Let {B_t}_t greaterthanorequalto 0 be Brownian motion, let X_t = x_0 exp(mu t +

Question

Let {B_t}_t greaterthanorequalto 0 be Brownian motion, let X_t = x_0 exp(mu t + sigma B_t) be the stock price model (where sigma > 0), and let D_t = e^-rt X_t be the discounted stock price. (a) Show that if mu = r - sigma^2/2, then {D_t} is a martingale. (b) Show that mu = r - sigma^2/2, then E[e^-rS max(0, X_s - K)] = X_0 Phi ((r + sigma^2/2)S - log (K/X_0)/sigma Squareroot S) -e^-rS K Phi ((r - sigma^2/2)S - log(K/X_0)/sigma Squareroot S), where Phi(u) = integral_-infinity^u 1/Squareroot 2 pi e^-upsilon^2/2 d upsilon is the cdf of a standard normal distribution.

Explanation / Answer

There is not a question on the board.

No question is there available

So that no solve the question

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.