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Financial Econometrics

If we define financial econometrics in broader terms, it can be said to be the study of quantitative problems which arise out from finance. Financial econometric finds its application in addressing a variety of financial problems which are addressed and solved by using the economic theory and different statistical techniques. The measures include building financial models, volatility estimation, estimation and inferences of financial problems, testing of financial economic theory, derivative pricing, risk adjustment returns, portfolio allocation, hedging strategies, simulation of financial systems etc. Financial econometrics can be said to be an active fields which is born by the integration of various disciplines of study like finance, probability, economics, applied mathematics and statistics. The economics is used to for the foundation and guidance for solving quantitative methods and the quantitative methods like statistics, applied mathematics and probability provide the tools which are essential for solving quantitative problems of finance.

The econometrics of financial derivatives

The introduction of the financial derivatives is for reduction of various kinds of exposures which constitute market risks. They are also used or increasing leverages in the speculative trading. Various options included are stocks, bonds, stock indices, options on future as well as futures on commodities and currencies etc. By exercising the option, a holder can buy or sell an owned asset at a certain price. This price is also called strike price and the option can only be exercised at or before the expiration deadline. This makes the options valuable. There are many ways of giving value to the options, but the more celebrated is the formula given by Black and Scholes in the year 1973. This formula is based on the ‘relative pricing’ method. In this method, trading strategy is devised which balances dynamically the holdings of an underlying asset and a risk less bond in such a way that the portfolio obtained is risk less and gives the payoff which is same as the option. We can obtain the values of corresponding options by tracking the prices of theses dynamic options. The price of option obtained is explicit and depends on the strike price, the stock price, the risk free state of interest, the volatility of the asset as well as the time of maturity. A lot of statistics and econometric is involved for the actual implementation of the Black-Scholes formula.

The pricing of asset and CAPM

By asset pricing, we try to understand the prices of claims or other uncertain payments. As an example, the stock holders are entitled for the dividend payments which occur over the life time of a stock pocession, the values of which are uncertain.

One of the fundamental problems of financial econometrics is the quantification of the tradeoffs which occur between the risk and the expected return. After the birth of capital asset pricing model (CAPM), the quantification of the risks and devising of the rewards for baring it could be done successfully by the economists. The groundwork of the CAPM was laid by Markowitz in the year 1959, which postulated various investors’ portfolio selection problems in terms of variance and expected returns. The work of Markowitz was further developed by Sharpe and Lintner in 1965, which showed that the market portfolios are a mean variance efficient portfolio. Over the passage of time, many new versions of CAPM have been devised and testing and validification of these versions does attract a lot of attention in the discipline of empirical finance. Many statistical methods and testing procedures have been proposed and studied so far. For example, for explaining the expected and excessive returns of the assets, a three factor CAPM was devised by Fama and French in the year 1993.

Stochastic modeling and statistical inferences

The financial derivative valuation depends largely on the stochastic models assumptions which are done on the price dynamics of the underlying assets. Different asset classes require different classes of stochastic models. The mangement and modeling of risks like natural disaster and weather change undertake different class of stochastic models. The stochastic models are used for capturing certain fixed aspect of the underlying stochastic dyanamics. This is the reason why many models are being introduced for studying the price dynamics of various kinds of asset classes. The use of non parametric models occurs naturally in financial modeling. They are simple and convenient and help in reducing modeling biases of parametric models as well as validate their ability to fit to financial data. The use of nonparametric approaches have been increased in various fields like estimating returns, transition densities, volatility, bond yields, transition and state price densities, in checking the consistency of option prices, management of market risks etc.

Volatility, risk management and portfolio optimization

In very facet of financial econometrics, volatility prevails. It is used for pricing financial derivatives, for control and management of risks and foe portfolio allocation. It also measures the risk of portfolio and is also associated with various capital requirements in the banking regulations. The two widely used methods used for studying the volatility of discretely observed time series are ARCH and GARCH models. These models also have various extensions. Another important class used for capturing the stylized features of volatilities of financial data is the stochastic volatility model. The basic idea behind portfolio allocation is to maximize the expected returns and simultaneously controlling the risks. Risk management is undertaken to identify the risk sources, and to measure, control and manage risks. The statistical community has undertaken some large efforts for the defining and forecasting of risk measures. These efforts are related directly towards calculating the volatilities of asset returns and are used widely in making security regulations, risk management and proprietary training.