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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