Pricing Collar Option With Random Strike Price Under The Double Exponential Jump-diffusion Model In Fuzzy Environment

As an important financial derivative,option has always been a hot research object in the financial field.With the continuous expansion and development of the world financial market,various new options have emerged,and the issue of option pricing has become one of the core issues that scholars around the world pay attention to.Among them,the collar option and the option with an uncertain strike price have gained high popularity due to their low risk.If the two options are combined,it will be beneficial to further control the option risk and also ensure the relative return.But there are relatively few researches in this area,so this paper proposes to study collar options with uncertain prices.The option price is based on the price changing of the stock price,so the price model of the underlying asset must first be constructed correctly.The B-S option pricing model has been overwhelmingly favorable since it was proposed in the 70s,the end of the 19th centrury.This model assumes that changes in underlying prices is a geometric Brownian motion.However,a large amount of actual market data has shown that the price changes of the underlying assets show volatility smiles and asymmetric spikes.Thick tail distribution characteristics.The double exponential jump diffusion model is an improvement of the traditional model to make up for this defect.It can better describe the trajectory of the underlying asset price.On the other hand,the uncertainty of the financial market not only contains randomness,but also contains ambiguity,the two permeate and combine with each other.In recent years,the application of fuzzy theory in option pricing has provided a necessary and useful supplement to traditional option pricing methods.However,there is no relevant literature using fuzzy stochastic theory in the pricing of collar options with stochastic strike prices.In view of this The far-reaching significance of domain pricing research,this paper chooses to price collar options with random strike prices under fuzzy environment and double exponential jump diffusion model.We first introduces collar options with uncertain strike prices,and introduces a non-fuzzy double exponential jump diffusion model.Using mea-surement transformation,the analytical pricing of collar options with uncertain strike prices in which the underlying asset obeys the double exponential jump diffusion model is given.result.Considering that in the actual financial market,volatility and interest rates are often the most subjective and uncertain,these two parameters are replaced with fuzzy numbers in the non-fuzzy pricing results to obtain the double exponential jump diffusion model in the fuzzy environment The pricing formula of collar option with uncertain strike price,and according to the four operations of fuzzy number,give the fuzzy price interval of any level set of option,then elicit the crisp possible mean of fuzzy price by calculation method of crisp possible mean of fuzzy number.At the end of the article,numerical calculations are performed to discuss the price range of options under different confidence levels,the comparison of option pricing results under different models,and the sensitivity analysis of parameters.It is concluded that the model used in this article is more in line with the actual market than the classic model,in conclusion.