CASE STUDY: Hedging Portfolio of Options with Expectile (XVaR)

CASE STUDY: Hedging Portfolio of Options with Expectile (XVaR)

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Case study background and problem formulations

Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, PSG MATLAB Subroutines and PSG R.

PROBLEM: problem_cs_hedging_portfolio_of_options_with_XVaR
Minimize XVaR(x) (minimizing hedging error)
subject to
P(x) ≤ Const (constraint on initial portfolio value)
Box constraints (non-negativity constraints on positions)
XVaR = Expectile of residual
P(x) = initial price of the hedging portfolio (linear function)
Box constraints = constraints on individual decision variables

parameter values: q in range (0.5, 1.0)
# of Variables # of Scenarios Objective Value Solving Time, PC 2.50GHz (sec)
Dataset 1 121 45,000 192,…, 920 30.0
Run-File Problem Statement Data Solution
Matlab Problem Statement Data Solution

This case study hedges a Portfolio of Options by a Portfolio of Stocks and Options. The goal is to create a hedging portfolio with a cost that does not exceed a specified upper limit at the start time (t=0). The effectiveness of the hedge at the end time period (t=T) is measured by Expectile. We optimized hedging portfolio weights with several parameter value q of the Expectile. PSG code optimizes problems with different parameter q using a cycle operation.
Rockafellar, R.T., and S. Uryasev (2000): Optimization of conditional value-at-risk. Journal of Risk. 2 (3). 21–41.