Option hedging for small investors under liquidity costs

Çetın, Umut; Soner, H. Meté; Touzi, Nizar

doi:10.1007/s00780-009-0116-x

Cited by 112 publications

(79 citation statements)

References 30 publications

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“…In particular, we specify in which way markets are finitely liquid when transaction costs are introduced and the role of transaction costs in determining the size and the frequency of adjustment. Our paper provides results that are consistent with the approach of Cetin et al (see, for example, Cetin et al, 2004;Cetin et al, 2006;Cetin et al, 2007), although they do not deal with models of feedback effects. Instead of concentrating on the feedback effects that govern the dependence of the equilibrium stock price on the portfolio actions of programme traders, as we do in our paper, they have a reduced form illiquidity model, introducing a supply curve which excludes strategic trading and where liquidity costs are increasing in the position to liquidate.…”

Section: Introductionsupporting

confidence: 90%

(S,s)-adjustment Strategies and Hedging under Markovian Dynamics

Agliardi

Andergassen

2010

Geneva Risk Insur Rev

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We study the destabilizing effect of hedging strategies under Markovian dynamics with transaction costs. Once transaction costs are taken into account, continuous portfolio rehedging is no longer an optimal strategy. Using a non-optimizing (local in time) strategy for portfolio rebalancing, explicit dynamics for the price of the underlying asset are derived, focusing in particular on excess volatility and feedback effects of these portfolio insurance strategies. Moreover, it is shown how these latter depend on the heterogeneity of the insured payoffs. Finally, conditions are derived under which it may be still reasonable, from a practical viewpoint, to implement Black-Scholes strategies.

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Section: Introductionsupporting

confidence: 90%

(S,s)-adjustment Strategies and Hedging under Markovian Dynamics

Agliardi

Andergassen

2010

Geneva Risk Insur Rev

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“…The consequence is a nonlinear term in the wealth equation and a liquidity premium in option prices. Our analysis also has some common features with the liquidity cost model of [10], and in particular the Taylor expansion of the super-hedging cost of [39] who use the PDE characterisation of [11]. The main difference however is that in these models the price impact is momentary, whereas we regard it as a longer-lasting phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Option prices under liquidity risk as weak solutions of semilinear diffusion equations

Fahrenwaldt

Roch²

2017

Nonlinear Differ. Equ. Appl.

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Abstract. Prices of financial options in a market with liquidity risk are shown to be weak solutions of a class of semilinear parabolic partial differential equations with nonnegative characteristic form. We prove the existence and uniqueness of such solutions, and then show the solutions correspond to option prices as defined in terms of replication in a probabilistic setup. We obtain an asymptotic representation of the price and the hedging strategy as a liquidity parameter converges to zero. Mathematics Subject Classification. Primary 35K65, Secondary 91G20.

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“…Super-replication cost or related problems were studied in (Cetin, Soner & Touzi, 2010), (Gokay & Soner, 2012), (Dolinsky & Soner, 2012) and (Xing, 2015). In (Cetin, Soner & Touzi, 2010), the existence of the continuous time super-replication cost from a binomial model was shown. (Gokay & Soner, 2012) showed that a stochastic optimal control problem could be seen as a dual of the super-replication problem.…”

Section: Introductionmentioning

confidence: 99%

Existence Conditions of Super-Replication Cost in a Multinomial Model

Mei¹

2017

JMR

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This paper gives a theorem for the continuous time super-replication cost of European options in an unbounded multinomial market. An approximation multinomial scheme is put forward on a finite time interval [0,1] corresponding to a pure jump Lévy model with unbounded jumps. Under the assumption that the expected underlying stock price at time 1 is bounded, the limit of the sequence of the super-replication cost in a multinomial model is proved to be greater than or equal to an optimal control problem. Furthermore, it is discussed that the existence conditions of a super-replication cost and a liquidity premium for the multinomial model. This paper concentrates on a multinomial tree with unbounded jumps, which can be seen as an extension of the work of (Xing, 2015). The super-replication cost and the liquidity premium under the variance gamma model and the normal inverse Gaussian model are calculated and illustrated.

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Option hedging for small investors under liquidity costs

Cited by 112 publications

References 30 publications

(S,s)-adjustment Strategies and Hedging under Markovian Dynamics

(S,s)-adjustment Strategies and Hedging under Markovian Dynamics

Option prices under liquidity risk as weak solutions of semilinear diffusion equations

Existence Conditions of Super-Replication Cost in a Multinomial Model

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