摘要
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.
基金
support of the China National Social Science Fund under Grant No.15BJL093
Yanchu Liu is partially supported by the National Natural Science Foundation of China under Grant No.71501196,No.71231008,No.71721001
the China National Social Science Fund under Grant No.17ZDA073
the Natural Science Foundation of Guangdong Province of China under Grant No.2014A030312003
the Innovative Research Team Project of Guangdong Province of China under Grant No.2016WCXTD001
the Fundamental Research Funds for the Central Universities under Grant No.14wkpy63
research grants from Lingnan(University)College and Advanced Research Institute of Finance at Sun Yat-sen University.
