Option Pricing using Artificial Neural Networks

Abstract

Neural networks have an increasingly important role in the financial market, by offering a solution to stationarity and non-linearity whilst also providing robustness and predictive power. Options and option pricing are a fundamental area of interest in the daily activities of investment banks, hedge funds and trading firms in the financial market. Implied volatility is the focal point of these operations and an intricate and essential parameter to be taken under consideration as it provides the user a numerical estimation of risk and provides the basis for modeling and risk management. There are a number of numerical root solving algorithms which form the basis of determining the implied volatility from a given data set. However, these algorithms bring an inherent trade-off between convergence, robustness and computational efficiency. An artificial neural network approach to determining implied volatility aims to address these issues and provide the most suitable, stable and computationally efficient method. In addition, due to the extended complexity of the network, it is possible to determine the most popular options related metrics denoted as -- The Greeks -- from the weights of the trained network. These metrics provide the investor with the sensitivity of the respective option prices to the underlying parameters present in the market. This is of particular importance in models where a closed form solution is not available. Furthermore, this paper will attempt to generalize the option framework, providing opportunity to encompass both European and American options while also giving rise to further extensions into the exotic option modeling process.

Popular Abstract

Society is ever changing. Technology is at the forefront of our thoughts and the era of automation has begun. Can a machine understand the market? This thesis will show that an artificial neural network approach to modeling implied volatility is in fact more reliable, faster and more durable than it's counterparts while also capable of being generalised to more complex pricing models, without the loss of accuracy.

It is said that everyone, at some point in their life will own a stock, make a bet or take a calculated risk or investment. With each passing generation, new opportunities present themselves for the retail investor or the wall street shark, with trading patterns and strategies becoming ever more complex or yet simple in nature. This notion can be as simple as simple as risk vs reward, yet how we do we measure risk? One approach is to explore is the complex trading of options, elaborate contracts and agreements made in the present with promises in the future. Hidden within the price of these products, is the underlying market risk, which can be quantified and is commonly denoted as implied volatility.

This risk gives an investor an overlook of the market. The implied volatility is time sensitive, changing each and every day yet gives the investor the opportunity to adjust their portfolio accordingly, to tweak their trading strategies and most importantly, to neutralise your risk. Thus our goal becomes clear, to extract the implied volatility from the prices of these options, but how is it achieved?

The method is tricky, the risk is hidden. In the past investors would use root solving algorithms, methods of iteration which start by giving an educated guess of the current implied volatility. From here, they would evaluate the price of an option with their initial guess and then compare that value with the true price of the option in the market. The difference in prices would be measured and the procedure repeated until the investors estimates matched the price in the market. These methods came with a lot of uncertainty, were performed with computers and relied on a number of assumptions and ideal market conditions. But perhaps there is a more elegant way?

The solution; a machine trained on market or simulated data, capable of determining implied volatility with remarkable speed and precision. It could learn how to see the risk through the eyes of the options. Faster, more durable and reliable, it is a perfect solution.

Even though options come in a variety of makeups, American, European, Bermudan etc. and even having sub-categories to sparkle the investors interest, the neural network is shown to be capable of mastering the recipe for each of these dishes while providing as good or better accuracy than their rivals. Not only that but the neural network achieves these results in a fraction of time compared to their counterparts and within the mind of the machine, provides a deeper outlook of the market; additional metrics and information at the investors disposal.

Volatility is only one piece of the puzzle, complimenting the time value of money, the effects of interest rates, liquidity and market activity. Through the mind of the machine, the puzzle becomes recognizable and the artificial brain spits out these sensitivity metrics, more formally known as The Greeks.

Thus, the neural network provides the complete package, being faster, more robust and stable than its peers, capable of being generalised to a variety of recipes and more in depth knowledge of its terrain and surroundings. More impressively, these neural networks give opportunity for more generalised, complex and intricate models.

• author: Müller, Jan
• supervisor: Mattias Ohlsson
• organization: Computational Biology and Biological Physics - Undergoing reorganization
• course: FYTK02 20202
• year: 2021
• type: M2 - Bachelor Degree
• subject: Physics and Astronomy
• language: English
• id: 9042460
• date added to LUP: 2021-04-06 09:11:42
• date last changed: 2021-04-06 09:11:42