Deep Learning Slashes CSI 300 Option Pricing Error by 32.2 Percent

If option prices keep missing the mark, traders and risk managers are working with a blurry compass. This paper tackles that problem for CSI 300 index options by moving beyond the Black–Scholes–Merton formula, which assumes constant volatility and uses a simple linear pricing rule. The new approach learns a nonlinear generator inside a deep Forward–Backward Stochastic Differential Equation framework, pairing a value network that predicts option prices with a generator network that learns the pricing mechanism. It also feeds in volatility trajectories and market sentiment, so the model can react to changing market conditions instead of treating them as background noise. On CSI 300 index options, this setup reduced Mean Absolute Error by 32.2% and Mean Absolute Percentage Error by 35.3% compared with Black–Scholes–Merton. The paper also finds that the gains are not evenly explained: call option improvements are driven mainly by sentiment features, while put options draw more evenly from both volatility trajectory and sentiment. That asymmetry suggests the model is not just fitting numbers better, but capturing different forces at work in different option types.

A 32.2% drop in pricing error sounds dry until real money is on the line. Option prices guide trades, risk checks, and hedges. If the price is off, the whole chain blurs. This work tackles CSI 300 index options. Those options track a major Chinese stock index. It moves beyond Black–Scholes–Merton, the classic pricing formula. That formula treats price swings as flat and steady. The new model lets volatility trajectory, the path of swings, and market sentiment speak at once. The surprise is that calls and puts do not use those clues the same way.

Why the old rule falls short

Two scores tell the story. Mean Absolute Error, or average miss size, fell by 32.2% versus Black–Scholes–Merton. Mean Absolute Percentage Error, or average miss in percent terms, fell by 35.3%. That means the new model stayed closer to real CSI 300 option prices on average. The gains did not stop at the headline score. Interpretability checks show what parts of a model matter most. They found benefits across all option types. Architectural gains were not tied to one path. The same design helped both calls and puts. The signal split by direction. Call options improved mainly from sentiment features. Put options drew more evenly from volatility trajectory and sentiment. That split matches economic intuition. A single rule misses that split.

How Deep g-Pricing learns the rule

Deep g-Pricing uses two neural networks, or pattern-finders built from data. The value network learns the option price. The generator network learns the pricing rule. An FBSDE, a math setup that ties price and hedge together, links the two. The model starts from a learnable initial price. Then it runs forward in time. It also takes volatility trajectory and sentiment features as inputs. A hedging strategy, or risk-offset trade, comes from automatic differentiation. That is a software trick that finds slopes inside the network. Those slopes tell the model how price changes with the market state. The design lets the system learn the rule and the price at once.

Why the call-put split matters

A better price is not the only win. The model also shows where its gains come from. Call prices rely mainly on sentiment. Put prices use both sentiment and volatility trajectory. That matters for anyone who prices, hedges, or watches risk. It says one feature set is not enough for every option type. The new system makes those differences visible. It does not treat calls and puts like twins. It treats them like cousins with different habits. Old formulas hide that split. Deep g-Pricing pulls it into view. So the model helps both price and explain. That is a useful map for risk teams.

What the split leaves open

The surprise is not just the 32.2% gain. It is the split between calls and puts. That split makes a more selective pricing system plausible. Calls can lean harder on sentiment. Puts can keep both sentiment and volatility path in view. A future test should ask if the same pattern holds beyond CSI 300 options. If it does, Deep g-Pricing would be more than a better fit. It would be a cleaner way to read how markets hide their clues. If it does not, the split still points to where the model should look next. Either way, calls and puts do not listen the same way.