Pricing and Hedging European Options in Incomplete Markets with Neural Networks
Paper explores neural network pricing and hedging of European options in incomplete markets, surpassing Black-Scholes benchmarks.
What it examines
This study uses machine learning to jointly price and hedge European options in an incomplete market. A single neural network estimates both the option price and its hedging strategy by leveraging the self-financing condition, comparing its performance against traditional Black-Scholes methods.
What it concludes
The results show that enhancing neural networks with endogenous terminal conditions and arbitrage constraints improves hedging performance. Applications include better risk management and pricing in volatile markets. The research paves the way for advanced pricing tools and future work on complex options in incomplete markets.
Evidence objects
Researchers introduce an innovative neural network framework for pricing and hedging European options in incomplete markets, estimating option prices and hedging strategies while outperforming traditional Black-Scholes methods under stochastic volatility.
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By incorporating an endogenous terminal condition and enforcing arbitrage constraints via a novel violation loss function, the approach handles non-differentiable payoffs, ensuring price bounds despite the challenges of market incompleteness.
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Extensive simulations optimize the neural network via gradient descent with Adam algorithm, revealing improvements that evolve into enhanced hedging strategies mitigating extreme losses, though discrete hedging and market incompleteness persist.
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Utilizing a single neural network, the paper innovatively integrates pricing and hedging of European options in incomplete markets. Combining these functions demonstrates significant originality and practical relevance, advancing derivative modeling. The methodology is fresh and compelling, promising quantitative finance strategies while employing $ neural network $ techniques enrich volatility analysis and risk management.
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Raw abstract and provenance
- … pricing and hedging European options in an incomplete financial market using machine learning … to simultaneously determine the option price and its hedging strategy. In …
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