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Pricing discretely monitored barrier options under exponential-Levy processes

One of the main factors in pricing barrier options is deciding whether to monitor the underlying asset price in continuous time or for a fixed set of time points. Most actively traded barrier options are monitored in discrete time due to reasons such as regulation and practical implementation. This...

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Main Author: Camroodien, Ayesha
Other Authors: Ouwehand, Peter
Format: Thesis
Language:English
Published: African Institute of Financial Markets and Risk Management 2020
Subjects:
Mathematical Finance
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access_status_str Open Access
author Camroodien, Ayesha
author2 Ouwehand, Peter
author_browse Camroodien, Ayesha
Ouwehand, Peter
author_facet Ouwehand, Peter
Camroodien, Ayesha
author_sort Camroodien, Ayesha
collection Thesis
description One of the main factors in pricing barrier options is deciding whether to monitor the underlying asset price in continuous time or for a fixed set of time points. Most actively traded barrier options are monitored in discrete time due to reasons such as regulation and practical implementation. This dissertation presents transform methods for pricing discretely monitored barrier options under exponential-Levy ´ processes. Single-barrier knock-out options are evaluated under the Black-Scholes framework, the normal inverse Gaussian model and the Variance Gamma model. These models are widely implemented when dealing with pricing options sensitive to jumps. A diffusion component is included in the Variance Gamma model for comparison purposes. We focus on the COS method using Fourier-cosine series expansions and the Hilbert transform method to obtain prices fast and accurately. These option pricing approaches are suitable for Levy processes where the ´ analytical form of their characteristic function is available. Furthermore, standard Monte Carlo pricing is used as a reference and an outline of the pricing algorithms is presented. Both methods are easy to implement across the different asset price dynamics. In particular, the COS method produces results faster than the Hilbert transform method, however, the truncation assumptions under the COS method derived in (Fang and Oosterlee, 2009) prove to be unreliable. We observe the truncation range requires adjustment under the different asset price dynamics, as well as the different types of knock-out barrier options.
format Thesis
id oai:open.uct.ac.za:11427/31432
institution University of Cape Town (South Africa)
language eng
last_indexed 2026-06-10T12:34:38.153Z
license_str Not specified — see source repository
provenance_str_mv Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository
publishDate 2020
publishDateRange 2020
publishDateSort 2020
publisher African Institute of Financial Markets and Risk Management
publisherStr African Institute of Financial Markets and Risk Management
record_format dspace
source_str UCTD — University of Cape Town Open Access Repository
spelling oai:open.uct.ac.za:11427/31432 Pricing discretely monitored barrier options under exponential-Levy processes Camroodien, Ayesha Ouwehand, Peter Mathematical Finance One of the main factors in pricing barrier options is deciding whether to monitor the underlying asset price in continuous time or for a fixed set of time points. Most actively traded barrier options are monitored in discrete time due to reasons such as regulation and practical implementation. This dissertation presents transform methods for pricing discretely monitored barrier options under exponential-Levy ´ processes. Single-barrier knock-out options are evaluated under the Black-Scholes framework, the normal inverse Gaussian model and the Variance Gamma model. These models are widely implemented when dealing with pricing options sensitive to jumps. A diffusion component is included in the Variance Gamma model for comparison purposes. We focus on the COS method using Fourier-cosine series expansions and the Hilbert transform method to obtain prices fast and accurately. These option pricing approaches are suitable for Levy processes where the ´ analytical form of their characteristic function is available. Furthermore, standard Monte Carlo pricing is used as a reference and an outline of the pricing algorithms is presented. Both methods are easy to implement across the different asset price dynamics. In particular, the COS method produces results faster than the Hilbert transform method, however, the truncation assumptions under the COS method derived in (Fang and Oosterlee, 2009) prove to be unreliable. We observe the truncation range requires adjustment under the different asset price dynamics, as well as the different types of knock-out barrier options. 2020-03-02T10:08:31Z 2020-03-02T10:08:31Z 2019 2020-03-02T09:39:28Z Master Thesis Masters MPhil http://hdl.handle.net/11427/31432 eng application/pdf African Institute of Financial Markets and Risk Management Faculty of Commerce
spellingShingle Mathematical Finance
Camroodien, Ayesha
Pricing discretely monitored barrier options under exponential-Levy processes
thesis_degree_str Master's
title Pricing discretely monitored barrier options under exponential-Levy processes
title_full Pricing discretely monitored barrier options under exponential-Levy processes
title_fullStr Pricing discretely monitored barrier options under exponential-Levy processes
title_full_unstemmed Pricing discretely monitored barrier options under exponential-Levy processes
title_short Pricing discretely monitored barrier options under exponential-Levy processes
title_sort pricing discretely monitored barrier options under exponential levy processes
topic Mathematical Finance
url http://hdl.handle.net/11427/31432
work_keys_str_mv AT camroodienayesha pricingdiscretelymonitoredbarrieroptionsunderexponentiallevyprocesses

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