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Financial Mathematics
Financial Mathematics is that part of the mathematics which deals with the mathematical methods used in the evaluation of the financial markets. It also helps in the evaluation of the financial economics which is concerned with a lot of theories. For example, a financial mathematician takes the share price, and try to use all the probabilities at random to see the fair value of base of the stocks. Financial Mathematics involves interesting mathematical areas like Risk Management, Estimation methodologies for Econometric models for Algorithmic trading, forecasting and predictions, Investment portfolio optimization, Financial models, helpsThere are various theorems in the financial mathematics help in the calculation required for the pricing of the shares like The Fundamental theorem of arbitrage-free pricing.
In Practical, financial mathematics is similar to the computational finance. The Computational Finance is the one which deals with the problems of practical finance. In the Computational Finance, there is the study of the data and algorithms used in finance and the use of computer languages to form programs that can realize the financial models or systems.
There are two advanced quantitative techniques required for the financial calculations, one is the Derivatives Pricing and the other is the Risk and Portfolio Management.
Both the quantitative techniques use probability for the financial calculations, but they use different probabilities, named as the Risk-neutral Probability “Q” and the Actual Probability “P”.
- Derivatives Pricing:– the Risk –Neutral Probability “Q”
The main aim of the derivatives pricing is to meet the fair price of the security in terms of more liquid securities whose price is determined by the basic law of economics “the supply and demand law”.
- The Risk and Portfolio Management: - the Actual Probability “P”
The main aims of the risk and portfolio management are at modeling the probability distribution of the market prices of all the securities at a given future investment horizon.
Financial Mathematics is interesting as it is a technical and abstract branch of maths measures theoretical probability, with practical applications affecting people’s everyday life. It is exciting too, as by using advanced mathematics, we are developing foundations of finance and economics. Financial Mathematics not only explains what people need to do but also they explain what actually the people do.
