A New Distortion-based Option Pricing Model And Its Application In Financial Modeling

A large body of research has shown that time series of financial asset returns exhibit features such as leptokurtosis,fat tails,and asymmetry,with the asymmetry in the thickness of the left and right tails being an important characteristic of the logarithmic returns of financial assets.Existing option pricing models do not have the flexibility to capture this feature of the distribution of the logarithmic returns of the underlying asset prices.However,Jiang(2000)used the idea of quantile modeling to construct two families of probability distributions,and the first family of distributions has the ability to flexibly capture tail changes,which has been validated in empirical studies in a variety of financial markets.Therefore,this paper proposes a new option pricing model based on the Quantile class I distribution and combined with the option pricing theory under a distortion function.The new model has stronger capabilities to capture the typical features of financial time series,and fills the gap left by existing option pricing models.To establish a new option pricing framework,this paper first extends the past survival function-based distorted functional option pricing framework through two theorems,and establishes an option pricing framework based on the distribution function and quantile function.Then,under the new framework,two new classes of option pricing models are established by choosing specific distortion functions,one of which is based on the Quantile class I distribution.As is well known,investors often adopt an attitude of avoidance towards large losses.Interestingly,these two new models can assign higher probabilities to high-risk events than usual models and provide new ways to measure extreme behaviors.We then focus on studying the option pricing model based on the Quantile class I distribution.After exploring and summarizing the properties and parameter estimation methods of this model,we find that due to the explicit expressions of the quantile function,probability density function,and cumulative distribution function of this class of distribution,our method is simple to implement,fast,and easy to connect with related modeling work in constructing new option pricing models and conducting empirical research.For the programming of the related procedures in the model,we use MATLAB R2022 b to complete it.In the empirical section at the end of this paper,we first selected the latest data of two A-share stocks(Han’s Laser,BYD)and two stock indices(Shanghai Composite Index,Shenzhen Component Index),and once again examined and verified the good and robust fitting ability of Quantile class I distribution for logarithmic returns of asset prices.Then,we applied the new option pricing model to empirical research on domestic option pricing,selecting price data for 50 ETF call options,300 ETF call options,and 500 ETF call options with the same remaining maturity listed on the Shanghai Stock Exchange,and price data for SZSE-listed SZSE 100 ETF put options,SSE 300 ETF put options,and CSI 500 ETF put options with different remaining maturities.The pricing results were satisfactory from the perspective of bid-ask spread testing.Finally,we further analyzed parameter estimation results under different situations based on parameters estimated when the underlying asset price was rangebound,such as dividing the underlying asset of 50 ETF call options into three situations of range-bound,downward trend,and upward trend,and found that the model could reasonably explain the parameter estimation results under different situations.After performing the same work for 300 ETF call options and dividing them into four situations,we found that the results still matched the reality.Through a series of empirical studies,we demonstrated the good performance of the new model in option pricing,its potential for application in other research,and further directions for improving the pricing model.