Calibration Uncertainty in Barrier Options Pricing under the Hull-White Interest Rate Framework

The pricing of derivative contracts requires modelling assumptions about the behaviour of the underlying asset, followed by calibration of the model on market data. It’s standard market practice to disregard the variability in model parameters, treating them as if there were no uncertainty in the calibration output. This leads to calibration risk, i.e. potential mispricing of contracts due to inaccurate model calibration, which may result in losses for financial institutions. The thesis, working within the Hull-White interest rate framework, studies calibration risk in barrier option pricing - an exotic derivative where the option gets either knocked-in or knocked-out if the underlying breaches a given barrier level during the contract lifetime. Building on asymptotic results, the thesis provides confidence intervals for calibrated parameters and model prices, proposes diagnostics of collinearity issues in calibration and implements global sensitivity analyses to identify the most influential parameter when dependencies among parameter estimators are accounted for. Reduced calibration strategies based on global optimization algorithms and time-series calibration are also proposed. In doing so, a range of numerical methods for options pricing and parameter sensitivities evaluation is explored: Monte Carlo provides the starting points, but the heavy computational cost creates the need for more efficient methodologies. Recursive quadrature based on Gauss-Legendre rule and the Fourier transform method named COS are proposed: significant efforts are devoted to an adaptation of the latter to non-Lévy processes, representing a novel application in the literature.