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We investigate the relation between the fair price for European-style vanilla options and the distribution of short-term returns on the underlying asset ignoring transaction and other costs. We compute the risk-neutral probability density…
The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…
We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is…
Building on a prominent agent-based model, we present a new structural stochastic volatility asset pricing model of fundamentalists vs. chartists where the prices are determined based on excess demand. Specifically, this allows for…
In this paper, we introduce a new time series model having a stochastic exponential tail. This model is constructed based on the Normal Tempered Stable distribution with a time-varying parameter. The model captures the stochastic…
We introduce and study a non-equilibrium continuous-time dynamical model of the price of a single asset traded by a population of heterogeneous interacting agents in the presence of uncertainty and regulatory constraints. The model takes…
This paper explores stochastic modeling approaches to elucidate the intricate dynamics of stock prices and volatility in financial markets. Beginning with an overview of Brownian motion and its historical significance in finance, we delve…
We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used efficient market hypothesis. We derive…
We consider the Black--Scholes model of financial market modified to capture the stochastic nature of volatility observed at real financial markets. For volatility driven by the Ornstein--Uhlenbeck process, we establish the existence of…
The integration and innovation of finance and technology have gradually transformed the financial system into a complex one. Analyses of the causesd of abnormal fluctuations in the financial market to extract early warning indicators…
We consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity) asymptotics for the corresponding asset price density, the call and put pricing functions, and the implied volatilities.…
We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible…
Throughout history, many countries have repeatedly experienced large swings in asset prices, which are usually accompanied by large fluctuations in macroeconomic activity. One of the characteristics of the period before major economic…
It is well documented from various empirical studies that the volatility process of an asset price dynamics is stochastic. This phenomenon called for a new approach to describing the random evolution of volatility through time with…
We consider stochastic control systems affected by a fast mean reverting volatility $Y(t)$ driven by a pure jump L\'evy process. Motivated by a large literature on financial models, we assume that $Y(t)$ evolves at a faster time scale…
Financial markets are prominent examples for highly non-stationary systems. Sample averaged observables such as variances and correlation coefficients strongly depend on the time window in which they are evaluated. This implies severe…
This paper proposes an enhanced approach to modeling and forecasting volatility using high frequency data. Using a forecasting model based on Realized GARCH with multiple time-frequency decomposed realized volatility measures, we study 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 the context of time-subordinated Brownian motion models, Fourier theory and methodology are proposed to modelling the stochastic distribution of time increments. Gaussian Variance-Mean mixtures and time-subordinated models are reviewed…
We introduce a local volatility model for the valuation of options on commodity futures by using European vanilla option prices. The corresponding calibration problem is addressed within an online framework, allowing the use of multiple…