Accelerated American option pricing with deep neural networks

Given the competitiveness of a market-making environment, the ability to speedily quote option prices consistent with an ever-changing market environment is essential. Thus, the smallest acceleration or improvement over traditional pricing methods is crucial to avoid arbitrage. We propose a method for accelerating the pricing of American options to near-instantaneous using a feed-forward neural network. This neural network is trained over the chosen (e.g., Heston) stochastic volatility specification. Such an approach facilitates parameter interpretability, as generally required by the regulators, and establishes our method in the area of eXplainable Artificial Intelligence (XAI) for finance. We show that the proposed deep explainable pricer induces a speed-accuracy trade-off compared to the typical Monte Carlo or Partial Differential Equation-based pricing methods. Moreover, the proposed approach allows for pricing derivatives with path-dependent and more complex payoffs and is, given the sufficient accuracy of computation and its tractable nature, applicable in a market-making environment

Application of Machine Learning: An Analysis of Asian Options Pricing Using Neural Netwoprk

Pricing Asian Option is imperative to researchers, analysts, traders and any other related experts involved in the option trading markets and the academic field. Not only trading highly affected by the accuracy of the price of Asian options but also portfolios that involve hedging of commodity. Several attempts have been made to model the Asian option prices with closed-form over the past twenty years such as the Kemna-Vorst Model and Levy Approximation. Although today the two closed-form models are still widely used, their accuracy and reliability are called into question. The reason is simple; the Kemna-Vorst model is derived with an assumption of geometric mean of the stocks. In practice, Average Priced Options are mostly arithmetic and thus always have a volatility high than the volatility of a geometric mean making the Asian options always underpriced. On the other hand, the Levy Approximation using Monte Carlo Simulation as a benchmark, do not perform well when the product of the sigma (volatility) and square root maturity of the underlying is larger than 0.2. When the maturity of the option enlarges, the performance of the Levy Approximation largely deteriorates. If the closed-form models could be improved, higher frequency trading of Asian option will become possible. Moreover, building neural networks for different contracts of Asian Options allows reuse of computed prices and large-scale portfolio management that involves many contracts. In this thesis, we use Neural Network to fill the gap between the price of a closed-form model and that of an Asian option. The significance of this method answers two interesting questions. First, could an Asian option trader with a systematic behavior in pricing learned from previous quotes improve his pricing or trading performance in the future? Second, will a training set of previous data help to improve the performance of a financial model? We perform two simulation experiments and show that the performance of the closed-form model is significantly improved. Moreover, we extend the learning process to real data quote. The use of Neural Network highly improves the accuracy of the traditional closed-form model. The model’s original price is not so much accurate as what we estimate using Neural network and could not capture the high volatility effectively; still, it provides a relative reasonable fit to the problem(Especially the Levy Model). The analysis shows that the Neural Network Algorithms we used affect the results significantly.Computer Scienc

Extending the feature set of a data-driven artificial neural network model of pricing financial option

Prices of derivative contracts, such as options, traded in the financial markets are expected to have complex relationships to fluctuations in the values of the underlying assets, the time to maturity and type of exercise of the contracts as well as other macroeconomic variables. Hutchinson, Lo and Poggio showed in 1994 that a non-parametric artificial neural network may be trained to approximate this complex functional relationship. Here, we consider this model with additional inputs relevant to the pricing of options and showthat the accuracy of approximation may indeed be improved. We consider volume traded, historic volatility, observed interest rates and combinations of these as additional features. In addition to giving empirical results on how the inclusion of these variables helps predicting option prices, we also analyse prediction errors of the different models with volatility and volume traded as inputs, and report an interesting correlation between their contributions

Applications in computational finance with a focus on approximation of financial time series by neurocomputing

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Modelling the volatility of currency exchange rate using GARCH model

This paper attempts to study GARCH models with their modifications, in capturing the volatility of the exchange rates. The parameters of these models are estimated using the maximum likelihood method. The performance of the within-sample estimation is diagnosed using several goodness-of-fit statistics and the accuracy of the out-of-sample and one-step-ahead forecasts is evaluated using mean square error. The results indicate that the volatility of the RM/Sterling exchange rate is persistent. The within sample estimation results support the usefulness of the GARCH models and reject the constant variance model, at least within-sample. The Qstatistic and LM tests suggest that long memory GARCH models should be used instead of the short-term memory and high order ARCH model. The stationary GARCH-M outperforms other GARCH models in out-of-sample and one-step-ahead forecasting. When using random walk model as the naive benchmark, all GARCH models outperform this model in forecasting the volatility of the RM/Sterling exchange rates

Statistical hedging with neural networks

This thesis investigates the problem of statistical hedging with artificial neural networks (ANNs). The statistical hedging is a data-driven approach that derives hedging strategy from data and hence does not rely on making assumptions of the underlying asset. Consider an investor who sells an option and wishes to hedge it with some amount of underlying asset. ANNs can be used to determine this number by minimising the discrete hedging error. In the first chapter, we provide a comprehensive literature review of papers on the topic of using ANNs for option pricing and hedging, as well as other related ones. Based on our research experience and summary of papers, we provide several advices that we believe are critical in using ANNs for option pricing and hedging problem. In particular, we point out an existing information leakage issue in the literature when preparing data. This review is invaluable for future researchers who are wish to work in this topic. In the second chapter, we consider the hedging problem in the single period case. The ANN is designed to output a hedging ratio directly, instead of first learning to prices. The experiments are taken on simulated Black-Scholes (BS), Heston, end-of-day S&P 500, and tick Euro Stoxx 50 datasets. The results show the ANN can significantly outperform the BS benchmark, but is only comparable to linear regressions on sensitivities. Hence, we illustrate that the edge of the two statistical hedging methods arises mainly from the existence of the leverage effect. Moreover, the information leakage found in the literature is reproduced. It’s shown that a wrong in- and out-of-sample split can overestimate the performance of statistical hedging methods. This leakage can be further exploited by tagging independent variables. Building on the previous chapter, sensitivity analysis are given in the third chapter. They concern data cleaning on the two historical datasets, different simulation parameters of the two simulated datasets, and data preparations. In particular, we show that the statistical hedging methods can also exploit drift and convexity apart from the leverage effect. In the last chapter, our model is extended to multiple periods on the Black-Scholes data. The replicating portfolio is rebalanced with a fixed frequency over the option’s life. We show again the ANN and linear regression methods outperform the BS benchmark, and their performance are comparable

Modelling the Dynamics of Credit Spreads of European Corporate Bond Indices

Credit spreads are important financial tools, since they are used as indicators of economic progression, investment decisions, trading and hedging, as well as pricing credit derivatives. Their role has become more significant for the European fixed income markets since the introduction of the Euro, which reshaped the mechanics of the financial environment. The introduction of single currency provided the means for a pan-European economic growth and cross-border development, liberalized a vast inflow of capital which was once fragmented into different currencies, and provided the dynamics of cross-border investments around a unified legislative framework. Thus, the main subject of the thesis is to provide further insight into and investigate the nature and the dynamics of credit spreads of European corporate bond indices during the credit crisis period. Traditional quantitative credit risk models assume that changes in spreads are normally distributed but empirical evidence shows that they are likely to be skewed and fat-tailed, and if they are ignored then the calculation of loss probabilities will be seriously compromised. Therefore, the first area of investigation aims to provide further insight into the dynamics of higher moments and regime shifts in credit spread changes by applying a GARCH-type model that allows for time-varying volatility, skewness and kurtosis, as well as a Markov regime-switching GARCH specification to capture the structural changes in the volatility of credit spreads. Furthermore, a comparison of the different specifications is undertaken in order to assess which model better fits the empirical distribution of the data and produces best Value-at-Risk estimates. The results presented have significant implications for risk management, as well as in the pricing of credit derivatives. The second area of investigation is to assess and evaluate time-varying correlation of credit spreads. Different multivariate GARCH models, such as Orthogonal-GARCH, the Constant and Dynamic Correlation GARCH models, Risk Metrics and Diagonal-BEKK, are applied to examine the behaviour and dynamics of time-varying correlation. Additionally, the performance of the proposed models is examined by determining whether they produce accurate VaR estimates. The study finds evidence in support of time-varying correlation coefficients between credit spreads which appears to be market dependent and has implications for pricing of derivatives, portfolio selection, trading and hedging activities, as well as risk management. Finally, the impact of economic determinants of credit spreads such as the risk-free rate, inflation, as well as equity and commodity indices and volatilities, are investigated over different market conditions using regime switching models. The results highlight how the effect of the determinants on credit spreads varies across different market conditions and point to the existence of non-linear relationship between the determinants and credit spread changes. The study reveals that the regime dependent determinants have significant explanatory power only in the high volatility regime. Finally, it is shown that the feed-forward neural network model out-performs the other specifications applied in this study in terms of estimating out-of-sample mean forecasts

Forecasting bitcoin volatility: Exploring the potential of deep learning

This study aims to evaluate forecasting properties of classic methodologies (ARCH and GARCH models) in comparison with deep learning methodologies (MLP, RNN, and LSTM architectures) for predicting Bitcoin's volatility. As a new asset class with unique characteristics, Bitcoin's high volatility and structural breaks make forecasting challenging. Based on 2753 observations from 08-09-2014 to 01-05-2022, this study focuses on Bitcoin logarithmic returns. Results show that deep learning methodologies have advantages in terms of forecast quality, although significant computational costs are required. Although both MLP and RNN models produce smoother forecasts with less fluctuation, they fail to capture large spikes. The LSTM architecture, on the other hand, reacts strongly to such movements and tries to adjust its forecast accordingly. To compare forecasting accuracy at different horizons MAPE, MAE metrics are used. Diebold-Mariano tests were conducted to compare the forecast, confirming the superiority of deep learning methodologies. Overall, this study suggests that deep learning methodologies could provide a promising tool for forecasting Bitcoin returns (and therefore volatility), especially for short-term horizons.info:eu-repo/semantics/publishedVersio