FITTING LOCAL VOLATILITY

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Focusing on local volatility and its model, this book addresses unresolved issues in mathematical finance, such as deriving analytical solutions for the Dupire equation and creating efficient calibration methods for local volatility surfaces. It explores no-arbitrage techniques for interpolating and extrapolating volatility surfaces and extends the local volatility concept beyond the Black-Scholes framework. Additionally, it examines the integration of deep learning and neural networks into financial engineering, offering fresh perspectives on classical financial problems.