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| Type | Master's Thesis |
| Scope | Discipline-based scholarship |
| Title | Approximation schemes for stochastic differential equations with applications to derivatives pricing and Greeks estimations |
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| Institution | University of Zurich |
| Faculty | Faculty of Business, Economics and Informatics |
| Number of Pages | 84 |
| Date | 2020 |
| Abstract Text | Pricing exotic derivatives under the local volatility model requires numerical methods that have an inherent trade-off between accuracy and efficiency. By increasing the number of simulations and choosing a dense discretization grid, smaller errors can be obtained, although at the cost of significantly higher computational complexity. In order to decrease the errors without increasing the computational complexity, alternative stochastic differential equation (SDE) approximation schemes and variance reduction methods can be considered. In this thesis, we investigate the benefit of higher order SDE approximation schemes and variance reduction methods in derivatives pricing under the local volatility model. Several strong and weak higher order stochastic Runge-Kutta approximation schemes are derived and applied to estimate errors present in fair prices and price sensitivities for vanilla and path-dependent financial products under differently shaped parabolic and real local volatility surfaces. Antithetic sampling, Quasi-Monte Carlo and Brownian bridge numerical schemes are also discussed and applied in search for a better Monte Carlo convergence. |
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