Theoretical And Empirical Study On Pricing Structured Stock Index Fund

Structured fund is one type of investment which divides the revenue into several parts with different return and risk characteristics.It can be viewed as a complex derivative.The pricing problem of structured fund is widely concerned in academia and industry and several methods have been proposed for different kinds of structured fund.We will focus on the pricing problem of structured stock index fund.Some people consider the irregular conversion as a type of barrier option.Black-Scholes formula and barrier option pricing theory are used for this pricing problem.However,the pay-off function after conversion is not the same as the barrier option.Thus such kind of methods has effect on structured stock index fund.Unlike this idea,some people propose that we can calculate the discounted pay-off with Monte Carlo simulation.The theoretical price is the summation of the discounted cash flow.The empirical result shows that this method works effectively.But the drawback is that Monte Carlo simulation requires large computation.In this article,we derive the theoretical formula of the structured fund under the risk-neutral condition and based on the discounted cash flow model as well as some assumptions and approximation.To calculate the final result,we need Monte Carlo simulation twice according to the formula.So we call it two-step Monte Carlo method.Besides,we find a simple method to decide the discount interest rate.The simulation result shows that this formula has the same result with the direct Monte Carlo method and has greater efficiency.We find that the discount interest rate and the volatility of the stock index have great impact on the theoretical price.The empirical result shows that the theoretical fair price has great consistency with the real price.