Dynamic hedging in incomplete markets using risk measures
Author:
Gaillardetz Patrice1,
Hachem Saeb1
Affiliation:
1. Department of Mathematics and Statistics, Concordia University, Montreal, Quebec H3G 1M8, Canada
Abstract
Abstract
In this paper, we consider the pricing of financial derivatives that involve dynamic hedging strategies and payments within the planning horizon. Equity-indexed annuities (EIAs), guaranteed investment certificates (GICs) and American and barrier options are typical examples of these products. Our exploration involves the use and comparison of alternative models that use risk measures. Although the hedging is done for each observation of the input stochastic process, the appropriate mix of risk measures and state dynamic equations helps the issuer to appropriately tailor the overall risk exercise. These different models are solved by a unified backward stochastic dynamic programming framework that we imbed with parametric techniques to shorten the running time and manage the curse of dimensionality in dynamic programming. To demonstrate the flexibility of this framework we present numerical examples featuring GICs and point-to-point EIAs. Finally, by using sampling techniques, optimal hedging strategies and specific indicators of the hedging performance, we make recommendations on how to fine tune the risk measure parameters.
Funder
Natural Sciences and Engineering Research Council of Canada
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Management Science and Operations Research,Strategy and Management,General Economics, Econometrics and Finance,Modeling and Simulation,Management Information Systems
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