# Question: Verify that e r T t N d2 satisfies the Black Scholes equation

Verify that e−r(T−t)N(d2) satisfies the Black-Scholes equation.

## Answer to relevant Questions

Use the answers to the previous two problems to verify that the Black-Scholes formula, equation (12.1), satisfies the Black-Scholes equation. Verify that the boundary condition V [S(T), T ]= max[0, S(T ) − K] is satisfied. Suppose there are 1-, 2-, and 3-year zero-coupon bonds, with prices given by P1, P2, and P3. The implied forward interest rate from year 1 to 2 is r0(1, 2) = P1/P2 − 1, and from year 2 to 3 is r0(2, 3) = P2/P3 − 1. ...Suppose that S1 and S2 follow geometric Brownian motion and pay continuous proportional dividends at the rates δ1 and δ2. Use the martingale argument to show that the value of a claim paying S1(T ) if S1(T) > KS2(T ) ...Suppose the stock price is $50, but that we plan to buy 100 shares if and when the stock reaches $45. Suppose further that σ = 0.3, r = 0.08, T − t = 1, and δ = 0. This is a non cancellable limit order. a. What ...Verify that equation (23.14) (for both cases K >H and KPost your question