458 research outputs found
Incorporating prior financial domain knowledge into neural networks for implied volatility surface prediction
In this paper we develop a novel neural network model for predicting implied
volatility surface. Prior financial domain knowledge is taken into account. A
new activation function that incorporates volatility smile is proposed, which
is used for the hidden nodes that process the underlying asset price. In
addition, financial conditions, such as the absence of arbitrage, the
boundaries and the asymptotic slope, are embedded into the loss function. This
is one of the very first studies which discuss a methodological framework that
incorporates prior financial domain knowledge into neural network architecture
design and model training. The proposed model outperforms the benchmarked
models with the option data on the S&P 500 index over 20 years. More
importantly, the domain knowledge is satisfied empirically, showing the model
is consistent with the existing financial theories and conditions related to
implied volatility surface.Comment: 8 pages, SIGKDD 202
Pricing options and computing implied volatilities using neural networks
This paper proposes a data-driven approach, by means of an Artificial Neural
Network (ANN), to value financial options and to calculate implied volatilities
with the aim of accelerating the corresponding numerical methods. With ANNs
being universal function approximators, this method trains an optimized ANN on
a data set generated by a sophisticated financial model, and runs the trained
ANN as an agent of the original solver in a fast and efficient way. We test
this approach on three different types of solvers, including the analytic
solution for the Black-Scholes equation, the COS method for the Heston
stochastic volatility model and Brent's iterative root-finding method for the
calculation of implied volatilities. The numerical results show that the ANN
solver can reduce the computing time significantly
FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs
Here, we introduce a new approach for generating sequences of implied
volatility (IV) surfaces across multiple assets that is faithful to historical
prices. We do so using a combination of functional data analysis and neural
stochastic differential equations (SDEs) combined with a probability integral
transform penalty to reduce model misspecification. We demonstrate that
learning the joint dynamics of IV surfaces and prices produces market scenarios
that are consistent with historical features and lie within the sub-manifold of
surfaces that are essentially free of static arbitrage. Finally, we demonstrate
that delta hedging using the simulated surfaces generates profit and loss (P&L)
distributions that are consistent with realised P&Ls.Comment: 30 pages, 12 figures, 5 table
No-Arbitrage Deep Calibration for Volatility Smile and Skewness
Volatility smile and skewness are two key properties of option prices that
are represented by the implied volatility (IV) surface. However, IV surface
calibration through nonlinear interpolation is a complex problem due to several
factors, including limited input data, low liquidity, and noise. Additionally,
the calibrated surface must obey the fundamental financial principle of the
absence of arbitrage, which can be modeled by various differential inequalities
over the partial derivatives of the option price with respect to the expiration
time and the strike price. To address these challenges, we have introduced a
Derivative-Constrained Neural Network (DCNN), which is an enhancement of a
multilayer perceptron (MLP) that incorporates derivatives in the output
function. DCNN allows us to generate a smooth surface and incorporate the
no-arbitrage condition thanks to the derivative terms in the loss function. In
numerical experiments, we apply the stochastic volatility model with smile and
skewness parameters and simulate it with different settings to examine the
stability of the calibrated model under different conditions. The results show
that DCNNs improve the interpolation of the implied volatility surface with
smile and skewness by integrating the computation of the derivatives, which are
necessary and sufficient no-arbitrage conditions. The developed algorithm also
offers practitioners an effective tool for understanding expected market
dynamics and managing risk associated with volatility smile and skewness.Comment: 9 pages, 7 figure
American Option Pricing using Self-Attention GRU and Shapley Value Interpretation
Options, serving as a crucial financial instrument, are used by investors to
manage and mitigate their investment risks within the securities market.
Precisely predicting the present price of an option enables investors to make
informed and efficient decisions. In this paper, we propose a machine learning
method for forecasting the prices of SPY (ETF) option based on gated recurrent
unit (GRU) and self-attention mechanism. We first partitioned the raw dataset
into 15 subsets according to moneyness and days to maturity criteria. For each
subset, we matched the corresponding U.S. government bond rates and Implied
Volatility Indices. This segmentation allows for a more insightful exploration
of the impacts of risk-free rates and underlying volatility on option pricing.
Next, we built four different machine learning models, including multilayer
perceptron (MLP), long short-term memory (LSTM), self-attention LSTM, and
self-attention GRU in comparison to the traditional binomial model. The
empirical result shows that self-attention GRU with historical data outperforms
other models due to its ability to capture complex temporal dependencies and
leverage the contextual information embedded in the historical data. Finally,
in order to unveil the "black box" of artificial intelligence, we employed the
SHapley Additive exPlanations (SHAP) method to interpret and analyze the
prediction results of the self-attention GRU model with historical data. This
provides insights into the significance and contributions of different input
features on the pricing of American-style options.Comment: Working pape
Deep learning for trading and hedging in financial markets
Deep learning has achieved remarkable results in many areas, from image classification, language translation to question answering. Deep neural network models have proved to be good at processing large amounts of data and capturing complex relationships embedded in the data. In this thesis, we use deep learning methods to solve trading and hedging problems in the financial markets. We show that our solutions, which consist of various deep neural network models, could achieve better accuracies and efficiencies than many conventional mathematical-based methods.
We use Technical Analysis Neural Network (TANN) to process high-frequency tick data from the foreign exchange market. Various technical indicators are calculated from the market data and fed into the neural network model. The model generates a classification label, which indicates the future movement direction of the FX rate in the short term. Our solution can surpass many well-known machine learning algorithms on classification accuracies.
Deep Hedging models the relationship between the underlying asset and the prices of option contracts. We upgrade the pipeline by removing the restriction on trading frequency. With different levels of risk tolerances, the modified deep hedging model can propose various hedging solutions. These solutions form the Efficient Hedging Frontier (EHF), where their associated risk levels and returns are directly observable. We also show that combining a Deep Hedging model with a prediction algorithm ultimately increases the hedging performances.
Implied volatility is the critical parameter for evaluating many financial derivatives. We propose a novel PCA Variational Auto-Enocder model to encode three independent features of implied volatility surfaces from the European stock markets. This novel encoding brings various benefits to generating and extrapolating implied volatility surfaces. It also enables the transformation of implied volatility surfaces from a stock index to a single stock, significantly improving the efficiency of derivatives pricing
Option valuation under no-arbitrage constraints with neural networks
In this paper, we start from the no-arbitrage constraints in option pricing and develop a novel hybrid gated neural network (hGNN) based option valuation model. We adopt a multiplicative structure of hidden layers to ensure model differentiability. We also select the slope and weights of input layers to satisfy the no-arbitrage constraints. Meanwhile, a separate neural network is constructed for predicting option-implied volatilities. Using S&P 500 options, our empirical analyses show that the hGNN model substantially outperforms well-established alternative mod els in the out-of-sample forecasting and hedging exercises. The superior prediction performance stems from our model’s ability in describing options on the boundary, and in offering analytical expressions for option Greeks which generate better hedging results
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