Exercise 15.2.4 Explain why the formula er X (y X) 1 y 2

Exercise 15.2.4 Explain why the formula e−rτ

 ∞

X

(y− X)

1

σ y

√

2πτ

exp



−

{ ln(y/S)−(r −σ2/2)τ }2 2σ2τ



dy, is equivalent to the Black–Scholes formula for European calls. (Hint: Review Eq. (6.10).)