The Pricing Model Of Leverage Fund Based On BSDE

With the development of our country’s economy and the improvement of people’s living standard, the saving account interest rate is not high enough to meet the investors’need of profiting. But not every investor can take the risk of Stoke Markets, so the investors are in urgent demand of hiring experts to manage money matters for them. Then the fund appears in financial mar-kets.But,very quickly, the normal fund cannot attract all kinds of investors, because of the lack of the risk difference. Prudent investors want to invest the product with less risk and higher return of rate than saving account and activist investor prefer to the product which can bring leverage benefit. After learning the European financial markets and American financial markets ex-perience, UBS Redford classification fund, the first leverage fund in Chinese financial markets, distributed in 2007.Chinese leverage fund becomes open from semi-closed and closed. The first generation of leverage fund is the semi-closed and two kinds of sub-funds distribute respectively. One of the sub-funds can trade in the market and the fund don’t have the mother-fund can be purchased and redeemed from the fund corporation. The second generation of leverage fund is the closed fund which has two kinds of tradable sub-funds and investors can purchase and redeem mother-fund of the closed fund every year at the given time. The latest generation is open fund, the only difference with the second generation is that the open fund’s mother-fund can be purchased and redeemed at any time.About pricing the leverage fund, there are two ways. One is use the Black-scholes model and the other is use the monte-carlo method. Based on the Black-Scholed model,some scholars proposed option-decomposition method to price the leverage fund,with which investors take the sub-fund as a portfolio consisting of the stocks,bonds and contingent claims, price each asset of the portfolio and calculate the addition of every asset as the price of the sub-fund. In this article I first divide the contingent claims into European claims and American claims,according to the tradability of the sub-fund. And then we can prove that if the claim-portfolio is among European claims or between an American claim and European claims we can use the option-decomposition method. On the other hand, if the portfolio is among American claims, we cannot use the method. Because the price of an American option has some connection with a optimal stopping time problem,and different American op-tions always have different optimal stopping time. Then we can find that the claims in the same sub-funds must be exercised at the same time, so the claim portfolio can be take as an American option with complex clauses. The exer-cise price can be an obstacle of the price of the American option,so we can use the reflected backward differential equation to price the portfolio.By using the model with the three generations of leverage fund,we should assign different asset into the portfolio according to the clauses mentioned in the fund contract.When we price the third generation of leverage fund,we take the last day of every operation year as the terminal time because of the high turnover rate of the open leverage funds and take the return rate of the AA corporate bond as the riskless rate after verifying the connection between the return rate and the sub-funds’ discount premium.At last I take my model into practice.I choose the UBS Redford classification fund and UBS Redhe classification fund as the example to do the model validation.