Numerical Pricing of Equity Barrier Options with Local Volatility

Numerical Pricing of Equity Barrier Options with Local Volatility

Stout, M.I.

Oosterlee, C.W. (mentor)

Electrical Engineering, Mathematics and Computer Science

Applied mathematics

Numerical Analysis

2014-09-26

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 surface. Dupire's model is implemented based on a Stochastic Volatility Inspired parameterization of the implied volatility surface. The Dupire-SVI model can accurately reproduce the implied volatility smile. Furthermore, we show how to incorporate dividends into our local volatility model. Lastly, we discuss option pricing by solving forward-backward stochastic differential equations with the BCOS method, a Fourier cosine expansion method. We propose a novel pricing method for barrier options by applying the BCOS method to reflected forward-backward stochastic differential equations. We compare the BCOS results to those of the Crank-Nicolson scheme.

equity derivatives
barrier options
local volatility
Dupire
no-arbitrage conditions
Stochastic Volatility Inspired model
dividends
Fourier cosine expansion method
(reflected) forward-backward stochastic differential equations

http://resolver.tudelft.nl/uuid:3d888331-9f15-4ac2-9cfd-63d0b281cab8

Student theses

master thesis

(c) 2014 Stout, M.I.