Calibration of Equity Models

This technical paper explores the calibration of equity models, focusing primarily on the local volatility surface and the Heston stochastic volatility model. It addresses the limitations of the Black-Scholes framework, highlighting the volatility smile phenomenon and its implications on option pricing. The paper delves into the mathematical complexities involved in identifying local volatility surfaces, referencing the generalized Black-Scholes model and the use of Tikhonov regularization to address the ill-posed nature of inverse problems.

The implementation details within the UnRısk framework are discussed, outlining the methodologies for solving partial differential equations and minimizing discrepancies between observed and modeled option prices. Additionally, the paper discusses the calibration of the Heston model, involving a five-parameter optimization process to match market-observed implied volatility surfaces. It emphasizes the challenges of parameter identification in stochastic volatility models and the strategies employed to navigate local minima in optimization routines.