Repeated Richardson extrapolation and static hedging of barrier options under the CEV model

2020 ◽  
Vol 40 (6) ◽  
pp. 974-988
Author(s):  
Jia‐Hau Guo ◽  
Lung‐Fu Chang
Keyword(s):  
Richardson Extrapolation ◽  
Barrier Options ◽  
Cev Model ◽  
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

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

WHAT A DIFFERENCE ONE PROBABILITY MAKES IN THE CONVERGENCE OF BINOMIAL TREES

2020 ◽  
Vol 23 (06) ◽  
pp. 2050040
Author(s):  
GUILLAUME LEDUC ◽  
KENNETH PALMER
Keyword(s):  
Richardson Extrapolation ◽  
Second Order ◽  
Barrier Options ◽  
Numerical Evidence ◽  
First Order ◽  
Black Scholes ◽  
Binomial Trees ◽  
Smooth Convergence ◽  
First Time ◽  
Flexible Model

In the [Formula: see text]-period Cox, Ross, and Rubinstein (CRR) model, we achieve smooth convergence of European vanilla options to their Black–Scholes limits simply by altering the probability at one node, in fact, at the preterminal node between the closest neighbors of the strike in the terminal layer. For barrier options, we do even better, obtaining order [Formula: see text] convergence by altering the probability just at the node nearest the barrier, but only the first time it is hit. First-order smooth convergence for vanilla options was already achieved in Tian’s flexible model but here we show how second order smooth convergence can be achieved by changing one probability, leading to convergence of order [Formula: see text] with Richardson extrapolation. We illustrate our results with examples and provide numerical evidence of our results.

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