Related papers: A stochastic volatility approximation for a tick-b…
In this paper, we price European Call three different option pricing models, where the volatility is dynamically changing i.e. non constant. In stochastic volatility (SV) models for option pricing a closed form approximation technique is…
We propose model-free (nonparametric) estimators of the volatility of volatility and leverage effect using high-frequency observations of short-dated options. At each point in time, we integrate available options into estimates of the…
We develop a theory of bid and ask price dynamics where the two prices form due to interaction of buy and sell orders. In this model the two prices are represented by eigenvalues of a 2x2 price operator corresponding to "bid" and "ask"…
In this chapter we review some recent results on the dynamics of price formation in financial markets and its relations with the efficient market hypothesis. Specifically, we present the limit order book mechanism for markets and we…
In the over-the-counter market in derivatives, we sometimes see large numbers of traders taking the same position and risk. When there is this kind of concentration in the market, the position impacts the pricings of all other derivatives…
Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the…
We consider the consumption-based asset pricing model, derive a new modified basic pricing equation, and present its successive approximations using the Taylor series expansions of the investor's utility during the averaging time interval.…
We present an agent based model of a single asset financial market that is capable of replicating several non-trivial statistical properties observed in real financial markets, generically referred to as stylized facts. While previous…
Tick-sizes not only influence the granularity of the price formation process but also affect market agents' behavior. We investigate the disparity in the microstructural properties of the Limit Order Book (LOB) across a basket of assets…
We present a novel agent-based approach to simulating an over-the-counter (OTC) financial market in which trades are intermediated solely by market makers and agent visibility is constrained to a network topology. Dynamics, such as changes…
The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…
We propose a price impact model where changes in prices are purely driven by the order flow in the market. The stochastic price impact of market orders and the arrival rates of limit and market orders are functions of the market liquidity…
In the past, financial stock markets have been studied with previous generations of multi-agent systems (MAS) that relied on zero-intelligence agents, and often the necessity to implement so-called noise traders to sub-optimally emulate…
Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar…
We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of…
A dynamical model is introduced for the formation of a bullish or bearish trends driving an asset price in a given market. Initially, each agent decides to buy or sell according to its personal opinion, which results from the combination of…
In this paper, we employ the Heston stochastic volatility model to describe the stock's volatility and apply the model to derive and analyze the optimal trading strategies for dealers in a security market. We also extend our study to option…
Hawkes processes were first introduced to obtain microscopic models for the rough volatility observed in asset prices. Scaling limits of such processes leads to the rough-Heston model that describes the macroscopic behavior. Blanc et al.…
On a capital market the social group is formed from traders. Individual behaviour of agents is influenced by the need to associate with other agents and to obtain the approval of other agents in the group. Making decisions an individual…
We develop a theoretical trading conditioning model subject to price volatility and return information in terms of market psychological behavior, based on analytical transaction volume-price probability wave distributions in which we use…