| As a derivative instrument,the option has the function of diversifying risk,which helps to strengthen the overall risk resistance of the financial market.Therefore,studying the option market is of great significance for improving the capital market business.On February 9,2015,the launch of the Shanghai 50ETF(SH50ETF)option contract,the first stock option product in China’s securities market,signified that China’s financial market has entered the option era.However,there are currently fewer varieties of exchange-traded options,and over-the-counter options have developed rapidly since their official launch in 2013.Since there is no third-party to supervise the OTC option market and no special clearing institution to guarantee the fulfillment of option sellers’ obligations,the holder of the option will face credit risk.With the advancement of the RMB internationalization process and the reform of the exchange rate marketization,there have been a large amount of infrastructure investment in the Belt and Road Initiative and ever-expanding cross-border capital transactions,which have caused an increase in demand for foreign currency asset risk management.Many institutions,by buying and selling foreign exchange derivatives,hedge exchange rate risk.Therefore,in the current market environment,it is of great theoretical and practical significance to study the SH50 ETF option market,option pricing with credit risk and option pricing with exchange rate risk.The core issue of option pricing is the characterization of the underlying asset price dynamic process.Although the traditional Black-Scholes option pricing formula is widely used,a large number of empirical results indicate that the assumption that the asset price follows the geometric Brownian motion is not in line with the actual situation.A large number of scholars have proposed many different option pricing models.The jump-diffusion model can characterize the underlying asset price jumps because of burst information.The regime-switching model can well describe the structural change of the risk asset price caused by market economy cycle.Therefore,the application of these two types of financial models in option pricing has attracted the interest of many researchers.Based on the regime-switching jump-diffusion model,this dissertation empirically studies the SH50 ETF option,and constructs the regime-switching multi-scale jump-diffusion models to price the multi-asset options with credit risk or exchange rate risk.The details are as follows:In the first part,we use extensive empirical data sets from SH50 ETF and SH50 ETF options markets in China to study how regime-switching jump-diffusion models improve goodness of fit and option pricing performance.Numerically,the SH50 ETF data over the period 2012-2017 are used to estimate the model parameters using maximum likelihood estimation.The numerical analysis indicates that the regime-switching jump-diffusion models outperform a range of other models.On the other hand,the analytical option pricing formula is obtained via the fast Fourier transform under the regime-switching jump-diffusion model.For empirical analysis,the actual market prices of at-the-money options which expired in September 2017 are used to examine the empirical fit performance.Our findings indicate that the calculated option prices in the case of a two-regime economy with lognormal jumps are in good agreement with the actual market price.In the second part,we study the pricing problem of vulnerable European options with credit risk.Under the framework of structural model,the RS multi-scale jumpdiffusion model is constructed for the underlying asset price and company value.Based on the RS multi-scale jump-diffusion model,the regime-switching Esscher transform is adopted to identify an equivalent martingale measure for pricing vulnerable European options considering the market risk price of common jump.Explicit analytical pricing formulae for vulnerable European options are derived by risk neutral pricing theory.For comparison,the other two cases are also considered separately.The first case considers all jump risks as unsystematic risks while the second one assumes all jumps risks to be systematic risks.Finally,the Monte Carlo method is used to give numerical results.The analysis shows that the economic state transition and the market price considering different scale jump risks have a significant impact on the value of vulnerable options.In the third part,we study the valuation of stock option with exchange rate risk.Based on the RS multi-scale jump-diffusion model,the foreign equity option with the domestic currency as the strike price,the foreign equity option with the foreign currency as the strike price,and the equity linked foreign exchange option pricing problem are studied.The Esscher transform is used to identify an equivalent martingale measure,and the risk neutral drift parameters of the asset price processes are obtained.Three kinds of stock option pricing formulas with exchange rate risk are derived by using Fourier transform method under the martingale measure.Finally,the numerical results are given by the fast Fourier transform algorithm.The analysis shows that the economic state transition,the jump process and the different important parameters of the models have significant effects on the pricing of the three options and the impact between the three is different.Finally,considering the mean reversion of the real exchange rate process,the RS mean reversion multi-scale jump-diffusion model for the exchange rate and stock price process is constructed.We study the valuation of equity linked foreign exchange call option under the RS multi-scale jump-diffusion model.The measure change and Fourier transform technique are adopted to calculate the price of equity linked foreign exchange call option.Taking the double exponential jump distribution as an example,numerical comparative analyses are also provided by the fast Fourier transform algorithm.Numerical results reveal that RS,common jump process,mean reversion speed and other important parameters have a significant impact on the pricing of equity linked foreign exchange options. |
