in the S&P500 index the following features:…
This paper mainly utilizes the ARDL model and principal component analysis to investigate the relationship between the volatility of China's Shanghai Composite Index returns and the variables of exchange rate and domestic and foreign bond…
We show that the moments of the distribution of historic stock returns are in excellent agreement with the Heston model and not with the multiplicative model, which predicts power-law tails of volatility and stock returns. We also show that…
We study the volatility of the S&P500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log-normal function. Further, using detrended fluctuation analysis we show that the volatility is…
In this note, we introduce how to use Volatility Index (VIX) for postprocessing quantitative strategies so as to increase the Sharpe ratio and reduce trading risks. The signal from this procedure is an indicator of trading or not on a daily…
We consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Lo\`{e}ve expansion for the…
In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation…
In this paper we show the convergence of the long-term return $t^{-\mu}\int_0^tX(s)\d s$ for some $\mu\geq1$, where $X$ is the short-term interest rate which follows an extension of Cox-Ingersoll-Ross type model with jumps and memory, and,…
Predicting the S&P 500 index volatility is crucial for investors and financial analysts as it helps assess market risk and make informed investment decisions. Volatility represents the level of uncertainty or risk related to the size of…
In this paper, we propose a novel methodology for pricing equity-indexed annuities featuring cliquet-style payoff structures and early surrender risk, using advanced financial modeling techniques. Specifically, the market is modeled by an…
In this paper we propose a new stochastic model based on a generalization of semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted indexed…
A problem of optimal debt management is modeled as a noncooperative game between a borrower and a pool of lenders, in infinite time horizon with exponential discount. The yearly income of the borrower is governed by a stochastic process.…