Pricing Power Exchange Options Based On Exchange Rate And Default Risk

The power exchange option studied in this paper is a new type of financial derivative product under the combination of exchange option and power option.It gives the option holder the right to exchange two types of underlying assets according to their own needs on the expiration date.Under the influence of exponential power,its nonlinear characteristics can be effectively used to hedge linear price risk.However,as a typical OTC option,investors should carefully select the trading object without the supervision of the exchange,so as to avoid the face of the counterparty default event caused by the bankruptcy of the company,which will bring huge economic losses.At the same time,in the context of financial internationalization,cross-border transactions have become the norm,and the application of power exchange options on dual-currency options is more common,but transactions between dual-currency assets are bound to face exchange rate problems.When the situation is turbulent,the risk of exchange rate fluctuations will cause extremely significant changes in asset prices.In addition,the price of the asset and the value of the company may be subject to large fluctuations in the short term due to the occurrence of certain major events.This is the significance of introducing the Poisson jump process in the model.Based on the power exchange option model proposed by Blenman and Clark,this paper first considers the first type of power exchange option model that can exchange foreign securities for national securities and the second type of foreign power exchange option model purchased in the country.The prices of both types of options are closely related to exchange rate fluctuations.Secondly,the company’s asset process was introduced to study the possible default of the counterparty in bankruptcy and liquidation.When doing this part of the analysis,we adopt a structured model,that is,when the value of the asset reaches or falls below a certain boundary,trigger a default event.Under this new model,we use the computational tools in Steven’s financial stochastic analysis,mainly the Girsanov ’s theorem in the measure transformation,to solve the model,and we can calculate the power exchange option pricing formula under the double risk of exchange rate and default.Then we add the composite Poisson process to the model,which represents the impact of a major incident,including financial crisis or policy changes.Due to the addition of jumping risk,the driving equations of various assets and exchange rates are optimized.However,based on the original calculation,we also need to use Ito’s theorem and measure transformation related to the jump process.Then according to the Girsanov ’s theorem,the parameters of the jump strength obeying the Poisson distribution and the parameters of the jump amplitude obeying the normal distribution are changed.The rest of the steps are roughly the same as the calculation process of the basic model,and then the pricing formula of the power exchange option based on the double risk of exchange rate and default is obtained.Finally,according to the improved power exchange option pricing formula in this paper,we can basically deduct a series of relevant conclusions that appear in the current literature.