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Pricing with Bivariate Unspanned Stochastic Volatility Models
Unspanned stochastic volatility (USV) models have gained popularity in the literature. USV models contain at least one source of volatility-related risk that cannot be hedged with bonds, referred to as the unspanned volatility factor(s). Bivariate USV models are the simplest case, comprising of one...
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| Format: | Thesis |
| Language: | English |
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African Institute of Financial Markets and Risk Management
2020
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| _version_ | 1867613167850356736 |
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| access_status_str | Open Access |
| author | Wort, Joshua |
| author2 | Backwell, Alex |
| author_browse | Backwell, Alex Wort, Joshua |
| author_facet | Backwell, Alex Wort, Joshua |
| author_sort | Wort, Joshua |
| collection | Thesis |
| description | Unspanned stochastic volatility (USV) models have gained popularity in the literature. USV models contain at least one source of volatility-related risk that cannot be hedged with bonds, referred to as the unspanned volatility factor(s). Bivariate USV models are the simplest case, comprising of one state variable controlling the term structure and the other controlling unspanned volatility. This dissertation focuses on pricing with two particular bivariate USV models: the Log-Affine Double Quadratic (1,1) – or LADQ(1,1) – model of Backwell (2017) and the LinearRational Square Root (1,1) – or LRSQ(1,1) – model of Filipovic´ et al. (2017). For the LADQ(1,1) model, we fully outline how an Alternating Directional Implicit finite difference scheme can be used to price options and implement the scheme to price caplets. For the LRSQ(1,1) model, we illustrate a semi-analytical Fourierbased method originally designed by Filipovic´ et al. (2017) for pricing swaptions, but adjust it to price caplets. Using the above numerical methods, we calibrate each (1,1) model to both the British-pound yield curve and caps market. Although we cannot achieve a close fit to the implied volatility surface, we find that the parameters in the LADQ(1,1) model have direct control over the qualitative features of the volatility skew, unlike the parameters within the LRSQ(1,1) model. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/31323 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:50.330Z |
| 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:11427/31323 Pricing with Bivariate Unspanned Stochastic Volatility Models Wort, Joshua Backwell, Alex Mathematical Finance Unspanned stochastic volatility (USV) models have gained popularity in the literature. USV models contain at least one source of volatility-related risk that cannot be hedged with bonds, referred to as the unspanned volatility factor(s). Bivariate USV models are the simplest case, comprising of one state variable controlling the term structure and the other controlling unspanned volatility. This dissertation focuses on pricing with two particular bivariate USV models: the Log-Affine Double Quadratic (1,1) – or LADQ(1,1) – model of Backwell (2017) and the LinearRational Square Root (1,1) – or LRSQ(1,1) – model of Filipovic´ et al. (2017). For the LADQ(1,1) model, we fully outline how an Alternating Directional Implicit finite difference scheme can be used to price options and implement the scheme to price caplets. For the LRSQ(1,1) model, we illustrate a semi-analytical Fourierbased method originally designed by Filipovic´ et al. (2017) for pricing swaptions, but adjust it to price caplets. Using the above numerical methods, we calibrate each (1,1) model to both the British-pound yield curve and caps market. Although we cannot achieve a close fit to the implied volatility surface, we find that the parameters in the LADQ(1,1) model have direct control over the qualitative features of the volatility skew, unlike the parameters within the LRSQ(1,1) model. 2020-02-25T11:48:22Z 2020-02-25T11:48:22Z 2019 2020-02-25T09:16:02Z Master Thesis Masters MPhil http://hdl.handle.net/11427/31323 eng application/pdf African Institute of Financial Markets and Risk Management Faculty of Commerce |
| spellingShingle | Mathematical Finance Wort, Joshua Pricing with Bivariate Unspanned Stochastic Volatility Models |
| thesis_degree_str | Master's |
| title | Pricing with Bivariate Unspanned Stochastic Volatility Models |
| title_full | Pricing with Bivariate Unspanned Stochastic Volatility Models |
| title_fullStr | Pricing with Bivariate Unspanned Stochastic Volatility Models |
| title_full_unstemmed | Pricing with Bivariate Unspanned Stochastic Volatility Models |
| title_short | Pricing with Bivariate Unspanned Stochastic Volatility Models |
| title_sort | pricing with bivariate unspanned stochastic volatility models |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/31323 |
| work_keys_str_mv | AT wortjoshua pricingwithbivariateunspannedstochasticvolatilitymodels |