Research On The Influence Of Volatility And Distribution Characteristics On The Value Of Foreign Exchange Options

With the rapid development of domestic and foreign economies,the exchange rate environment has become more complex,and the need to avoid exchange rate risks has become more urgent.Foreign exchange options have been favored by people.The study of foreign exchange option pricing has great realistic and theoretical significance.At present,the research methods of foreign exchange option pricing include partial differential equation method,numerical method,and non-parametric pricing method.Most of the existing research is to improve the B-S model in the partial differential equation method.This paper is also based on the B-S model,considering the volatility characteristics and distribution characteristics of the exchange rate,introducing the volatility index and distribution index,and modifying the model.At the same time,compare the revised model with the original model.This paper first combs through the previous literature and finds that the volatility of exchange rate does not obey the normal distribution,but present a "peak fat tail" pattern.Combined with empirical research on Euro,Japanese Yen,British Pound,Swiss Franc,Canadian Dollar,and Australian Dollar data from 2008 to 2019,we finds that with the increase of the time interval,the volatility of exchange rate showed an upward trend and then a downward trend,which contradicts with B-S model,the volatility of exchange rate is constant,that is,volatility index Y = 0.5.Therefore,a volatility index is introduced to study the volatility characteristics of the exchange rate.At the same time,it is found that the exchange rate has long memory,that is,the exchange rate has a fractal characteristic,which contradicts the exchange rate distribution in the B-S model,which is a standard random process,that is,distribution index H = 0.5.Therefore,the paper introduces the distribution index to study the distribution characteristics of exchange rates.Secondly,this paper uses the regression analysis method and the rescaled range analysis method to calculate the volatility index and distribution index of the six currencies,revises the B-S model,and discusses the scope of application of the original model.Finally,from the perspectiveof exchange rate volatility and option price,the modified model is compared with the original model,the rationality of the modified model is verified,and a relatively reliable pricing method for foreign exchange options is finally provided.