Research To The Structured Mutual Fund Pricing In China

According to the income distribution terms, structured mutual fund can be divided into two parts with different risk and return characteristics. Part A and Part B. Part B borrowed at a fixed rate from Part A, and Part B use total assets to invest in equity, fixed income or index. As a result, Part A earns a fixed return, and Part B has a leveraged effect.At present, the kind of pricing for structured mutual funds usually are the Black-Scholes option pricing method (or options decomposition method) and monte carlo simulation method. All of pricing methods have a lot of assumptions, for example, Black-Scholes model has the following seven major assumptions:(1) share price volatility obey the lognormal distribution, and the mean and volatility is constant;(2) allow short-selling;(3) no transaction costs;(4) the period of validity without dividends;(5) there is no risk-free arbitrage opportunities;(6) securities trading is continuous,(7) the risk-free interest rate is constant. Obviously, some assumptions can’t keep up with the actual. In order to solve this problem, this article first loosens assumption (1), try to use the GARCH pricing method to establish a volatility equation, by solving the equation of regression methods. The equation modifies the results of Black-Scholes option pricing method. Then this article loosens the Black-Scholes option pricing model assumptions (1) and (7), using stochastic volatility model for structured mutual fund pricing. This paper compares several stochastic volatility models, and finds that the Heston model itself has a closed form solution, better than the other stochastic volatility models, so using Heston model for structured mutual fund pricing is the best. In the process of using Heston model, the biggest difficulty is how to choose the appropriate financial products for model parameter calibration. Through reading literature and comparative analysis, the paper finally uses the FTSE China25index options as the calibration parameter, because this index option can reflect the Chinese market objectively. From the above, this paper gets the following conclusion:First, using the Black-Scholes model directly on structured mutual fund pricing, the theoretical price does not greatly deviate from the actual price. Although the Black-Scholes model has a lot of assumptions, for investors who require roughly estimated prices, the Black-Scholes model has strong practical sense. Secondly, using GARCH model to price structured mutual fund, improve the precision of the pricing. Volatility equation is obtained by simulation volatility curves, makes the quality of structured mutual fund pricing improved, reducing the theoretical price and the actual price of premium range, but the effect is not obvious. Third, Heston model further loosen the assumptions, through the FTSE China25index options for parameter calibration, using Isqnonlin function of Matlab and the simulated annealing algorithm to solve nonlinear least squares problems, compared with the above two models, the quality of structured mutual fund pricing has been greatly improved.