Abstract
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.
Highlights
Nowadays, with the rising of volatility in financial market, financial institutions and investors pay much more attention to manage the exposure to market risk of stocks, interest rates or exchange rates
We find that the risk hedging strategy with liquidity-adjustment differs from the hedging strategy based on Black-Scholes model
We investigate the statistical properties of the optimal strike price and the minimal VaR by conducting posterior inference based on Metropolis-Hastings sampling
Summary
With the rising of volatility in financial market, financial institutions and investors pay much more attention to manage the exposure to market risk of stocks, interest rates or exchange rates. Many literatures study how to optimally manage the VaR of risky asset by using options, related researches have paid little attention to the method of parameter estimations. By Esscher measure transforms, we firstly obtain a closed-form pricing formula of European put option in the incomplete market This model allows for the effect of stock liquidity on risk hedging. Considering the influence of parameter estimations on hedging strategy, we propose a new perspective to investigate the statistical properties of the optimal strike price and the minimal VaR. Unlike existing literatures usually providing only a point estimation, we provide more information about the optimal strike price and the minimal VaR from a probabilistic perspective These results are useful for financial institutions and investors with different risk preferences to make better decisions.
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