scholarly journals Static Hedging of Barrier Options with a Smile: An Inverse Problem

2002 ◽  
Vol 8 ◽  
pp. 127-142 ◽  
Author(s):  
Claude Bardos ◽  
Raphaël Douady ◽  
Andrei Fursikov
Keyword(s):  
Inverse Problem ◽  
Barrier Options ◽  
Static Hedging

SEMI-STATIC HEDGING OF BARRIER OPTIONS UNDER POISSON JUMPS

2011 ◽  
Vol 14 (07) ◽  
pp. 1091-1111 ◽  
Author(s):  
PETER CARR
Keyword(s):  
Barrier Options ◽  
Barrier Option ◽  
Poisson Jumps ◽  
Classical Dynamic ◽  
Continuous Processes ◽  
Static Hedging ◽  
Dynamic Replication ◽  
Independent Process ◽  
The Difference ◽  
Riskless Asset

We show that the payoff to barrier options can be replicated when the underlying price process is driven by the difference of two independent Poisson processes. The replicating strategy employs simple semi-static positions in co-terminal standard options. We note that classical dynamic replication using just the underlying asset and a riskless asset is not possible in this context. When the underlying of the barrier option has no carrying cost, we show that the same semi-static trading strategy continues to replicate even when the two jump arrival rates are generalized into positive even functions of distance to the barrier and when the clock speed is randomized into a positive continuous independent process. Since the even function and the positive process need no further specification, our replicating strategies are also semi-robust. Finally, we show that previous results obtained for continuous processes arise as limits of our analysis.

Duality in static hedging of barrier options

Optimization ◽  
2009 ◽  
Vol 58 (3) ◽  
pp. 319-333 ◽  
Author(s):  
J.H. Maruhn
Keyword(s):  
Barrier Options ◽  
Static Hedging

Static hedging and model risk for barrier options

2006 ◽  
Vol 26 (5) ◽  
pp. 449-463 ◽  
Author(s):  
Morten Nalholm ◽  
Rolf Poulsen
Keyword(s):  
Barrier Options ◽  
Model Risk ◽  
Static Hedging

Static Hedging of Barrier Options under General Asset Dynamics

2006 ◽  
Vol 13 (4) ◽  
pp. 46-60 ◽  
Author(s):  
Morten Nalholm ◽  
Rolf Poulsen
Keyword(s):  
Barrier Options ◽  
Static Hedging

Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model

2014 ◽  
Vol 15 (12) ◽  
pp. 1995-2010 ◽  
Author(s):  
José Carlos Dias ◽  
João Pedro Vidal Nunes ◽  
João Pedro Ruas
Keyword(s):  
Barrier Options ◽  
Double Barrier ◽  
Cev Model ◽  
Static Hedging

scholarly journals A numerical scheme based on semi-static hedging strategy

2014 ◽  
Vol 20 (4) ◽  
Author(s):  
Yuri Imamura ◽  
Yuta Ishigaki ◽  
Toshiki Okumura
Keyword(s):  
Diffusion Process ◽  
Numerical Scheme ◽  
Numerical Results ◽  
Barrier Options ◽  
Barrier Option ◽  
Hedging Strategy ◽  
Underlying Process ◽  
Static Hedging ◽  
Black Scholes ◽  
Path Dependent

AbstractIn the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier options. To get the static hedging formula, the underlying process needs to have a symmetry. We introduce a way to “symmetrize” a given diffusion process. Then the pricing of a barrier option is reduced to that of plain options under the symmetrized process. To show how our symmetrization scheme works, we will present some numerical results of path-independent Euler–Maruyama approximation applied to our scheme, comparing them with the path-dependent Euler–Maruyama scheme when the model is of the type Black–Scholes, CEV, Heston, and (λ)-SABR, respectively. The results show the effectiveness of our scheme.

A modified static hedging method for continuous barrier options

2010 ◽  
Vol 30 (12) ◽  
pp. 1150-1166 ◽  
Author(s):  
San-Lin Chung ◽  
Pai-Ta Shih ◽  
Wei-Che Tsai
Keyword(s):  
Barrier Options ◽  
Static Hedging
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