-We consider a Black-Scholes model for the price (Xt)t20 of a risky asset, with continuous interest rater = 0.03 per year, expected return u 0.05 per year, volatility o = = 0.2 year-¹/2, and we takeXo = 100 Gils. We look at a strap : it is a portfolio which is long 1 vanilla European put (payoff(payoff § = (K – XÃ)+) and long 2 vanilla European calls (payoff § = (XÃ − K)+), both withmaturity T and strike K.Compute the value of thecontract with maturity Tinvestment in the underlying assets in the replicating portfolio today for such a= 105 Gils.=1 year and KGive your answer(s) with 2 decimal digits.По-Gils.

Given: Black-Scholes model To find: Solution

Answered: We consider a Black-Scholes model for…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose you have inherited K100,000 from your father-in-law that can be invested in a combination of only two stock portfolios, with the maximum investment allowed in either portfolio set at K75,000 . The first portfolio has an average rate of return of 10%, whereas the second has 20%. In terms of risk factors associated with these portfolios, the first has a risk rating of 4 (on a scale 0 to 10), and the second has 9. Since you wish to maximize your return, you will not accept an average rate of return below 12% or risk factor above 6. Formulate the linear programming model for the problem. How much should you invest in each portfolio? Solve the problem by simplex method.
Two pumps capable of delivering 100 hp to an agricultural application are being evaluated in a present economy study. The selected pump will only be utilized for one year, and it will have no market value at the end of the year. Pertinent data are summarized as given follows. If electric power costs $0.10 per kWh and the pump will be operated 4,000 hours per year, which pump should be chosen? Recall that 1 hp = 0.746 kW.
Use the basic equation for the capital asset pricing model (CAPM) to Find the risk-free rate for a firm with a required return of 15% and a beta of 1.25 when the market return is 14%
The quoted futures price corresponds to a forward rate of 8% per annum with quarterly compounding and actual/360. The parameters for Black’s model are therefore:Fk = 0.08, K=0.08, R=0.075, tk=0.75, SDk=0.15and P(0,tk+1)=e-0.075x1=0.9277 . Use these information to estimate the call price.
Consider the following initial-value problem.
Suppose stock A is priced at $30/share and the company will pay a dividend of $0.30/share after two months. An investor purchases 100 shares of A and invests all dividends received at a continuosuly compunded risk-free rate of 5%. After 3 months the stock is sold when the price is $35.40/share. Calculate the 3-month profit.
An interest rate of 15% is used to evaluate a new system that has a first cost of $212,400, annual operating and maintenance costs of $41,200, annual savings of $94,600, a life of 6 years, and a salvage value of $32,500. After initial evaluation, the firm receives word from the vendor that the first cost is 5% higher than originally quoted. The percentage error in the system's present worth from this is closest to what value?
You are considering an investment in Justus Corporation's stock, which is expected to pay a dividend of $1.75 a share at the end of the year (D1 = $1.75) and has a beta of 0.9. The risk-free rate is 5.4%, and the market risk premium is 6%. Justus currently sells for $21.00 a share, and its dividend is expected to grow at some constant rate, g. Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of 3 years? (That is, what is ?) Do not round intermediate calculations. Round your answer to the nearest cent.
3.12 Suppose the spot rates of interest for investment horizons of 1 to 5 years are 4%, and for 6 to 10 years are 5%. (a) Compute the forward rates of interest iFt for t = 1, 2, 3, .., 10 years.
It is observed that a certain bacteria culture has a relative growth rate of 12% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 5% per hour. The initial number of bacteria in the culture is 22. Find the projected population after 24 hours for the following conditions.(a) No antibiotic is present, so the relative growth rate is 12%.(b) An antibiotic is present in the culture, so the relative growth rate is reduced to 5%.
IVP: Initial-Value-Problem
Please answer this question using the assumptions from the Solow Model In a country, the production function in terms of output per capita, y, and capital per labor, k, is y = k(12) The fraction of output saved, s, is 25% and the depreciation rate, δ, is 0.05. Assume that the population does not grow. What is the steady-state of capital per worker, k*, and output per worker, y*? What happens to the steady-state values if the population growth rate rises to 5%? By how much would the country have to increase its savings rate in b) in order to reach the same levels of steady-state values as in a)? Does the country’s growth rate increase in c) compared to a)? how?

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