Application of Microlocal Analysis to an Inverse Problem Arising from Financial Markets

One of the most interesting problems discerned when applying the Black--Scholes model to financial derivatives, is reconciling the deviation between expected and observed values. In our recent work, we derived a new model based on the Black--Scholes model and formulated a new mathematical approach to an inverse problem in financial markets. In this paper, we apply microlocal analysis to prove a uniqueness of the solution to our inverse problem. While microlocal analysis is used for various models in physics and engineering, this is the first attempt to apply it to a model in financial markets. First, we explain our model, which is a type of arbitrage model. Next we illustrate our new mathematical approach, and then for space-dependent real drift, we obtain stable linearization and an integral equation. Finally, by applying microlocal analysis to the integral equation, we prove our uniqueness of the solution to our new mathematical model in financial markets

Consentaneous agent-based and stochastic model of the financial markets

We are looking for the agent-based treatment of the financial markets considering necessity to build bridges between microscopic, agent based, and macroscopic, phenomenological modeling. The acknowledgment that agent-based modeling framework, which may provide qualitative and quantitative understanding of the financial markets, is very ambiguous emphasizes the exceptional value of well defined analytically tractable agent systems. Herding as one of the behavior peculiarities considered in the behavioral finance is the main property of the agent interactions we deal with in this contribution. Looking for the consentaneous agent-based and macroscopic approach we combine two origins of the noise: exogenous one, related to the information flow, and endogenous one, arising form the complex stochastic dynamics of agents. As a result we propose a three state agent-based herding model of the financial markets. From this agent-based model we derive a set of stochastic differential equations, which describes underlying macroscopic dynamics of agent population and log price in the financial markets. The obtained solution is then subjected to the exogenous noise, which shapes instantaneous return fluctuations. We test both Gaussian and q-Gaussian noise as a source of the short term fluctuations. The resulting model of the return in the financial markets with the same set of parameters reproduces empirical probability and spectral densities of absolute return observed in New York, Warsaw and NASDAQ OMX Vilnius Stock Exchanges. Our result confirms the prevalent idea in behavioral finance that herding interactions may be dominant over agent rationality and contribute towards bubble formation.Comment: 17 pages, 6 figures, Gontis V, Kononovicius A (2014) Consentaneous Agent-Based and Stochastic Model of the Financial Markets. PLoS ONE 9(7): e102201. doi: 10.1371/journal.pone.010220

Does Gibrat's law hold amongst dairy farmers in Northern Ireland?

We introduce a new hybrid approach to joint estimation of Value at Risk (VaR) and Expected Shortfall (ES) for high quantiles of return distributions. We investigate the relative performance of VaR and ES models using daily returns for sixteen stock market indices (eight from developed and eight from emerging markets) prior to and during the 2008 financial crisis. In addition to widely used VaR and ES models, we also study the behavior of conditional and unconditional extreme value (EV) models to generate 99 percent confidence level estimates as well as developing a new loss function that relates tail losses to ES forecasts. Backtesting results show that only our proposed new hybrid and Extreme Value (EV)-based VaR models provide adequate protection in both developed and emerging markets, but that the hybrid approach does this at a significantly lower cost in capital reserves. In ES estimation the hybrid model yields the smallest error statistics surpassing even the EV models, especially in the developed markets

The Markov switching ACD model

We propose a new framework for modelling time dependence in duration processes on financial markets. The well known autoregressive conditional duration (ACD) approach introduced by Engle and Russell (1998) will be extended in a way that allows the conditional expectation of the duration process to depend on an unobservable stochastic process, which is modelled via a Markov chain. The Markov switching ACD model (MSACD) is a very flexible tool for description and forecasting of financial duration processes. In addition the introduction of an unobservable, discrete valued regime variable can be justified in the light of recent market microstructure theories. In an empirical application we show, that the MSACD approach is able to capture several specific characteristics of inter trade durations while alternative ACD models fail. Furthermore, we use the MSACD to test implications of a sequential trade model

Shift Contagion in Asset Markets

The authors develop a new methodology to investigate how crises cause the relationship between financial variables to change. Two possible sources of increased co-movement between markets during high-variance episodes are considered: larger common shocks operating through standard market linkages, and a structural change in the propagation of shocks between markets, called “shift contagion.” The methodology has three key features: (i) high- and low-variance episodes are model-determined, rather than exogenously assigned; (ii) the markets where crises originate need not be known; and (iii) the approach provides an unambiguous test of shift contagion. Applications to bivariate returns in currency markets of developed countries and bond markets of emerging-market countries suggest that shift contagion occurs among the former but not the latter.Financial markets; Econometric and statistical methods

Comparison of MSACD models

We propose a new framework for modelling time dependence in duration processes on financial markets. The well known autoregressive conditional duration (ACD) approach introduced by Engle and Russell (1998) will be extended in a way that allows the conditional expectation of the duration process to depend on an unobservable stochastic process which is modelled via a Markov chain. The Markov switching ACD model (MSACD) is a very flexible tool for description and forecasting of financial duration processes. In addition, the introduction of an unobservable, discrete valued regime variable can be justified in the light of recent market microstructure theories. In an empirical application we show that the MSACD approach is able to capture several specific characteristics of inter trade durations while alternative ACD models fail. JEL classification: C22, C25, C41, G1

Developing methods for strategic evaluation in agricultural research and production

We analyze instruments to evaluate investment strategies as new options for co-operatives within the wheat production chain. Using a value-based management the extension of our concept, a “cooperative balanced scorecard” is discussed as we propose the further differentiation of the scorecard’s financial perspective. This is a market development-driven approach as cooperatives may be regarded as commodity-price-intermediators for their members. Proposing this approach we use a simple model of conjoint-hedging in intermediating firms within agribusiness.Agribusiness, Wheat Production, Cooperatives, Intermediation, Value-based Management, Commodity Markets., Agricultural and Food Policy,

Risk-Neutral Pricing of Financial Instruments in Emission Markets: A Structural Approach

We present a novel approach to the pricing of financial instruments in emission markets, for example, the EU ETS. The proposed structural model is positioned between existing complex full equilibrium models and pure reduced form models. Using an exogenously specified demand for a polluting good it gives a causal explanation for the accumulation of CO2 emissions and takes into account the feedback effect from the cost of carbon to the rate at which the market emits CO2. We derive a forward-backward stochastic differential equation for the price process of the allowance certificate and solve the associated semilinear partial differential equation numerically. We also show that derivatives written on the allowance certificate satisfy a linear partial differential equation. The model is extended to emission markets with multiple compliance periods and we analyse the impact different intertemporal connecting mechanisms, such as borrowing, banking and withdrawal, have on the allowance price.Comment: Section 5 in this version is new and contains an asymptotic analysis of the problem under consideratio

Hybrid Historical Simulation VaR and ES: Performance in Developed and Emerging Markets

We introduce a new hybrid approach to joint estimation of Value at Risk (VaR) and Expected Shortfall (ES) for high quantiles of return distributions. We investigate the relative performance of VaR and ES models using daily returns for sixteen stock market indices (eight from developed and eight from emerging markets) prior to and during the 2008 financial crisis. In addition to widely used VaR and ES models, we also study the behavior of conditional and unconditional extreme value (EV) models to generate 99 percent confidence level estimates as well as developing a new loss function that relates tail losses to ES forecasts. Backtesting results show that only our proposed new hybrid and Extreme Value (EV)-based VaR models provide adequate protection in both developed and emerging markets, but that the hybrid approach does this at a significantly lower cost in capital reserves. In ES estimation the hybrid model yields the smallest error statistics surpassing even the EV models, especially in the developed markets.value at risk, expected shortfall, hybrid historical simulation, extreme value theory, bootstrapping