基于高阶精度紧致差分法求解非线性Black-Scholes方程

In the past two decades, due to taking into account more realistic assumptions, such as transaction costs, portfolio risk, large investors liquidity preferences or the market (which may affect the stock price) volatility, drift rates and options their prices, making the nonlinear Black - Scholes equation of option pricing research gradually deepened. A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized implicitly using high order compact finite difference schemes。The numerical results are compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.