Abstract
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 models 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.
Highlights
Option valuation is a much devoted area in the financial economics literature
We show that the hybrid gated neural network (hGNN) model exhibits significantly improved performance compared with traditional stochastic volatility with random jumps (SVJ), stochastic volatility and stochastic interest rate (SVSI), and stochastic volatility (SV) models with much smaller mean absolute percentage error (MAPE) and root mean square errors (RMSE)
The recent literature has seen substantial advancement in a number of new option pricing models based on data science methods that generate more precise option price forecasts
Summary
Option valuation is a much devoted area in the financial economics literature. Since the seminal work of Black and Scholes (1973), many pricing models have been developed that extend restrictive assumptions of the Black and Scholes (BS) model and advance our understanding of options and the market in which they are traded. Motivated by the above strands of the literature, in this paper we propose an economically meaningful hybrid gated neural network (hGNN) based option valuation model. We contribute to the literature by offering comprehensive empirical evidence that our hGNN model outperforms popular neutral network based models as well as economically motivated models such as those featuring stochastic volatility and jumps in underlying asset returns They include a deep neural network (dNN) model, the best-performing specification in Andreou et al (2008, 2010) (AnNN), a stochastic volatility model, a stochastic volatility model with stochastic interest, and a stochastic volatility model with jumps. Our hGNN model is constructed based on no-arbitrage conditions, including option boundary conditions, and is trained by synthetic prices for thinly traded options, it substantially outperforms the other two neural network based models in predicting options in Group 1 This underscores the empirical prowess of our model.
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