C63 - Computational Techniques; Simulation ModelingReturn

The main goal of this paper is to compare the classical MCMC estimation method with a universal Neural Network (NN) approach to estimate unknown parameters of the Heston stochastic volatility model given a series of observable asset returns. The main idea of the NN approach is to generate a large training synthetic dataset with sampled parameter vectors and the return series conditional on the Heston model. The NN can then be trained reverting the input and output, i.e. setting the return series, or rather a set of derived generalized moments as the input features and the parameters as the target. Once the NN has been trained, the estimation of parameters given observed return series becomes very efficient compared to the MCMC algorithm. Our empirical study implements the MCMC estimation algorithm and demonstrates that the trained NN provides more precise and substantially faster estimations of the Heston model parameters. We discuss some other advantages and disadvantages of the two methods, and hypothesize that the universal NN approach can in general give better results compared to the classical statistical estimation methods for a wide class of models.

Recently, there has been a considerable interest in machine learning (ML) applications to valuation of options. The main motivation is the speed of calibration or, for example, calculation of the credit valuation adjustments (CVA). It is usually assumed that there is a relatively liquid market with plain vanilla option quotations that can be used to calibrate (using an ML model) the volatility surface, or to estimate parameters of an advanced stochastic model. In the second stage the calibrated volatility surface (or the model parameters) are used to value given exotic options, again using a trained NN (or another ML model). The NNs are typically trained “off-line” by sampling many model and market parameters´ combinations and calculating the options´ market values. In our research, we focus on the quite common situation of a non-liquid option market where we lack sufficiently many plain vanilla option quotations to calibrate the volatility surface, but we still need to value an exotic option or just a plain vanilla option subject to a more advanced stochastic model as it is typical on energy and carbon derivative markets. We show that it is possible to use selected moments of the underlying historical price return series complemented with a volatility risk premium estimate to value such options using the ML approach.

Three different classes of data mining methods (k-Nearest Neighbour, Ridge Regression and Multilayer Perceptron Feed-Forward Neural Networks) are applied for the purpose of quantitative trading on 10 simulated time series, as well as real world time series of 10 currency exchange rates ranging from 1.11.1999 to 12.6.2015. Each method is tested in multiple variants. The k-NN algorithm is applied alternatively with the Euclidian, Manhattan, Mahalanobis and Maximum distance function. The Ridge Regression is applied as Linear and Quadratic, and the Feed-Forward Neural Network is applied with either 1, 2 or 3 hidden layers. In addition to that Principal Component Analysis (PCA) is eventually applied for the dimensionality reduction of the predictor set and the meta-parameters of the methods are optimized on the validation sample. In the simulation study a Stochastic-Volatility Jump-Diffusion model, extended alternatively with 10 different non-linear conditional mean patterns, is used, to simulate the asset price behaviour to which the tested methods are applied. The results show that no single method was able to profit on all of the non-linear patterns in the simulated time series, but instead different methods worked well for different patterns. Alternatively, past price movements and past returns were used as predictors. In the case when the past price movements were used, quadratic ridge regression achieved the most robust results, followed by some of the k-NN methods. In the case when past returns were used, k-NN based methods were the most consistently profitable, followed by the linear ridge regression and quadratic ridge regression. Neural networks, while being able to profit on some of the time series, did not achieve profit on most of the others. No evidence was further found of the PCA method to improve the results of the tested methods in a systematic way. In the second part of the study, the models were applied to empirical foreign exchange rate time series. Overall the profitability of the methods was rather low, with most of them ending with a loss on most of the currencies. The most profitable currency was EURUSD, followed by EURJPY, GBPJPY and EURGBP. The most successful methods were the linear ridge regression and the Manhattan distance based k-NN method which both ended with profits for most of the time series (unlike the other methods). Finally, a forward selection procedure using the linear ridge regression was applied to extend the original predictor set with some technical indicators. The selection procedure achieved limited success in improving the out-sample results for the linear ridge regression model but not the other models.