摘要
用有限差分方法研究欧氏看涨期权定价问题.首先,将Black-Scholes方程通过等价代换化成一个标准的抛物型偏微分方程.其次,在求解区域构造时间精度为O(△τ~3)、空间精度为O(h^6)的差分格式,并通过Fourier分析方法证明该差分格式是无条件稳定的;边界区域选用精度较高、稳定性好的Crank-Nicolson格式,建立迭代方程.然后,用GMRES(generalized minimal residual)方法求解该方法.最后,给出一个欧氏看涨期权的数值算例,并与解析解进行比较,验证差分格式的有效性.
In this paper,we study European call option pricing by the finitedifference method.First,we equivalently transform the Black-Scholes equation into a standard parabolic partial differential equation.Second,we construct a difference scheme over the inner domain,with the order O（h^6 ＋ △τ^3）,and it is proved to be unconditionally stable by the Fourier analysis.The Crank-Nicolson method with high precision and good stability is adopted for border domain.Therefore,we present an algebraic equation.Third,we adopt the GMRES（generalized minimal residual） method to solve the equation.Last,the numerical example verifies the efficiency.
出处
《应用数学与计算数学学报》
2014年第4期518-528,共11页
Communication on Applied Mathematics and Computation
基金
国家自然科学基金资助项目(11371243)
上海市教委科研创新重点资助项目(13ZZ068)
上海市重点学科建设资助项目(S30104)
