Category: English Published: Tuesday, 13 April 2021 Written by GONG

In recent years, fascinating technologies such as Machine Learning, Deep Learning, and Artificial Intelligence developed quickly and achieved predominated results for many applications, attracting lots of interest and attention. A couple of knowledge sharing platforms specialized in the area are also flourishing.

Many financial modelling problems are also good candidates for those data-driven algorithms, which could be solved much more efficiently than conventional methods. However, compared with popular applications (i.e. Computer Vision and Natural Language Processing), there are neither many industries nor academic entities devoted to promoting the benefits of advanced computational financial modelling. It is even harder to find a proper knowledge-sharing platform focusing on this area.

Therefore, we create this platform and name it QuantGutu. We wish to devote our knowledge and ambitions to developing and promoting intelligent computer technologies specialized in (financial) quantitative applications. We are also keen to attract more talents who share the same vision as us.

We are very honoured if our articles could, by any chance, inspire anybody. We also welcome all friendly criticisms and discussions. Please contact us at: This email address is being protected from spambots. You need JavaScript enabled to view it..

As Steve Jobs once told us, "Stay hungry, Stay foolish." We will always be ready to learn more, devote more, and of course, share more.

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## Deep Hedging --- Trading Vanilla Options with Neural Network

Category: English Published: Wednesday, 26 May 2021 Written by GONG

The first article discussed using neural network models for pricing and hedging financial derivatives could be dated back to 1994. Based on the Universal Approximation Property of neural networks, Hutchinson et al. (1994) proposed that learning networks could be valuable substitutes when conventional parametric methods fail. They also experimented with S&P 500 futures options data from 1987 to 1991.

After that, there were not many developments in this direction. We think the accessibility of powerful computing resources is one of the constraints, only made available to many industries and academics until recent years.

Deep Hedging was proposed in 2018. The writers are from JP Morgan and ETH. We have reasons to believe this neural networks based solution for pricing and hedging have already been imposed in the trading floor.

#### Background and Assumptions

Assume you are the seller of a European call option, which means the option buyer could only exercise it at maturity. We set it to 30 days from now. During this period, you need to keep adjusting your holdings of the underlying asset to hedge your risks exposed in the option contract. If there is no trading cost and continuous trading (trade at every second) is possible, you will be guaranteed zero profits or losses at the end of the 30 days. However, this is nothing that will even happen in real life. So you will incur an overall loss at the termination, and the premium you charged when signing the contract reflected your expectation of this loss.

## How do we simulate stock price movements? (Part I)

Category: English Published: Wednesday, 26 May 2021 Written by GONG

In our previous article, Deep Hedging --- Trading Vanilla Options with Neural Network, we mentioned that in order to access the overall risk profile of our hedging algorithm, an extensive amount (e.g., $$10^6$$) of simulated stock price trajectories are needed. These trajectories could each represent a market projection consists of a particular set of random variables. As we never know the future shape of a market, it is necessary to cover as many random scenarios as possible. We cannot just use historical paths to mimic what will happen in the future, as there is always something unprecedented. Therefore, what we always do in practice is, first, to get the parameters’ values for the stochastic model(s) we think is suitable for our purpose, which is called the model calibration process. Then we simulate many possible future scenarios (trajectories) of the time series we are interested in. Finally, we will analyse these scenarios and conclude what results from our algorithm will possibly get in the future.

Here we will talk about several most common stochastic models for financial time series analysis.

#### Brownian Motion: The History

Brownian motion is not directly used in financial modelling nowadays, but it is the foundation of everything.