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Zabr modelling

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par Kaiza Amouh
Ecole Polytechnique (X) - DEA Probabilités et Finance 2014
  

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3.3 Fast calibration of the model's parameters ........... 29

4 Finite difference volatility ........................ 30

5 Calibrating the Volatility function .................... 32

Conclusion 35

Appendices 35

A Numerical pricing under Normal SABR model 37

1 Density for Normal SABR ........................ 37

2 Computation of functions Ö and ê ................... 38

viii CONTENTS

CONTENTS

B Equivalence between Normal and Log-normal Implied Volatility 41

1 Another pricing formula for call options in the Bachelier model . . . . 42

2 Asymptotics of the implied normal volatility .............. 45

2.1 First and Second order expansion ................ 45

2.2 Accuracy of asymptotic expansions ............... 47

3 Comparing greeks and delta-hedged portfolios ............. 49

Bibliography 53

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