Research Article
Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations
Algorithm 1
Algorithm of adaptive time-stepping strategy.
| Require: Set the initial conditions and , the expiry time , the maximum and minimum | | time steps and , tolerance tol, truncation error , safety | | factor , time , iteration number . | | While do | | | | if then | | Set . | | else | | Set . | | end if | | if then | | Set . | | Solve (4) with time step and set its approximation as . | | end if | | Solve (4) twice with time step and set its approximation as . | | Solve (4) with time step and set its approximation as . | | Calculate where and is the total number of . | | while do | | Set . | | if then | | Set . | | end if | | Solve (4) twice with and set its approximation as . | | Solve (4) with and set its approximation as . | | Calculate | | end while | | Set . | | Set and . | | end while |
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