Applied Mathematics: at the Core of today’s Financial Industry


On Wednesday, March 7, 2018, in the context of the annual Toronto Campus, PolyFinances’ 2018 cohort had the chance to visit the Bank of Montreal (BMO) offices in Toronto to meet with Christian Maxwell (PhD), a Vice President at BMO Capital Markets. During this meeting, our speaker discussed the important role of a “quant” in the financial sector while simplifying the complex mathematical roots behind the financial products traded on the market today.


Christian Maxwell 

After completing his BASc in Engineering Science, Christian volunteered abroad and joined Ernst & Young after returning to Canada.  Following that, he honed his analytical skills with a Ph.D. in Applied Mathematics at the University of Western Ontario and also had a summer internship at CIBC. In 2014, he joined BMO Capital Markets as an Associate. He is now a Vice President at BMO Capital Markets.

The conference

Working as a quant / engineer at BMO

To begin, it is important to define what a quant actually is: this term comes from the phrase quantitative analyst and simply represents professionals who use mathematics applied in finance.

In a broad manner, the quant has the responsibility of modeling mathematically complex, and often ambiguously posed problems. Here are some examples of financial mathematics applications that our speaker shared with us. These originate from real estate and credit because of its rapid growth and economic weight in Canada.

Modeling mortgage backed securities

The large volume of debt generated by mortgages necessitates lenders to issue Mortgage Backed Security (MBS). Simply put, this product is the agglomeration of large amounts of mortgage loans within one “package”. This product is then divided into several tranches of risk and subsequently sold by issuers to institutional investors. Determining how to tranche and which loans to allocate comprise an optimization problem.

Modeling a rate commitment

A mortgage rate commitment is a commitment to lend to a borrower at a key rate, usually for a 90-day period. Since borrowers can shop their mortgage rate around with other lenders, rate commitments translate into offering a free lookback option to the bank’s customers on the mortgage rate.

This is beneficial for both parties, since the customer is sure to obtain the best deal and the lender gets a mortgage pipeline.

Like any option, its modeling can be complex, which is why technical know-how is necessary. Moreover not all customers “exercise” the option which means data analytics and statistics are required to determine which customers are more likely to fund.

To conclude, during this conference, Dr. Maxwell found a way to explain complex products with simple math. This meeting allowed the PolyFinances cohort to better understand the mathematical theory that underpins financial products.

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