On the optimal choice of strike conventions in exchange option pricing
An important but rarely-addressed option pricing question is how to choose appropriate strikes for implied volatility inputs when pricing more exotic multi-asset derivatives. By means of Malliavin calculus, we construct an asymptotically optimal log-linear strike convention for exchange options unde...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Pompeu Fabra |
| Repositorio: | Repositorio Digital de la UPF |
| OAI Identifier: | oai:repositori.upf.edu:10230/70654 |
| Acceso en línea: | http://hdl.handle.net/10230/70654 http://dx.doi.org/10.3390/math12193028 |
| Access Level: | acceso abierto |
| Palabra clave: | Exchange option Implied volatility Margrabe formula Malliavin calculus |
| Sumario: | An important but rarely-addressed option pricing question is how to choose appropriate strikes for implied volatility inputs when pricing more exotic multi-asset derivatives. By means of Malliavin calculus, we construct an asymptotically optimal log-linear strike convention for exchange options under stochastic volatility models. This novel approach allows us to minimize the difference between the corresponding Margrabe computed price and the true option price. We show that this optimal convention does not depend on the specific stochastic volatility model chosen and, furthermore, that parameter estimation can be dramatically simplified by using market observables as inputs. Numerical examples are given that provide strong support for the new methodology. |
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