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On an optimization problem related to static super-replicating strategies

Xinliang Chen, Griselda Deelstra, Jan Dhaene, Daniël Linders, Michèle Vanmaele
2015 Journal of Computational and Applied Mathematics  
In this paper, we investigate an optimization problem related to super-replicating strategies for European-type call options written on a weighted sum of asset prices, following the initial approach in  ...  This theory is then applied to static super-replication strategies for some exotic options in a stochastic interest rate setting.  ...  The first issue is the (non-)uniqueness of the optimal solution to (7) and hence to the related static super-replicating strategy.  ... 
doi:10.1016/j.cam.2014.10.003 fatcat:a27hjx7wsngxxdofr2v75owtsa

On an Optimization Problem Related to Static Super-Replicating Strategies

Xinliang Chen, Griselda Deelstra, Jan Dhaene, Daniil Linders, Michhle Vanmaele
2014 Social Science Research Network  
In this paper, we investigate an optimization problem related to super-replicating strategies for European-type call options written on a weighted sum of asset prices, following the initial approach in  ...  This theory is then applied to static super-replication strategies for some exotic options in a stochastic interest rate setting.  ...  The first issue is the (non-)uniqueness of the optimal solution to (7) and hence to the related static super-replicating strategy.  ... 
doi:10.2139/ssrn.2436027 fatcat:2atlixobpfe3plkaqye357m77u

Robust static hedging of barrier options in stochastic volatility models

J. H. Maruhn, E. W. Sachs
2008 Mathematical Methods of Operations Research  
In this paper we develop a new semi-infinite programming formulation of the static super-replication problem in stochastic volatility models which allows to incorporate the model parameter uncertainty  ...  After proving existence of robust hedge portfolios and presenting an algorithm to numerically solve the underlying optimization problem, we apply the approach to a detailed real world example.  ...  The authors wish to thank A. M. Giese (HypoVereinsbank AG, HVB Group, Corporates & Markets, Equity Linked Products, Munich, Germany) for his encouragement and support.  ... 
doi:10.1007/s00186-008-0273-2 fatcat:caopsuti5ffkroy4n53ry6jcn4

Option pricing bounds via semidefinite programming

J.A. Primbs
2006 2006 American Control Conference  
This paper develops optimization based bounds on option prices by using a sub or super replicating portfolio of assets whose value at discrete time points can be expressed as piecewise polynomial functions  ...  A dual formulation is then developed, which formulates bounds in terms of an optimization problem involving moment matrices of measures consistent with the prices of tradable assets.  ...  definiteness conditions on moment and localizing matrices, we may write an optimization problem that is dual to the piecewise polynomial super and sub replication problem presented in section 3.  ... 
doi:10.1109/acc.2006.1656391 fatcat:hi7bk72qwzhefhdqlympcjhiay

Computing arbitrage upper bounds on basket options in the presence of bid–ask spreads

Javier Peña, Juan C. Vera, Luis F. Zuluaga
2012 European Journal of Operational Research  
We study the problem of computing the sharpest static-arbitrage upper bound on the price of a European basket option, given the bid-ask prices of vanilla call options in the underlying securities.  ...  We illustrate our results by computing upper bounds on the price of a DJX basket option. The MATLAB code used to compute these bounds is available online at Proof of Lemma 1.  ...  Acknowledgments We thank Hansen Chen at Susquehanna International Group for providing numerous insightful comments on a preliminary version of this manuscript.  ... 
doi:10.1016/j.ejor.2012.04.035 fatcat:aznxczs7h5hsfetpzafyuokcme

Static hedges for reverse barrier options with robustness against skew risk: an empirical analysis

Jan H. Maruhn, Morten Nalholm, Matthias R. Fengler
2011 Quantitative finance (Print)  
We conduct an empirical evaluation of a static super-replicating hedge of barrier options. The hedge is robust to uncertainty about the future skew.  ...  The main result is that the robustness of the static super-replicating portfolio is also empirically confirmed in practice such that the hedge sets an upper bound for the price of skew risk for barrier  ...  Our analysis shows that in contrast to typical dynamic hedging strategies the robust static super-replicating hedge neither takes a view on the forward skew nor on the volatility surface dynamics.  ... 
doi:10.1080/14697680903154241 fatcat:y6rku33eivafpn56s7qeiapbzi

Rebalancing static super-replications

Akihiko Takahashi, Yukihiro Tsuzuki
2017 International Journal of Financial Engineering  
This paper proposes a trading strategy that dynamically rebalances static super-replicating portfolios, which is very useful for both investment and hedging strategies.  ...  Also, we obtain more concrete features for cross-currency and one-touch options based on our general framework.  ...  First, the super-replicating portfolio is constructed at time t = 0 as the cheapest one by solving the optimization problem (3.1) below.  ... 
doi:10.1142/s2424786317500037 fatcat:j7k2e3m6ibhhnesmu5n5dmpka4

Static-arbitrage lower bounds on the prices of basket options via linear programming

Javier Peña, Juan C. Vera, Luis F. Zuluaga
2010 Quantitative finance (Print)  
The LP formulations readily yield super-replicating (subreplicating) strategies for the upper (lower) bound problem.  ...  We show that the problem of computing sharp upper and lower static-arbitrage bounds on the price of a European basket option, given the prices of other similar options, can be cast as a linear program  ...  We next present an optimal super-replication trading strategy that solves (12), and whose value is consequently (14).  ... 
doi:10.1080/14697680902956703 fatcat:l23twf5snnea3dc2xqs5fuyokq

Optimal semi-static hedging in illiquid markets [article]

Teemu Pennanen, Udomsak Rakwongwan
2020 arXiv   pre-print
Galerkin method and integration quadratures are used to approximate the hedging problem by a finite dimensional convex optimization problem which is solved by an interior point method.  ...  Semi-static hedging improves considerably on the purely static options strategy as well as dynamic trading without options.  ...  We use a Galerkin method to approximate the hedging problem by a finite-dimensional convex optimization problem which is then numerically solved by an interior point method much like in [APR18] in a purely  ... 
arXiv:2008.01463v1 fatcat:rzhiz3jq5bf4ni5yqi56xiyjpy

Option replication with large transactions costs

Ariane Reiß
1999 OR spectrum  
The optimal strategy depends on the relation of Sif, and S. In case Sj discounted to T -n exceeds the ask price (case c) no shares are optimum.  ...  The nonlinear optimization problem yields an optimal strategy that requires revising in every trading date.  ... 
doi:10.1007/s002910050080 fatcat:e7yp25uqozburmnmuahvtfw4wq

Option Replication With Large Transactions Costs

Ariane Reiss
1998 Social Science Research Network  
The optimal strategy depends on the relation of Sif, and S. In case Sj discounted to T -n exceeds the ask price (case c) no shares are optimum.  ...  The nonlinear optimization problem yields an optimal strategy that requires revising in every trading date.  ... 
doi:10.2139/ssrn.53208 fatcat:2bpq5ijd7vg5hlepxdmqqw7lkq

Model uncertainty and the pricing of American options

David Hobson, Anthony Neuberger
2016 Finance and Stochastics  
The bound is enforced by a hedging strategy involving these call options which is robust to model error.  ...  This paper quantifies the potential value of this flexibility by identifying the supremum on the price of an American option when we do not impose a model, but rather consider the class of all models which  ...  Similarly, there is a super-replicating Markovian semi-static strategy for which the cost of the strategy is the lowest amongst the class of all super-replicating semi-static strategies. Proof.  ... 
doi:10.1007/s00780-016-0314-2 fatcat:m47gel4gejazhhrx5q4skhhsxq

Page 9440 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
These methods include among others, the method of super-replicating strategies and the utility maximiza- tion theory.”  ...  They present an equilibrium comparative statics analysis to identify those condi- tions under which leader-follower behaviour can be endogenized.  ... 

NEYMAN-PEARSON THEORY AND ITS APPLICATION TO SHORTFALL RISK IN FINANCE

Ju Hong Kim
2012 The Pure and Applied Mathematics  
Minimizing shortfall risk can be reduced to the problem of finding a randomized test ψ in the static problem.  ...  The optimization problem can be solved via the classical Neyman-Pearson theory, and can be also explained in terms of hypothesis testing.  ...  The first one is to find an optimal modified claimψH whereψ is the solution of the static problem min ψ∈R 0 ρ((1 − ψ)H) = ρ((1 −ψ)H). (4.17) The second one is to find a superhedging strategy for the modified  ... 
doi:10.7468/jksmeb.2012.19.4.363 fatcat:7342zxq7cvajbgm6bgyyt7kspq

On the value of being American [article]

David Hobson, Anthony Neuberger
2016 arXiv   pre-print
This paper quantifies the potential value of this flexibility by identifying the supremum on the price of an American option when no model is imposed on the data, but rather any model is required to be  ...  The bound is enforced by a hedging strategy involving these call options which is robust to model error.  ...  Let S = S X ,T (a) be the set of super-replicating semi-static strategies.  ... 
arXiv:1604.02269v1 fatcat:i5bda5ptevcpzc3wocj3h5lurm
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