Level-dependent volatility in jumping short-rate models

Chitambo, Nigel Elton Nyasha

Level-dependent volatility in jumping short-rate models

Thesis / Dissertation

2025

Publisher

Universiy of Cape Town

Department

Department of Finance and Tax

Faculty

Faculty of Commerce

Abstract

This dissertation constructs a no-arbitrage term structure with deterministically timed randomly sized jumps to price interest rate contingent claims while accounting for level-dependent volatility. This dissertation will price such claims using an implicit finite difference scheme to implement a modelling framework that prices bonds, bond options and caplets with scheduled shocks to the short-term interest rate to simulate macroeconomic announcements and other sudden developments. This dissertation found that the prices derived from the implicit finite difference scheme agree with those derived from Monte-Carlo simulations and, where applicable, analytical solutions. Moreover, this dissertation shows how innovations in the short-term rate affect the valuations of interest rate contingent claims.

Keywords

finance

tax

Reference:

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Masters

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