CoachA jump condition links a pricing equation’s solution across a date at which the state variable jumps deterministically: for a cash dividend, , applied on the grid by interpolation, followed by a fresh Rannacher start-up, since the interpolated profile is no longer smooth where American exercise bites.
Examples
Example 22.5 (A three-unit dividend in six months)
With a dividend of 3 paid at six months, the one-year European put is worth 6.835 on the grid, against 6.719 from Black–Scholes on the spot less the dividend’s present value, the escrowed approximation at the same volatility. The American put is worth 7.407, against 6.090 without the dividend.