By analyzing the closing price of Shanghai 50ETF options from 2017 to 2018, the authors find that the logarithmic return of 50ETF options has fractional characteristics. The fractional B-S model is used to analyze 50ETF option pricing. Firstly, the authors make R/S analysis of 50ETF option logarithmic return and get the Hurst index of the fractional B-S model. Secondly, the authors build the GARCH (1,1) model to characterize the volatility of 50ETF option's yield and use the R software to get the historical volatility. Then the authors use fractional B-S model and the Matlab software to get the implied volatility. The authors make an empirical analysis on the pricing of 50ETF option based on the two kinds of volatility. The authors calculate the AMSE of results from the models with the market price, and compare them fully. It is found that the fractional B-S models based on the two kinds of volatility have good fitting effect on the pricing of 50ETF option, and the implicit volatility model has better fitting effect on the pricing of 50ETF option than the historical volatility model.

This paper examines the issue of loans obtained by the small and medium-sized enterprises (SMEs) from banks through the mortgage inventory of goods. And the loan-to-value (LTV) ratio which affects the loan business is a very critical factor. In this paper, we provide a general framework to determine a bank's optimal loan-to-value (LTV) ratio when we consider the collateral value in the financial market with Knightian uncertainty. We assume that the short-term prices of the collateral follow a geometric Brownian motion. We use a set of equivalent martingale measures to build the models about a bank's maximum and minimum levels of risk tolerance in an environment with Knightian uncertainty. The models about the LTV ratios are established with the bank's maximum and minimum risk preferences. Applying backward stochastic differential equations (BSDEs), we get the explicit solutions of the models. Applying the explicit solutions, we can obtain an interval solution for the optimal LTV ratio. Our numerical analysis shows that the LTV ratio in the Knightian uncertainty-neutral environment belongs to the interval solutions derived from the models.

This paper studied the relationship between policies and stock market volatility. This paper used the volatility point discrimination method to identify the variance increase points of stock market volatility from 2014 to 2018. It finds out the policy events causing stock market fluctuations through the event research method. After regression analysis of index return and policy event return, index return volatility and policy return volatility, it is found that the impact of policy events before the shock of stock market is greater than that after the shock of stock market.

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