w_exam_one_solutions

Then the estimate of the mean continuously compounded

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: e of return of this stock α is less than 3%. ˆ Solution: FALSE α = ln (114/110) ≈ 0.0357. ˆ 9. A caplet is a ﬁnancial instrument used as protection against the increase in the interest rate for all repayment installments of a loan to be repaid over multiple periods. Solution: FALSE The caplet only applies to one installment; it’s the cap that provides protection over multiple periods. 3 10. Assume the Black-Scholes stock-pricing model is in force. Let E∗ denote the expectation under the risk-neutral probability measure P∗ . Let {S (t), t ≥ 0} denote the price of a continuous-dividend-paying stock. Then, in our usual notation, E∗ [S (T )] = S (0)e(r−δ)T . Solution: TRUE 11. In the Black-Derman-Toy model, the interest rate at any node is the geometric average of the rates at the two nodes at adjacent heights. Solution: TRUE 12. The Black-Scholes option pricing formula can always be used for pricing American-type call options on non-dividend-paying assets. Solution: TRUE Part II. Free-response problems Please, explain carefully all your statements and assumptions. Numerical results or single-word answers without an explanation (even if they’re correct) are worth 0 points. 1. (25 points) Let S (0) = \$120, K = \$100, σ = 0.3, r = 0 and δ = 0.08. a. (10 pts) Let VC (0, T ) denote the Black-Scholes European call price for the maturity T . Does the limit of VC (0, T ) as T → ∞ exist? If it does, what is it? b. (10 pts) Now, set r = 0.001 and let VC (0, T, r) denote the Black-Scholes European call price for the maturity T . Again, how does VC (0, T, r) behave as T → ∞? c. (5 pts) Interpret in a sentence or two the diﬀerences, if any, between your answers to questions in a. and b. Solution: a. By the Black-Scholes pricing formula, the function VC (0, T ) has the form VC (0, T ) = S (0)e−δT N (d1 ) − Ke−rT N (d2 ) = S (0)e−δT N (d1 ) − K N (d2 ), where N denotes the distribution function of the unit normal distribution and 1 S (0) d1 = √ ln K σT...
View Full Document

Ask a homework question - tutors are online