Study On Pricing Of Leveraged Volatility ETF Options With Random Volatility Under Jump Process

ETF(Exchange Traded Fund)is a fund used to track changes in the underlying index and traded on the exchange,and LETF(Leveraged ETF)is a special kind of ETF,LETF is designed to track multiple daily returns for a given ETF or underlying index.Depending on the LETF tracking target,we refer to the LETF used to track the S&P 500 index as Leveraged equity ETF,and the LETF to track the S&P 500 VIX short-term futures index as Leveraged volatility ETF.In recent years,the trading of LETF options is very active in the market,and many scholars have studied Leveraged equity ETF and related derivatives.However,the study of Leveraged volatility ETF and related derivatives is rare.In this dissertation,we first study the option pricing problem of Leveraged volatility ETF in LRSV(logarithmic model with stochastic volatility)model,then consider the LRJSV(LRSV with jump in price)model with constant jump,and extend the constant jump intensity in LRJSV model to random jump intensity.Because LETF is a path-dependent option,we need to refer to the Asian option state extension to deal with the model,and by guessing the correct affine solution to solve the model,we can get the European Leveraged volatility ETF call option in the LRSV model.The analytical solutions of LRJSV model with constant jump strength and LRJSV model with random jump strength.However,the analytical solution contains Fourier integral and can not be solved directly,so the European Leveraged volatility ETF call option in LRSV model can be obtained by discretization of the above analytical solution by using FFT algorithm,ladder integral rule and Thompson rule.The approximate solutions of LRJSV model with constant jump strength and LRJSV model with random jump strength.Finally,the approximate solution of Leveraged volatility ETF option obtained by FFT algorithm under the above three models is programmed by MATLAB software,and the numerical example is given and analyzed.