Suppose that a binomial tree has n steps, and the stock has initial price S0 and then at each step, its price can only move up by a factor u or down by a factor d. Let Sk, k = 0, 1, · · · , n, be the price of the stock at the end of the k-th step. Denote by τ time length between consecutive steps, and r the risk-free interest rate. Consider a call option with strike price K with maturity nτ .

(a) In the risk-neutral world, what is the probability that the stock moves down at each step?

(b) For n = 3, calculate the fair price for the option at current time corresponding to the initial node of the tree (please write out explicit formula).

Assume n = 10, τ = 1, r = 6%, S0 = 100, u = 1.1, d = 0.9, K = 110.

(c) In the risk-neutral world, find the probability that the stock price moves up five times and down four times in the first nine steps. What is the corresponding price value?

When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers on her grave every Sunday as long as he lived. The week after she died in 1962, a bunch of fresh flowers that the former baseball player thought appropriate for the star cost about $8. Based on actuarial tables, “Joltin’ Joe” could expect to live for 25 years after the actress died. Assume that the EAR is 8.9 percent. Also, assume that the price of the flowers will increase at 3.8 percent per year, when expressed as an EAR. Assume that each year has exactly 52 weeks, and Joe began purchasing flowers the week after Marilyn died. What is the present value of this commitment?

When Marlyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers on her grave every Sunday for as long as he lived. The week after she died in 1962, a bunch of fresh flowers the the former baseball player thought appropriate for the star cost about $7. Based on the actuarial tables, "Jolton' Joe" could expect to live for 26 years after the actress died. Assume the the EAR is 10.4 percent. Also, assume that the price of the flowers will increase at 4.3 percent per year, when expressed as an EAR. Assuming that each year has exactly 52 weeks, what is the present value of his commitment? Joe began purchasing flowers the week after Marlyn died.

discount rate is 10%

1.A stream of cash flows that pays $100 every year for 10 year. The first cash flow is received at t=3 and you will receive additional $1000 at the end of the 12 years.,What is the PV at time zero? what is the FV at time 12?

2.A stream of cash flows that pays $100 every year for 10 year. The first cash flow is received at t=3.What is the PV at time zero? what is the FV at time 12?

3.A stream of cash flows that pays $100 every year for 10 year. The first cash flow is received at t=1 and you will receive additional $1000 at t=5.What is the PV at time zero? what is the FV at time 10

4.A stream of cash flows that pays $100 every year for 10 year. The first cash flow is received at t=1 .What is the PV at time zero? What is the FV at time 10?

5.A stream of cash flows that pays $100 every year for 10 year. The first cash flow is received at t=1 and you will receive additional $1000 at the end of the 10 years.,What is the PV at time zero? what is the FV at time 12?

C++ programming

Create an application for generating lottery tickets of random numbers. Each lottery ticket has a fixed count of numbers to be played with each number selected being within a given range. For example, when the range of numbers is 1 through 100, and 5 numbers are to be played, the lottery ticket will be composed of 5 unique values between 1 and 100. The values are selected at random.

The main function is responsible for obtaining the upper range of the numbers and the count of numbers to be played from the end user. The count of numbers must be less than the upper range. The main function will call the generateLotto function to generate the lottery ticket and then call the displayTicket function to display the resulting lottery ticket. Any number of lottery tickets may be generated.

The generateLotto function should accept two parameters. The first should be the upper range for the numbers while the second parameter represents a count of the numbers to be played. For example, lotto(51, 6) will select 6 numbers at random between 1 and 51 (inclusive.) The function should return a vector of unique integer values in sorted order.

The displayTicket function accepts a vector of integers and displays the vector.

Hints: Although the standard library defines a rand() function for generating random numbers, the function may produce duplicate numbers and hence, is not suitable for this application. To ensure that unique values are generated, create a vector that contains all possible values (1 through the given upper range) and then shuffle these values using the random_shuffle() function. This will result in a vector of numbers between 1 and the upper range in random order. From this vector, select the required number of values from the beginning of the vector, adding these values to the result vector. Lastly, use the sort() function to sort the result vector.

The random_shuffle() and sort() functions require two parameters that specify the beginning and ending elements on which to operate. To specify the beginning and ending of the vector, the begin() and end() methods of the vector class can be used. For example, when the vector allNumbers contains all the values between 1 and 51, the values within the vector can be rearranged (shuffled) using: random_shuffle(allNumbers.begin(),allNumbers.end());

The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their weddings in the Caribbean. A Caribbean vacation resort recently advertised in Bride Magazine that the cost of a Caribbean wedding was less than $30,000. Listed below is a total cost in $000 for a sample of 8 Caribbean weddings. At the 0.10 significance level, is it reasonable to conclude the mean wedding cost is less than $30,000 as advertised?

                        
29.1   28.5   28.8   29.4   29.8   29.8   30.1   30.6

Picture Click here for the Excel Data File

State the null hypothesis and the alternate hypothesis. Use a 0.10 level of significance. (Enter your answers in thousands of dollars.)

State the decision rule for 0.10 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

What is the conclusion regarding the null hypothesis?

The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their weddings in the Caribbean. A Caribbean vacation resort recently advertised in Bride Magazine that the cost of a Caribbean wedding was less than $30,000. Listed below is a total cost in $000 for a sample of 8 Caribbean weddings. At the 0.05 significance level, is it reasonable to conclude the mean wedding cost is less than $30,000 as advertised?

Click here for the Excel Data File

1. State the null hypothesis and the alternate hypothesis. Use a 0.05 level of significance. (Enter your answers in thousands of dollars.)

2. State the decision rule for 0.05 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

3. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

4. What is the conclusion regarding the null hypothesis?

Balance the following reactions and indicate which of the six types of chemical reaction are being represented. Assume that all reactions “take place.”    Remember: you want the simplest ratio of coefficients.

1)              ____ NaBr + ____ Ca(OH)₂ à ___ CaBr₂ + ____ NaOH

Type of reaction: _____________________________

2)              ____ NH₃+ ____ H₂SO₄ à ____ (NH₄)₂SO₄

Type of reaction: _____________________________

3)              ____ C₅H₉O + ____ O₂ à ____ CO₂ + ____ H₂O

Type of reaction: _____________________________

4)              ____ Pb + ____ H₃PO₄ à ____ H₂ + ____ Pb₃(PO₄)₂

Type of reaction: _____________________________

5)              ____ Li₃N + ____ NH₄NO₃ à ___ LiNO₃ + _____     Ammonium nitride (Write correct formula, balance)

                                 Type of reaction: _____________________________

6)              ____ HBr + ___ Al(OH)₃ à ___ H­₂O + _____            Aluminum bride (Write correct formula, balance)

Type of reaction: _____________________________

7)          ___ N₂H₄ +   ___ H₂O₂    à ___N₂ + _____ H₂O
                                                                                                                                   Type of reaction: _______________________

8)      ______P₄ +   _____O₂   à    ____               Diphosphorus trioxide      (Write correct formula, balance)    
                                                                                                           Type of reaction _________________________

9)     _____ Fe      +    ____O₂ -à   ________       Iron (III) oxide) (Write correct formula, balance)