The purpose of this paper is to present the theorical connection between the Itôstochastic calculus and the Financial Econometrics. This paper has two contributions. First, we give the backgrounds on how the ...The purpose of this paper is to present the theorical connection between the Itôstochastic calculus and the Financial Econometrics. This paper has two contributions. First, we give the backgrounds on how the stochastic calculus is used to model the real data with the uncertainties. Finally, by using Consumer Price Index (CPI) from the Central Bank of Congo and combining the Itôstochastic calculus and the AR (1)-GARCH (1, 1) model, we estimate the stochastic volatility of inflation rate measuring efficency of monetary policy. Thus the stochastic integrals are the powerful tools of mathematical modelling and econometric analysis.展开更多
The stochastic alpha beta rho(SABR)model introduced by Hagan et al.(2002)is widely used in both fixed income and the foreign exchange(FX)markets.Continuously monitored barrier option contracts are among the most popul...The stochastic alpha beta rho(SABR)model introduced by Hagan et al.(2002)is widely used in both fixed income and the foreign exchange(FX)markets.Continuously monitored barrier option contracts are among the most popular derivative contracts in the FX markets.In this paper,we develop closed-form formulas to approximate various types of barrier option prices(down-and-out/in,up-and-out/in)under the SABR model.We first derive an approximate formula for the survival density.The barrier option price is the one-dimensional integral of its payoff function and the survival density,which can be easily implemented and quickly evaluated.The approximation error of the survival density is also analyzed.To the best of our knowledge,it is the first time that analytical(approximate)formulas for the survival density and the barrier option prices for the SABR model are derived.Numerical experiments demonstrate the validity and efficiency of these formulas.展开更多
文摘The purpose of this paper is to present the theorical connection between the Itôstochastic calculus and the Financial Econometrics. This paper has two contributions. First, we give the backgrounds on how the stochastic calculus is used to model the real data with the uncertainties. Finally, by using Consumer Price Index (CPI) from the Central Bank of Congo and combining the Itôstochastic calculus and the AR (1)-GARCH (1, 1) model, we estimate the stochastic volatility of inflation rate measuring efficency of monetary policy. Thus the stochastic integrals are the powerful tools of mathematical modelling and econometric analysis.
基金support of the China National Social Science Fund under Grant No.15BJL093Yanchu Liu is partially supported by the National Natural Science Foundation of China under Grant No.71501196,No.71231008,No.71721001+4 种基金the China National Social Science Fund under Grant No.17ZDA073the Natural Science Foundation of Guangdong Province of China under Grant No.2014A030312003the Innovative Research Team Project of Guangdong Province of China under Grant No.2016WCXTD001the Fundamental Research Funds for the Central Universities under Grant No.14wkpy63research grants from Lingnan(University)College and Advanced Research Institute of Finance at Sun Yat-sen University.
文摘The stochastic alpha beta rho(SABR)model introduced by Hagan et al.(2002)is widely used in both fixed income and the foreign exchange(FX)markets.Continuously monitored barrier option contracts are among the most popular derivative contracts in the FX markets.In this paper,we develop closed-form formulas to approximate various types of barrier option prices(down-and-out/in,up-and-out/in)under the SABR model.We first derive an approximate formula for the survival density.The barrier option price is the one-dimensional integral of its payoff function and the survival density,which can be easily implemented and quickly evaluated.The approximation error of the survival density is also analyzed.To the best of our knowledge,it is the first time that analytical(approximate)formulas for the survival density and the barrier option prices for the SABR model are derived.Numerical experiments demonstrate the validity and efficiency of these formulas.
