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This paper considers the problem of hedging the risk exposure to imperfectly liquid stock by investing in put options. In an incomplete market, we firstly obtain a closed-form pricing formula of the European put option with liquidity-adjustment by measure transformation. Then, an optimal hedging strategy which minimizes the Value-at-Risk (VaR) of the hedged portfolio is deduced by determining an optimal strike price for the put option. Furthermore, we provide a new perspective to estimate parameters entering the minimal VaR, since the likelihood function is analytically intractable. A Bayesian statistical method is proposed to perform posterior inference on the minimal VaR and the optimal strike price. Empirical results show that the risk hedging strategy with liquidity-adjustment differs from the hedging strategy based on Black-Scholes model. The effect of the stock liquidity on risk hedging strategy is significant. These results can provide more decision information for institutions and investors with different risk preferences to avoid risk.

Bayesian Inference for Optimal Risk Hedging Strategy Using Put Options With Stock Liquidity