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Dynamic Feedback Hedging by a Large Player: from Theory to Practical Implementation

Tan, Xiaolu; Wang, Lihang; Kalife, Aymeric (2011), Dynamic Feedback Hedging by a Large Player: from Theory to Practical Implementation, 6th International Conference on Dynamic Systems and Applications, 2011-05, Atlanta, États-Unis

Type
Communication / Conférence
Date
2011
Titre du colloque
6th International Conference on Dynamic Systems and Applications
Date du colloque
2011-05
Ville du colloque
Atlanta
Pays du colloque
États-Unis
Métadonnées
Afficher la notice complète
Auteur(s)
Tan, Xiaolu
Wang, Lihang
Kalife, Aymeric
Résumé (EN)
Market liquidity risk refers to the degree to which large size transactions can be carried out in a timely fashion with a minimal impact on prices. Emphasized by the G10 report in 1993 and the BIS report in 1997, it is viewed as one factor of destabilization in the financial markets, as illustrated recently by the Asian crisis, the faillure of the hedge fund LTCM during the Russian crisis. So in order to assess welfare implications of portfolio insurance strategies, it would be useful to estimate the dynamic hedging activity in securities markets through a specific parsimonious and realistic model. In the paper, large traders hold sufficient liquid assets to meet liquidity needs of other traders, and so bear the risk of their imbalanced derivatives portfolio. Their dynamic hedging strategies entail non-linear positive feedback effects, and in turn buying and selling derivatives at prices shifted by an amount that depends on their net holding. And therefore, the replicating equation turns to be a fully nonlinear parabolic PDE, as proposed by Frey [1996]. It turns out that such a nonlinear PDE equation can be numerically unstable when using traditional finite-difference methods. Therefore we need some specific adequate numerical implementation in order to solve this equation with significant accuracy and flexibility, while keeping stability. In this paper we devise and customize two different numerical methods: one is a refined finite difference method; the other involves the probabilistic scheme proposed by Fahim and al [2005]. In contrast another method based on Lie algebra and developed by Bordag and al. only provides a generic, albeit analytical, formulation of solutions, and not the specific one consistent with our payoff. Still that method offers a reference for our proposed methods in terms of numerical accuracy. Using such a framework, a Large Player is then in a position to take into account those positive feedback effects in dynamic hedging. Lastly, we show how dynamic hedging may directly and endogenously give rise to empirically observed bid-offer spreads.
Mots-clés
Market liquidity risk; dynamic hedging
JEL
G12 - Asset Pricing; Trading Volume; Bond Interest Rates
G1 - General Financial Markets

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Affichage des éléments liés par titre et auteur.

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    Dynamic hedging by a large player: From theory to practical implementation 
    Kalife, Aymeric; Tan, Xiaolu; Wang, Lihang (2012) Article accepté pour publication ou publié
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    Forges, Françoise; Vida, Péter (2013-01) Article accepté pour publication ou publié
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