Solving the partial differential equation for pricing barrier options via trigonometric expansions

Barrier options, although highly liquid financial derivatives, present notable pricing challenges. In this thesis, we present a novel pricing approach for valuing continuously-monitored knock-out barrier options within the framework of stochastic volatility models.<br/><br/>The underlying process is firstly modelled under geometric Brownian...

Hedging error as generalized timing risk

This paper introduces a methodology to disentangle the hedging error associated with the hedging of exotic derivatives, whose payment time is unknown at inception. We derive the mathematical representation for a one-dimensional setting: we identify and characterize the hedging error and discuss the economic intuition of hedging error as a...

Collocating Volatility: A Competitive Alternative to Stochastic Local Volatility Models

We discuss a competitive alternative to stochastic local volatility models, namely the Collocating Volatility (CV) framework, introduced in [L. A. Grzelak (2019) The CLV framework-A fresh look at efficient pricing with smile, International Journal of Computer Mathematics 96 (11), 2209-2228]. The CV framework consists of two elements, a ...

Pricing and hedging options in a negative interest rate environment

This thesis is about pricing interest rate options in a negative interest rate environment and about pricing foreign exchange barrier options. Conventional interest rate option pricing models are unable to price interest rate options in the current negative interest rate environment. Displaced versions and free boundary versions of the...

Numerical Pricing of Equity Barrier Options with Local Volatility

This thesis is about the pricing of equity barrier options under local volatility. We study Dupire's nonparametric local volatility model, which can be defined in terms of call option prices or in terms of implied volatilities. No-arbitrage conditions are derived for the call option surface, and equivalent conditions for the total variance...