Genius Mathematics Consultants

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Quant Consulting Services

Are you financial services firm, prop trading firm or day trader?

We offer PhD level quantitative finance consulting including:

Financial risk modelling including operational, credit, and market risk modelling

Development of derivative pricing models including Black-Scholes, Monte Carlo, finite difference and Longstaff-Schwartz

Algorithmic trading including building backtesting software and automating your algorithms

Quantitative support to the cryptocurrency industry including risk and trading algorithms.

More generally, we tackle any kind of mathematical or statistical research project, including building algorithms in a wide range of coding languages such as python and C++.

Check us out at our website:

Financial modelling and quantitative analysis consulting for professionals. Risk & Pricing models in C++/python/VBA. PhD Mathematics researc

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Sensor data analysis and sensor algorithm consulting services

I run a mathematics consulting business that specializes in designing software / algorithms for many applications, including sensor fusion and sensor data analysis.

We can design custom-built and sophisticated algorithms for your multiple sensor applications including

Noise removal / compensation

Sensor fusion

Data transformations

Machine learning

If the information is there somewhere in the data, there’s almost no limit to the sophisticated mathematical techniques that you can apply, including machine learning, data transformations, noise compensation/removal.

There are many machine learning techniques that are excellent for use in sensor algorithms.

Many simple statistical techniques that were formally simply considered part of statistics, such as linear regression (or non-linear regression for that matter), are now considered “machine learning”. And these techniques are integral to most sensor data algorithms, or to any kind of data analysis.

Whether using regression or much more impressive techniques like neural networks or reinforcement learning, the essential application is the same. The algorithm needs to take some noisy, partial, spatially distorted data, or perhaps several partial datasets which overlap with discrepancy, and condense this data down to a single category or number.

You can do this by generating a large number of input datasets, labelled by the required output, allowing the algorithm to “learn” the relationship.

I run a mathematics consulting business that specializes in designing complex algorithms for many applications, including sensor fusion and sensor data analysis. We’re happy to explore how machine learning could be applied to build a decision making system on your sensor data. Check us out below!

Sensor algorithm consulting services

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Algorithmic Trading Consulting Services

We can backtest and optimize your trading strategies against historical data.

We can also automate your trading strategies by writing C++/python code to interact directly with the exchange

Do you have an idea for a trading strategy, but want to prove that it will work through backtesting against historical data? Or do you have a successful trading strategy but want to optimize the parameters of the strategy to maximise returns?

Or perhaps you’ve heard about machine learning and would like to find out how you could incorporate it into your trading. Machine learning can be used to trawl through large amounts of data looking for statistically significant signals to use in your trading. It can also be used to determine the optimal way to combine a number of possible signals or ideas into a single algorithm.

We provide cloud-based PhD quant support for traders. We offer trading algorithm development services for equity and FX markets on all major exchanges. We also offer bitcoin and cryptocurrency algorithmic trading services on major exchanges like Binance and Bitmex.

In fact, we offer a wide range of quant (quantitative finance) consulting services including algo trading, derivative pricing and risk modelling. We also offer more general mathematical and algorithmic consulting services.

Find out more about or algo trading and quant consulting services

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Custom-built Backtesting Software for Traders

We create custom-built backtesting software in languages like C++ and python for individual traders and institutions to backtest and optimize their strategies.

This includes strategies on equities, FX, options, futures and cryptocurrencies like Bitcoin.

While many exchange/brokers have some built-in functionality (for example for backtesting), it’s going to be limited in scope. For one thing, when doing data analysis and machine learning to find profitable signals, you may wish to use a large amount of data external to the exchange. For another, in order to backtest a strategy you first have to implement it. For more sophisticated strategies, these high-level interfaces will not suffice and you’re going to need to write computer code. For example, technical analysis patterns are actually non-trivial to implement in code, particularly since the trader may rely somewhat on intuition and not know exactly how to make the signal precise.

Furthermore, any pre-existing commercial software for algo trading is likely to be very expensive, very complex to set up, and inflexible. In order to provide the necessary flexibility, it would have to allow you to incorporate your own code. But in this case, why not just get a custom application built in the first place?

And languages like python have an excellent selection of built-in mathematics and statistical toolkits which you can use both to design your strategy, and to backtest it.

So we recommend getting software custom built for your specific needs and application. All major exchanges these days allow you to use coding languages like python to grab data which can be used in your backtest, and automate the posting of buy/sell orders. We create bespoke algo trading software to allow you to

Backtest your strategy against historical data

Optimize the parameters of your strategy to maximise profitability

Automate your strategy to automatically post buy/sell orders to the exchange

Whether you’re a lone day trader looking to test your strategy, or a sizable organisation looking for get your feet wet with algorithmic trading and machine learning, our cloud-based quant consulting service has got you covered.

In fact, we offer a wide range of quant (quantitative finance) consulting services including algo trading, derivative pricing and risk modelling. We also offer more general mathematical and algorithmic consulting services.

Visit our consulting website

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Volatility smoothing algorithms to remove arbitrage from volatility surfaces

Implied volatility surfaces are usually constructed from the market prices of a number of options of different strikes and expiries. Because of poor data quality, a trader valuing options from such a surface will typically generate arbitrage opportunities. In fact, even if the pillar observations are free of arbitrage, cubic spline interpolation can introduce arbitrage.

Volatility smoothing is the process of finding the cubic spline surface that fits the input data as closely as possible, under the restriction that it be arbitrage free. This turns out to be a quadratic optimization problem, as discussed in the very useful paper "Arbitrate Free Smoothing" of M.R Fengler.

We've implemented Fengler's algorithm in python, and in this short article we illustrate how it can be used to dramatically improve the quality of volatility data. The algorithm is fast enough to be run across millions of rows of volatility data.

Read the full article

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The Longstaff-Schwartz method for early exercise derivative pricing using machine learning and optimization techniques

If you're interested in pricing derivatives with early exercise using Monte-Carlo, you may have heard of the Longstaff-Schwartz method.

When pricing a derivative using Monte-Carlo, you generate a large number of potential price paths of the underlying, and determine the value of the derivative payoff on each path. The fair price of the derivative is then simply the average across all of the potential paths. When the derivative is callable / has an early exercise feature, an additional complexity is that to value the derivative on each path you need to work out at which time step the holder would exercise the derivative. This is the first time step at which the payoff from exercising is higher than the expected payoff from continuing.

Longstaff and Schwartz devised a clever method for determining the expected value of continuing. It involves fitting a straight line to a scatterplot, and then applying an optimization routine to adjust the line into the position that exercises/continues optimally.

I wondered, what if instead of a straight line we used a more complex non-parametric curve? Could we get better results?

What I found was interesting. The straight line approach is sufficient as long as the function representing the value of exercising and the function representing the value of continuing do not intersect at more than two points. For a derivative with a complex payoff with more than two intersection points, the straight line method would fail and a non-parametric curve fitting would succeed.

I also found that the essence of the Longstaff-Schwartz method is not really curve fitting, but something more akin to machine learning, and classification methods like a support vector machine.

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