The Exchange Option Pricing And Its Application In Convertible Bond Valuation

As an important financial derivative,options have the functions of risk management,asset allocation and price discovery.In 1973,the Chicago Board of options(CBOE)launched stock options,which opened the prelude of the global market options product innovation.After more than 40 years of development,the overseas market has formed a rich variety of options product system,options have become an integral part of the financial market.On February 9,2015,the 50 ETF option contract of Shanghai Stock Exchange was officially listed and traded in Shanghai Stock Exchange.After nearly six years of development,China's option market has begun to take shape,with business types,functional positioning and regulatory system basically taking shape.With the development of option market,financial products are gradually differentiated and personalized.Financial institutions develop various kinds of exotic options to meet the specific investment and risk aversion needs of customers.Strange option trading is generally conducted outside the market,and the trading scale is developing steadily and rapidly.In October 2020,the new initial nominal principal was388.297 billion yuan,an increase of 137.939 billion yuan compared with the previous period,with a month on month growth of 55.10%;by the end of October 2020,the outstanding initial nominal principal was 852.210 billion yuan,an increase of 1967.34 billion yuan compared with the previous period,with a month on month growth of30.01%.This paper will focus on the pricing theory and practical application of power exchange options.As a kind of exotic option,its income not only has the characteristics of power option nonlinear income,but also has the characteristics of exchange option two kinds of assets exchangeable,low cost,flexible use,relatively high income,widely used in daily economic and financial market activities.The research on power exchange option pricing theory and its application will help to enrich option pricing theory,increase option product innovation and derivatives market activity,and accelerate the development of option market.This paper mainly solves the following three problems: first,the pricing problem of power exchange options with default under Vasicek stochastic interest rate model.Under the assumption that the underlying asset price obeys geometric Brownian motion and that the underlying asset price,interest rate and default risk are independent of each other,many scholars have proposed pricing models for power exchange options or power exchange options with default under Vasicek stochastic interest rate model.However,in the actual market,asset price,interest rate and default event are affected by market fluctuation Therefore,the assumption of independence is not in line with the actual market.This paper will solve the pricing problem of power exchange options with default under Vasicek Interest Rate Model with correlated dynamic model.Second,the pricing problem of power exchange options with default under the generalized autoregressive conditional heteroskedasticity(GARCH)model.At present,the existing researches on Option Pricing under GARCH model mainly focus on European options.This paper will give the price of power exchange options under GARCH model.Third,the application of power exchange option in convertible bond pricing.The conversion right of convertible bond is essentially exchange option.At present,most of the researches on the pricing of convertible bond use black-Scholes(BS)option model and standard exchange option model are used to calculate the value of embedded options,but the research on the pricing model of convertible bonds based on other kinds of exchange options is insufficient,and the traditional methods have great limitations in estimating model parameters and comparing pricing effects.In this paper,particle swarm optimization(PSO)algorithm is used to study the application of BS option model,standard exchange option model,power exchange option model and other exchange option models in convertible bond pricing.The specific research contents of this paper are as follows: Chapter 1 introduces the research background and significance,content arrangement,innovation and deficiency.In Chapter 2,the theoretical research status of power exchange option pricing model is reviewed,the research results of existing theoretical models are discussed,and the research status and problems of common models in convertible bond pricing are sorted out.In Chapter 3,starting from the pricing principles and methods of power exchange options,the risk neutral theory and martingale pricing method are introduced;then the traditional assumptions of power exchange options are relaxed from Vasicek stochastic interest rate model and GARCH volatility model;finally,the default risk model used in power exchange options pricing is introduced.In Chapter 4 and 5,we give the pricing model of power exchange options with default under Vasicek stochastic interest rate model and the pricing model of power exchange options with default under GARCH model.In Chapter 6,we make a numerical empirical analysis on the influencing factors of the power exchange option pricing model,and compare it with other related models to obtain the rule of judging the risk of power exchange option in the transaction.Chapter7 makes an empirical study on the application of power exchange option in convertible bond pricing,compares and evaluates the application effect of power exchange option pricing model and other exchange option pricing models in convertible bond pricing,and gives reasons and suggestions.Finally,Chapter 8 gives the research conclusions,suggestions and prospects.The main conclusions are as follows:1.The closed form solution of power exchange option pricing model with default under Vasicek Interest rate.The main assumptions of the model are: the underlying asset obeys geometric Brownian motion;the interest rate is stochastic and obeys Vasicek model;the structured default model can default before maturity;the underlying asset,interest rate and default condition are correlated.2.The closed form solution of power exchange option pricing model with default under GARCH model.The main assumptions of the model are: the underlying asset follows the GARCH model with random volatility;the simplified default model can default before the maturity date;the introduction of market index follows the GARCH model,so that the underlying asset is related to the default intensity.3.Through numerical analysis,the price influencing factors and mechanism of power exchange option pricing model are obtained.Compared with the price influencing factors of other relevant models,the laws of underlying assets,power index parameters,volatility,maturity and default risk are obtained,which can provide reference for traders to judge the direction of risk in the market.4.This paper empirically analyzes the effect of power exchange option in the pricing of convertible bonds,and draws the conclusion: in the pricing of convertible bonds,the pricing model of power exchange option with default based on Vasicek Interest rate is the best,and the pricing model of convertible bonds based on B-S model is the worst.Moreover,whether it is the exchange option under Vasicek Interest Rate Model or the standard power exchange option,there is little difference in the pricing effect of convertible bonds.After adding the default risk,the pricing effect of convertible bonds is slightly improved.A reasonable explanation is given to this phenomenon.