Pricing and hedging contingent claims by entropy segmentation and Fenchel duality

  1. Vilar Zanón, José Luis 1
  2. Rogo, Barbara 2
  1. 1 Universidad Complutense de Madrid
    info

    Universidad Complutense de Madrid

    Madrid, España

    ROR 02p0gd045

  2. 2 Università de Roma La Sapienza
    info

    Università de Roma La Sapienza

    Roma, Italia

    ROR https://ror.org/02be6w209

Revista:
Methodology and Computing in Applied Probability

Año de publicación: 2024

Tipo: Artículo

DOI: 10.21203/RS.3.RS-3534168/V1 GOOGLE SCHOLAR lock_openAcceso abierto editor

Resumen

We present a new approach to the problem of characterizing and choosingequivalent martingale pricing measures for a contingent claim, in a finite-stateincomplete market. This is theentropy segmentationmethod achieved by meansof convex programming, thanks to which we divide the claim no-arbitrage pricesinterval into two halves, the buyer’s and the seller’s prices at successive entropylevels. Classical buyer’s and seller’s prices arise when the entropy level approaches0. Next, we apply Fenchel duality to these primal programs to characterize thehedging positions, unifying in the same expression the cases of super (resp. sub)replication (arising when the entropy approaches 0) and partial replication (whenentropy tends to its maximal value). We finally apply linear programming toour hedging problem to find in a price slice of the dual feasible set an optimalpartial replicating portfolio with minimal CVaR. A super (resp. sub) replicationsolution is obtained as the entropy level tends to 0. We apply our methodologyto a cliquet style guarantee, using Heston’s dynamic with parameters calibratedon EUROSTOXX50 index quoted prices of European calls. This wayprices andhedging positions take into account the volatility risk.

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