Pricing with Bivariate Unspanned Stochastic Volatility Models
| dc.contributor.advisor | Backwell, Alex | |
| dc.contributor.author | Wort, Joshua | |
| dc.date.accessioned | 2020-02-25T11:48:22Z | |
| dc.date.available | 2020-02-25T11:48:22Z | |
| dc.date.issued | 2019 | |
| dc.date.updated | 2020-02-25T09:16:02Z | |
| dc.description.abstract | 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. | |
| dc.identifier.apacitation | Wort, J. (2019). <i>Pricing with Bivariate Unspanned Stochastic Volatility Models</i>. (). ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management. Retrieved from http://hdl.handle.net/11427/31323 | en_ZA |
| dc.identifier.chicagocitation | Wort, Joshua. <i>"Pricing with Bivariate Unspanned Stochastic Volatility Models."</i> ., ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management, 2019. http://hdl.handle.net/11427/31323 | en_ZA |
| dc.identifier.citation | Wort, J. 2019. Pricing with Bivariate Unspanned Stochastic Volatility Models. | en_ZA |
| dc.identifier.ris | TY - Thesis / Dissertation AU - Wort, Joshua AB - 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. DA - 2019 DB - OpenUCT DP - University of Cape Town KW - Mathematical Finance LK - https://open.uct.ac.za PY - 2019 T1 - Pricing with Bivariate Unspanned Stochastic Volatility Models TI - Pricing with Bivariate Unspanned Stochastic Volatility Models UR - http://hdl.handle.net/11427/31323 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/31323 | |
| dc.identifier.vancouvercitation | Wort J. Pricing with Bivariate Unspanned Stochastic Volatility Models. []. ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management, 2019 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/31323 | en_ZA |
| dc.language.rfc3066 | eng | |
| dc.publisher.department | African Institute of Financial Markets and Risk Management | |
| dc.publisher.faculty | Faculty of Commerce | |
| dc.subject | Mathematical Finance | |
| dc.title | Pricing with Bivariate Unspanned Stochastic Volatility Models | |
| dc.type | Master Thesis | |
| dc.type.qualificationlevel | Masters | |
| dc.type.qualificationname | MPhil |