August 17, 2016    3 minute read

Financial Engineering And Quantitative Finance

The Mathematics Behind The Money    August 17, 2016    3 minute read

Financial Engineering And Quantitative Finance

Finance is an industry driven by innovation, and it was one of the first industries adapting to quantitative techniques to solve difficult problems.

Its history started with the question of valuing options, which is a financial derivative allowing the buyer to buy a stock at a particular price on a specific date. The first practical model for valuing options was the binomial tree, a discrete probability model that can still be found in lots of financial engineering textbooks. However, in many situations, traders would still prefer to use intuition and short-term demand-supply relationships to value options. A more sophisticated method was required.


Then the famous Black-Scholes formula, combining a stochastic differential equation and the Ito Calculus, became the most powerful tool in valuing options. It was derived from the idea of dynamic hedging – using options and stocks to build a risk-free portfolio. In this portfolio, with no uncertainty, the value of options can be expressed in terms of a range of basic inputs. The method was soon utilised in derivative valuation, trading and the bond market, and Myron Scholes and Robert C. Merton, who introduced the Ito Calculus to this model, won the Nobel Prize in 1997 for this achievement. Myron Scholes and Robert C. Merton started a hedge fund, LTCM, but after receiving exceptional returns for several years, the fund collapsed in 1998 as it put too much leverage on fixed income arbitrage. The Federal Reserve and major banks on Wall Street rescued the fund.

The Black-Scholes formula, as well as its applications, including asset pricing and OTC trading on volatility smile, are considered the world of Q quant. Q quants rely more on probability models, and there is another group of P quant relying more on statistical modelling, being active in quantitative trading and quantitative portfolio management.

Different Tools

P quants use a much more diverse set of tools and rely more on the real market data. More often, they are buy-side rather than sell-side. Aiming to make profits through trading (not the commission of selling structured products), buy-side P quants tend to be secretive about their quantitative strategies. For example, one of the most famous quantitative hedge funds, Renaissance Technologies, has never revealed its trading strategies, and people can only guess that the hidden Markov Model might have been used based on the fund’s founders’ education and research backgrounds. This is particularly different from Q quants, who publish reports to raise awareness for the services they provide.

In terms of education backgrounds, Q quants skills match closely with the skills in applied mathematics and theoretical physics. Some pioneers in the world of Q quant, for example, Dr Emanuel Derman, the author of the book My Life as a Quant, was previously a theoretical physicist. P quants tend to have probability, statistics backgrounds and sometimes high requirements in C, C++ or Java programming skills. Some P quants require skills in artificial intelligence, neural networks, or modelling skills in other fields, which are transferable into modelling the financial market.

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