Analytical Valuation of Vulnerable Exchange Options with Stochastic Volatility in a Reduced-Form Model
This paper investigates the valuation of vulnerable exchange options with two underlying assets that follow a two-factor volatility model. We employ a reduced-form model incorporating a Poisson process with stochastic intensity. The proposed reduced-form model depends on a stochastic intensity proce...
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MDPI AG
2024-12-01
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| Series: | Mathematics |
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| author | Junkee Jeon Geonwoo Kim |
| author_facet | Junkee Jeon Geonwoo Kim |
| author_sort | Junkee Jeon |
| collection | DOAJ |
| description | This paper investigates the valuation of vulnerable exchange options with two underlying assets that follow a two-factor volatility model. We employ a reduced-form model incorporating a Poisson process with stochastic intensity. The proposed reduced-form model depends on a stochastic intensity process that is guaranteed to remain positive and includes both systemic and idiosyncratic risks. Using measure change techniques and characteristic functions, we obtain an explicit pricing formula for vulnerable exchange options within the proposed framework. We also provide numerical examples demonstrating the sensitivity of option prices to significant parameters. |
| format | Article |
| id | doaj-art-cd3f106e07ae451ea10471a465135379 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-cd3f106e07ae451ea10471a4651353792025-08-20T02:00:34ZengMDPI AGMathematics2227-73902024-12-011224387910.3390/math12243879Analytical Valuation of Vulnerable Exchange Options with Stochastic Volatility in a Reduced-Form ModelJunkee Jeon0Geonwoo Kim1Department of Applied Mathematics, Kyung Hee University, Yongin 17104, Republic of KoreaSchool of Natural Sciences, Seoul National University of Science and Technology, Seoul 01811, Republic of KoreaThis paper investigates the valuation of vulnerable exchange options with two underlying assets that follow a two-factor volatility model. We employ a reduced-form model incorporating a Poisson process with stochastic intensity. The proposed reduced-form model depends on a stochastic intensity process that is guaranteed to remain positive and includes both systemic and idiosyncratic risks. Using measure change techniques and characteristic functions, we obtain an explicit pricing formula for vulnerable exchange options within the proposed framework. We also provide numerical examples demonstrating the sensitivity of option prices to significant parameters.https://www.mdpi.com/2227-7390/12/24/3879exchange optionvulnerable optionstochastic volatilityreduced-form model |
| spellingShingle | Junkee Jeon Geonwoo Kim Analytical Valuation of Vulnerable Exchange Options with Stochastic Volatility in a Reduced-Form Model Mathematics exchange option vulnerable option stochastic volatility reduced-form model |
| title | Analytical Valuation of Vulnerable Exchange Options with Stochastic Volatility in a Reduced-Form Model |
| title_full | Analytical Valuation of Vulnerable Exchange Options with Stochastic Volatility in a Reduced-Form Model |
| title_fullStr | Analytical Valuation of Vulnerable Exchange Options with Stochastic Volatility in a Reduced-Form Model |
| title_full_unstemmed | Analytical Valuation of Vulnerable Exchange Options with Stochastic Volatility in a Reduced-Form Model |
| title_short | Analytical Valuation of Vulnerable Exchange Options with Stochastic Volatility in a Reduced-Form Model |
| title_sort | analytical valuation of vulnerable exchange options with stochastic volatility in a reduced form model |
| topic | exchange option vulnerable option stochastic volatility reduced-form model |
| url | https://www.mdpi.com/2227-7390/12/24/3879 |
| work_keys_str_mv | AT junkeejeon analyticalvaluationofvulnerableexchangeoptionswithstochasticvolatilityinareducedformmodel AT geonwookim analyticalvaluationofvulnerableexchangeoptionswithstochasticvolatilityinareducedformmodel |