** 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)

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XVaR = Expectile of residual

P(x) = initial price of the hedging portfolio (linear function)

Box constraints = constraints on individual decision variables

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**parameter values: q in range (0.5, 1.0)**

# of Variables |
# of Scenarios |
Objective Value |
Solving Time, PC 2.50GHz (sec) |
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Dataset 1 | 121 | 45,000 | 192,…, 920 | 30.0 | |||
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Environments |
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Run-File | Problem Statement | Data | Solution | ||||

Matlab | Problem Statement | Data | Solution |

**CASE STUDY SUMMARY**

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.

**References**

Rockafellar, R.T., and S. Uryasev (2000): Optimization of conditional value-at-risk. Journal of Risk. 2 (3). 21–41. http://doi.org/10.21314/JOR.2000.038