Pricing Of Composite Options Under Scott Model And Its Application

Compound option is a kind of singular contract with right as the subject matter,It has been widely used in many financial practices and has achieved fruitful results.However,with the deep-ening of scholars'research,especially in recent years,the occurrence of major financial emergen-cies and many problems of financial reform,The discovered Black-Scholes model can no longer fully describe the changes in today's real financial markets,There are large deviations in actual motion,This bias is described as a smiling or tilting phenomenon of implicit volatility.In order to capture these phenomena accurately,Scholars have improved Black-Scholes model.The main improvement is to introduce jump risk into the underlying assets or to allow the volatility of the underlying assets to change randomly,The improvement can reduce the above deviation to a certain extent,but there are still gaps.Therefore,the advantages of stochastic volatility model and jump-diffusion model are considered in this paper,Further study on Compound Option Pricing under the Scott model with stochastic jump of interest rate volatility and it's application to the pricing of three options.The main research work and results of this paper are as follows:Firstly,the Scott model is extended.On the basis of the original model,the jumps of the under-lying assets and the stochastic volatility are added,and the affine diffusion model of the stochastic jumps of the volatility interest rate is established.Using ithato and Feynman-Kac theorem,the conditional discount joint eigenfunction under this model is derived.The European option price based on this model is obtained by martingale method,Girsanov transformation and Fourier in-verse transformation.On this basis,the compound option price formula is further derived.Some numerical examples are used to analyze the influence of some parameters on the price of compound options,and some problems which should be paid attention to in investment are given.Secondly,by using the iterative property of conditional expectation and the theorem?2.12?,the conditional discount joint eigenfunction of t at a known execution point is extended to the conditional discount joint eigenfunction of t₁,t₁,···,t_nat a known execution point of n.The pricing method of composite options is applied to the pricing of three options,using Girsanov transformation and multidimensional Fourier inverse transformation.Three options price formulas are obtained by using other methods.Some numerical examples are used to analyze the influence of some parameters on option price,and some problems which should be paid attention to in investment are given.Thirdly,using Mathematica 11.0 and MATLAB 9.0 programming software,the change of option price with co-jump coefficient and co-jump size is analyzed under given parameters.By comparing with the market model without considering co-jump,it shows that the market model with co-jump is a more realistic financial market and provides investors with more reasonable risk assessment,investment and hedging strategies.