Reference no: EM131246486
Question 1. The CRR model: European claim. Consider the CRR model of stock price S with T periods and parameters d < 1 + r < n, where r is the one-period interest rate.
(a) Consider the European claim X with expiry date T and the payoff
X = g(ST) = 1/ST 1|K, ∞)(ST)
Show that the arbitrage price Π0(X) at time t = 0 equals
Π0(X) = 1/S0 ∑Tk =k^ (T k) αkβT-k
for some constants α and β. Give explicit formulae for α, β and k^. in terms of So, u, d and r.
(b) Assume that p~ = 0.5, r = 0.25 and d = u-1. Compute u and d and deduce that
Π0(X) = 1/S0 ∑Tk =k^ (T k)(0.2)k(0.8)T-k
(c) We maintain the assumptions of part (b). Consider the European claim Y where
Y = h(ST) = 1/ST 1(-∞, k)(ST).
Find the arbitrage price Πo(Y) and show that Πo(X) + Πo(Y) = 1/So
(d) Let Z1 and Z2 be two European claims with maturity T in the CRR model. Assume that the equality Πt(Z1) = Πt(Z2) holds for every t ≤ U where U is a fixed date satisfying 0 < U < T. Does the equality Πt(Z1) = Πt(Z2) necessarily holds for every 0 ≤ t ≤ T?
What characteristics must an effective counselor possess
: Why are counseling theories important to professional counselors? What characteristics must an effective counselor possess? How has psychoanalytic theory influenced professional counseling today?
|
Factors of production-capital and labor
: Assume that Germany has only two factors of production, capital and labor, and two industries, capital-intensive car production and labor-intensive dairy production. Based on the Heckscher-Ohlin model, who gains and who loses in Germany if the wor..
|
Obvious reason is to raise tax revenues for the government
: Governments impose taxes for several reasons. The most obvious reason is to raise tax revenues for the government. If the goal of a government is to raise the maximum tax revenues, should a per unit tax be imposed on an item that has a price elastici..
|
Calculate the price elasticity of demand for medium pizzas
: When the price of pizza was $10.00 for a medium pizza, students at a college consumed 400 pizzas per week. When the price of pizza increased to $30.00 for a medium pizza, students at a college consumed 100 pizzas per week. Calculate the price elastic..
|
Find the arbitrage price
: Consider the CRR model of stock price S with T periods and parameters d
|
The faster rate of growth of output per worker
: Suppose that two countries are exactly alike in every respect (meaning they have the same levels of capital, output, depreciation, etc.) except that the citizens of country A have a higher saving rate than the citizens of country B. which country wil..
|
Should build a new theater downtown
: Irving owns a chain of movie theaters. He is considering whether he should build a new theater downtown. The expected rate of return is 15 percent per year. He can borrow money at a 12 percent interest rate to finance the project. Should Irving pr..
|
Explain what is meant by the structure of water
: Consider three (3) structures and functions of a cell then provide a 100 to 250 word explanation based on the following question: "How do varied membrane composition and the structural features of molecules in different cells contribute to membran..
|
The circular flow model depicts the exchange of money
: The circular flow model depicts the exchange of money, products, and resources between households and businesses. It includes the factor and the products markets. A peak is usually followed by a correction phase in which contraction occurs, growth sl..
|