100, t = 2) Exercise 5.1 Suppose you pay 10 to buy a European (K = call option on a given security. Assuming a continuously compounded nominal annual interest rate of 6 percent, find the present value of your return from this investment if the price of the security at time 2 is (а) 110; (b) 98.

100, t = 2) Exercise 5.1 Suppose you pay 10 to buy a European (K = call option on a given security. Assuming a continuously compounded nominal annual interest rate of 6 percent, find the present value of your return from this investment if the price of the security at time 2 is (а) 110; (b) 98.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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100%

hi could you please help solve exercise 5.1?

j=1W;C; or there is an arbitrage.
5.3
Exercises
Exercise 5.1 Suppose you pay 10 to buy a European (K = 100, t = 2)
call option on a given security. Assuming a continuously compounded
nominal annual interest rate of 6 percent, find the present value of your
return from this investment if the price of the security at time 2 is
%3D
(a) 110;
(b) 98.
Exercises
87
100,
Exercise 5.2 Suppose you pay 5 to buy a furopean (K
t = 1/2) put option on a given security. Assuming a nominal annual in-
terest rate of 6 percent, compounded monthly, find the present value of
%3D
VI

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Suppose you pay 10 to buy a European (K=100, t=2) call option on a given security. Assuming a continuously compounded nominal annual interest rate of 6 percent, find the present value of your return from this investment if the price of the security at time 2 is 110.
1. Suppose that, in each period, the cost of a security either goes up by a factor of u = 2 or down by a factor d = 1/2. Assume the initial price of the security is $100 and that the interest rate r is 0. c) Assuming the strike price of a European call option on this security is $90, compute the possible payoffs of the call option given that the option expires in two periods.
Find the hedge ratio a 1-period at-the-money put option on ¥300,000. The spot exchange rate is ¥100 = $1.00. In the next period, the yen can increase in dollar value by 15 percent or decrease by 10 percent. The risk-free rate in dollars is i$ = 5%; The risk-free rate in yen is i¥ = 1%. A.-0.44 B.-0.66 C.-0.60 D.-0.40
H4. Work out the value of European Call on a risky asset A, currently selling at $600. The European Call has a term to maturity of 1.5 years and a strike price of $675. SD(dA/A), the volatility of returns on the risky asset is 18% per year, and the discrete risk-free rate is 0.9% per year
Suppose that, in each period, the cost of a security either goes up by a factor of 2 or goes down by a factor of 1/2 (i.e. u=2, d=1/2). If the initial price of the security is 100, determine the no-arbitrage cost of a call option to purchase the security at the end of two periods for a price of 150.
Consider a European call option and a European put option that have the same underlying stock, the same strike price K = 40, and the same expiration date 6 months from now. The current stock price is $45. a) Suppose the annualized risk-free rate r = 2%, what is the difference between the call premium and the put premium implied by no-arbitrage? b) Suppose the annualized risk-free borrowing rate = 4%, and the annualized risk-free lending rate = 2%. Find the maximum and minimum difference between the call premium and the put premium, i.e., C − P such that there is no arbitrage opportunities.
5 Consider an asset with current price 26 that provides income 0.50 in 3 months time. The price of a 6-month European call on the asset with strike 24 is ct = 1.75 and the risk free rate is4.5% for all maturities.(i) Show that there is an arbitrage opportunity.(ii) Construct an appropriate arbitrage portfolio to take advantage of the situation and determine the profit per call option used.
Determine the risk-neutral value of a eight-month European put option to sell a FLB (First Local Bank) share for a price of R400 when the current price is R420, the interest rate is 10%, and the volatility of the security is 0.28? WITHOUT USING EXCEL
D6) Suppose that the risk-free zero curve is flat at 0.06 per annum with continuous compounding and that defaults can occur half way through each year in a new two-year credit default swap. Suppose that the recovery rate is 0.26 and the default probabilities each year conditional on no earlier default is 0.02 Estimate the credit default swap spread. Assume payments are made annually. Rates are quoted in numbers, i.e. 0.05 is 5% rate. Please write your answer also in numbers.
You have account receivables: ₤5 m in one year. o InterestUS: 6.10% per annum & InterestUK: 9% per annum o Spot exchange rate: $1.50/£ & Forward exchange rate: $1.46/£ (1-year maturity) o Put option strike price: $1.46/£ & Put option premium: $0.02/£ How much will you receive in $ if you use the money market hedge?
What is the price of a European CALL option that is expected to pay a dividend of $2 in three months with the following parameters? s0 = $40d = $2 in 3 monthsk = $42 r = 10%sigma = 20%T = 0.5 years (required precision 0.01 +/- 0.01)
I asked this question yesterday: Suppose that, in each period, the cost of a security either goes up by a factor of 2 or goes down by a factor of 1/2 (i.e. u=2, d=1/2). If the initial price of the security is 100, determine the no-arbitrage cost of a call option to purchase the security at the end of two periods for a price of 150. In the answer I got today the first step said: "We assume that the probability of moving up and moving down be 50% each, which means equal chances for both the movements. " I had learned that the risk neutral probability for the stock price to go up is: p=(1+r-d)/(u-d). In this particular problem, we'd have p=(1+0-.5)/(2-.5)=1/3. And so the probability going down would be 1-p or 2/3. Thus, my question is why weren't these probabilities used in the solution previously sent? And if they should be, what would be the new solution to the problem? Thank you for your help. I'm new to learning all of this and some of it is hard for me to understand.

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