| In recent years,the OTC(Over The Counter)market has developed rapidly and there are many products,among which a typical one is structured products which embed barrier options into fixed income certificates.On the one hand,such structured products are popular with investors because they can be tailored to their financial needs.On the other hand,it is these personalized product designs that make pricing and risk management of structured products very difficult.This thesis is devoted to the study of a callable fixed coupon note(FCN),which is a structured product linked to an underlying stock.Firstly,the pricing model of FCN products is established based on the risk neutral measure by applying financial engineering principles.Secondly,by using Feynman-Kac formula,we further characterize the FCN product in terms of a differential equation.Then,considering the jump risk in the underlying asset,this thesis analyzes the impact of jump risk on the price of FCN products from both theoretical and empirical aspects.Theoretically,an analytical solution of FCN product is provided in the absence of the jump risk.When the underlying asset price follows the Merton jump-diffusion model,the finite difference method is used to numerically solve the integro-differential equation and Monte Carlo simulation is also used to verify the result.Empirically,this thesis selects 9 representative stocks of large,medium and small market value for comparative analysis,and strives to get more accurate results.Finally,this thesis also studies the influence of various parameter changes on FCN product price.Based on theoretical model and empirical analysis,the main results of this paper are as follows:(1)through theoretical and numerical verification,the FCN pricing model established in this thesis is reasonable and effective.(2)Through the analysis of the statistical characteristics of 9 stocks,it is found that the returns of most stocks do not conform to the normal distribution hypothesis and the jump times are relatively frequent,so the jump risk is widespread.(3)Through an extensive numerical analysis,it is found that compared with Merton jump diffusion model,pricing FCN option under geometric Brownian motion has a large error.(4)By analyzing the influence of parameter changes on pricing,it is found that the option price of FCN structure product is most sensitive to the proportion of exercise price stipulated in the clause. |
