Browsing by Subject "option pricing"

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    Option pricing with physics-informed neutral networks (PINNS)
    (2024) Zamxaka, Nichume; Rudd, Ralph
    We investigate the application of physics-informed neural networks (PINNs) to option pricing. PINNs are neural networks that are trained to numerically solve partial differential equations (PDEs) by obeying the dynamics induced by the PDE as well as the initial/terminal conditions of the PDE. They are mesh-free to an extent and compute the derivatives of the PDE through backward-propagation. We construct a PINN toy example to solve the Black-Scholes-Merton PDE for a vanilla European option. The numerical solutions from the PINN are compared against the true analytical solution – the Black-Scholes-Merton equation. The problem is also extended by incorporating a local volatility model. Here, we derive the PDE of a vanilla European option under the constant elasticity of variance (CEV) model. We then construct and train a PINN to solve the PDE and compare it to the true analytical solution of a special case of the CEV model, the square-root process.
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    Quantifying the Model Risk Inherent in the Calibration and Recalibration of Option Pricing Models
    (2021-01-04) Feng, Yu; Rudd, Ralph; Baker, Christopher; Mashalaba, Qaphela; Mavuso, Melusi; Schlögl, Erik
    We focus on two particular aspects of model risk: the inability of a chosen model to fit observed market prices at a given point in time (calibration error) and the model risk due to the recalibration of model parameters (in contradiction to the model assumptions). In this context, we use relative entropy as a pre-metric in order to quantify these two sources of model risk in a common framework, and consider the trade-offs between them when choosing a model and the frequency with which to recalibrate to the market. We illustrate this approach by applying it to the seminal Black/Scholes model and its extension to stochastic volatility, while using option data for Apple (AAPL) and Google (GOOG). We find that recalibrating a model more frequently simply shifts model risk from one type to another, without any substantial reduction of aggregate model risk. Furthermore, moving to a more complicated stochastic model is seen to be counterproductive if one requires a high degree of robustness, for example, as quantified by a 99% quantile of aggregate model risk.