Hedging Conditional Value at Risk with options

• We derive an analytic formula for CVaR of stock hedged with put options.
• The CVaR of such position can be optimised using linear programming.
• The work is a generalisation of Ahn et al. (1999), where VaR was used instead of CVaR.

We present a method of hedging Conditional Value at Risk of a position in stock using put options. The result leads to a linear programming problem that can be solved to optimise risk hedging.