@misc{9234333,
  abstract     = {{The Stochastic Alpha Beta Rho (SABR) stochastic volatility model is widely used to price European options, but the lack of an exact closed-form solution leaves practitioners choosing between an analytical asymptotic approximation that loses accuracy in certain cases, and grid-based numerical solvers that must be rerun for every parameter set. This thesis investigates the application of a parametric Physics-Informed Neural Network (PINN) to option pricing under the SABR model. We train a single hybrid PINN on the SABR partial differential pricing equation, supervising it with reference prices computed by an accurate Alternating-Direction Implicit (ADI) solver across a grid of model parameters. Two free SABR model parameters enter the network as additional inputs, such that one trained model spans a continuous region of the parameter space rather than a single configuration. The supervised data loss is complemented with a residual term which enforces the governing dynamics in addition to the training labels. The trained PINN reproduces reference prices within single-digit basis points of implied volatility on average, with larger errors near the boundary of the trained domain. The PINN generalises to unseen parameter combinations, and outperforms the Hagan asymptotic formula in some of the regimes where the expansion is known to break down. The results suggest that a parametric PINN could serve as a SABR pricer covering a continuous region of the model parameter space, while being more accurate than the standard asymptotic approximation in some of the subdomains where it is known to be unreliable.}},
  author       = {{Haglund, Carl and Halabi, Pascal}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master’s Theses in Mathematical Sciences 2026:E63}},
  title        = {{A Parametric Physics-Informed Neural Network for SABR Option Pricing}},
  year         = {{2026}},
}