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Tasdighi, Alireza | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42462 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Zohuri Zangeneh, Bijan; Foroush Bastani, Ali
  7. Abstract:
  8. Modeling and simulating accurate patterns which are adapted to our real world is a hard and complicated task. The most important thing for these models is finding any explicite solution, or, finding any solution that is precise as much as possible. The knowledge of financial mathematics by gathering several sciences such as: probabilities, stochastic analysis, numerical analysis, and stochastic differential equations, attempt to determine such exact solutions, or, try to appoximate the explicit answers as precise as possible; in the world of financial trades and contracts. Moreover; one of the most important requirements to control the risk of these financial cotracts, and, then to optimize our financial decisions is controlling the error of our approximations of any stochastic differential equations that may arise from the models. In this dissertation, at first, our goal is, approximation of stochastic differential equations by Euler-Maruyama method and controlling the error of this method by using Adaptive method. Next; in the second step, we first introduce LIBOR market model(based on [4, 16]), then would bring one new concept to analyse the sensitivity of swaption Price(based on [9]) , and finally, as an application of Adaptive method, we approximate the price of swaption using Euler-Maruyama method and besides, would implement the Adaptive method to control the error of approximation
  9. Keywords:
  10. Stochastic Differential Equation ; Euler-Maruyama Method ; Sensitivity Analysis ; European and American Option ; Adaptive Method ; Weak Approximation

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