Local volatility models
| Autor: | Jelić, Magdalena |
|---|---|
| Přispěvatelé: | Wagner, Vanja |
| Jazyk: | chorvatština |
| Rok vydání: | 2022 |
| Předmět: |
lognormal-mixture
mješoviti lognormalni model hyperbolic sine density mixture Black-Scholes implied volatility Black-Scholesova podrazumijevana volatilnost kosi smiješak volatilnosti Dupire’s formula Dupireova formula model mješovitih sinus hiperbolnih gustoća shifted lognormal model Derman-Kani formula model konstantne elastičnosti varijance PRIRODNE ZNANOSTI. Matematika constant elasticity of variance model formula by Derman and Kani pomaknuti lognormalni model NATURAL SCIENCES. Mathematics |
| Popis: | U ovom radu promatrali smo modele lokalne volatilnosti. Nakon početnog uvođenja potrebnih preliminarija, proučili smo Dupireovu formulu, Derman-Kani formulu te lokalnu volatilnost kao funkciju Black-Scholesove podrazumijevane volatilnosti i opisali izvodenje tih parcijalnih diferencijalnih jednadžbi. Treći dio rada sastoji od samih modela, odnosno prikaza njihovih dinamika. Pomaknuti lognormalni model, kao i model konstantne elastičnosti varijance, postiže kosi smiješak volatilnosti, dok konveksne kombinacije lognormalnih gustoća pružaju bolju aproksimaciju smiješka volatilnosti. Mješoviti lognormalni model s različitim očekivanjima i model mješovitih sinus hiperbolnih gustoća, koje su razvili Brigo i Mercurio, ipak su najbolji medu njima, odnosno zadovoljavaju veći opseg struktura krivulje podrazumijevane volatilnosti. In this thesis, we have observed local volatility models. After introducing needed preliminaries, we have studied Dupire’s formula, formula by Derman and Kani and local volatility as a function of Black-Scholes implied volatility. Moreover, we have described derivation of their partial differential equations. The third part consists of local volatility models and the representation of their dynamics. The shifted lognormal model, as well as the constant elasticity of variance model, achieves only a skewed smile, while lognormal mixtures provide a better approximation of the volatility smile. However, a lognormal-mixture with different means and hyperbolic sine density mixture, developed by Brigo and Mercurio, are the best among these models, that is they accomodate rather general structures of the local volatility curve. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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