The Discrete-time Model With Liquidity Risk

After market risk and credit risk, liquidity risk is arguably the most important risk faced by the finance industry.Our research is related to Umut Cetin & Rogers, L. C. G (2007).First we restate the model of Umut Cetin & Rogers, L. C. G (2007).With further research, we find that no matter short selling is allowed or not in the market, the arbitrage opportunity and the optimal hedging strategy can be co-existed in the liquidity market. Then, we research the investment strategy on discrete time with liquidity effect, by using the principle of dynamic programming, we deduce an algorithm, also take binomal model for numerical study, all of these are based on the model of Umut Cetin & Rogers, L. C. G (2007). We see that the grater the liquidity risk in the market the smaller trading volume of the invester trade in short time. Then we further limit the transaction function and prove the cumulative liquidity costs are finite for a lot of strategies including the Black-Schole hedge.So liquidity costs are completely differ -rent from proportional transaction costs, for proportional transaction costs are infini -te cumulative costs. In this paper, we restate the European option pricing formula th -rough utility indifference pricing by Umut Cetin & Rogers, L. C. G (2007), then take a single-period option pricing for an example, Through the analysis we get the smaller the liquidity risk the closer the price of the option to no-arbitrage pricing.