# Financial sector in Canada: the application of mathematics and probability

Mathematics and probability are strongly connected to the financial sector, helping in terms of financial modelling, financial risk management, and stock exchange predictions. To understand the applications of the two branches, we'll start with the basics and provide examples of how mathematical and probability theories apply in Canada's financial sector.

## How are Mathematics and Probabilities Connected?

Probability focuses on the mathematical study and examination of random events. The theory of probability has evolved to provide a mathematical reasoning about the development of uncertain events in sectors such as economics and finance. Since Bachelier uncovered the mathematical analysis of Brownian motion to use it as a tool in financial market analysis, the theory of finance tries to explain how financial markets work and how to quantify financial risk across a wide range of economic activities.

### What Is the Brownian Method?

The Brownian motion is a stochastic process which studies random behavior that evolves over time. It's application in the financial world involves the study of asset and stock price fluctuations in the capital market. The theory has been refined by the Black-Scholes-Merton model which is based on assuming that all financial information which could affect the price fluctuations are already incorporated by the market's speculators in the prices.

### Financial Risk Modelling in Canada

Probability in the financial sector is used for risk modelling. Franck Peltier details the use of probabilities and mathematics in actuarial professions to identify, manage and measure financial risks. Banks and asset management firms in Canada are using financial risk modeling to optimize their clients' asset portfolios. One of the Big 4 accounting firms in Canada uses probabilities in evaluating market credit risk, market risk (foreign exchange, equity, liquidity and commodities) of their clients' business operations to stabilize and increase their assets. This form of financial modelling includes frameworks and systems which can be implemented by clients to prevent damages during asset trading.

### Financial Derivatives Used by Canadian Companies

Companies use financial derivatives to decrease the fluctuations of their income streams by hedging against exchange rates, commodity price risks and interest rates. About one third of Canadian listed companies use financial derivatives as an efficient means of mitigating risk during uncertain periods. By using options, forwards, swaps, and futures, corporations can prevent damages from unforeseen market changes in the exchange rate levels or commodity prices, therefore reducing their exposure to financial risk. Although Canadian financial enterprises are the big players of the derivative markets, other non-financial corporations make up for around 15% of the foreign exchange derivatives turnover in Canada.

## Using Probability in Forecasting Change Of Overnight Repo Rate (CORRA)

The market expectations for the CORRA rate of the Bank of Canada can be measured though the rate of the OIS (Overnight Index Swap) futures contract. Its end-of-day price is influenced directly by the Bank of Canada's (BoC) repo rate as the contract ends on the fixed announcement date of the BoC. As the market expects a 25 basis points increase and the next announcement date of the BoC's policy is set for October 25th, you can use the probability theory to establish the likelihood that the BoC will modify the overnight repo target price on the next announcement date, based on market predictions.

## Conclusion

Probabilities and mathematics play an important role in Canada's financial sector through the wide range of applications including credit risk management, market price fluctuations and asset risk control. Also, both financial and non-financial institutions listed on Canada's capital markets use products such as derivates which involve probability assessment to hedge against damages caused by price rate volatility.

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