Accurate Neural Network Option Pricing Methods with Control Variate Techniques and Data Synthesis/Cleaning with Financial Rationality

This paper enhances option pricing accuracy by incorporating financial expertise into a neural network (NN) design and optimizing data sample quality through cleaning and synthesis. Instead of directly estimating option values (OVs) with NNs, we leverage the concept of control variate by decomposing OVs as time values (TVs) estimated by NNs, plus the analytically solvable intrinsic values (IVs). TV surface can be decomposed into two scenarios with very different properties, and we design two NNs according to our derived no-arbitrage constraints for these two scenarios. To alleviate learning inaccuracy due to the kink of the TV surface along the scenario boundary, we synthesize training samples based on our derived constraints to smoothly extend the surface for each scenario. On the other hand, irrational option quotes commonly found in illiquid markets incur uneven surfaces, significantly deteriorating NN predictability. We develop a learnable data-cleaning method to remove potentially irrational quotes spotted by no-arbitrage constraints properly. Besides, unnecessary data syntheses proposed in previous literature can also be removed by incorporating corresponding constraints into our NN to enhance training efficiency. Comprehensive experiments on liquid S&P 500 and illiquid TAIEX option markets examine the superiority of our approach.