Dynamic Hedging: CVaR Minimization and Path-Wise Comparison

• Author / Creator

  Smirnov, Ivan

• Imposing constraints on the class of the available self-financing strategies may eliminate the possibility of using replicating or superhedging strategies, which leads to the problem of partial hedging. In the present work, the partial hedging problem is investigated from the viewpoint of the contingent claim seller who aims to minimize the shortfall risk through dynamic hedging un- der the constraint on the initial capital. The shortfall risk is measured via conditional value-at-risk, a coherent quantile risk measure. Another problem consists in finding a strategy that minimizes hedging costs under a constraint on conditional value-at-risk of the hedging portfolio. In a complete market, an explicit algorithm for constructing the optimal hedging strategy in both problems is presented, along with a number of detailed illustrations. In the incomplete case, the optimal solution is no longer explicit, however a cer- tain generalization of the Neyman-Pearson lemma may be used to deduce the general structure of the optimal strategy. Some of such generalizations as- sume weak compactness of the set of densities of equivalent sigma-martingale measures. We show that this requirement is in fact never satisfied in the in- complete market setting and provide detailed discussion of the matter in both the discrete- and continuous-time cases. Finally, we demonstrate how path- wise comparison can be used in the problem of approximate option hedging and pricing, and we illustrate the approach in the framework of the constant elasticity of variance model.

• Subjects / Keywords

  • Path-wise comparison theorem
  • Dynamic hedging
  • Neyman-Pearson lemma
  • Conditional value-at-risk
  • Stochastic modelling

• Graduation date

  Spring 2013

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R35D5F

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.