Financial Models in Excel

Consider the following specification Instead: for O 3 for 3 < t Question 1 .

d Estimate the parameters in the new term structure spacification with he restriction that the approximation must be continuous at t = 3. Show the term structure in a chart. Page 2 of 5 Exercise 2: Volatility prediction (25%) In the first part of this exercise, you will estimate volatility based on data you generate yourself with the random number generator. Although the data are artificial (and have constant standarddeviation) you should nevertheless treat them as empirical stock returns.And pretend that you are unaware of the constant volatility of the data.

Question 2. A Generate 52 normally distributed weekly stock returns {RL , or , ROR } tit mean value zero and standard deviation 0. 04. Estimate the standard deviation of the first "out-of' sample" weekly return o ( ROR ) according to a 20-weeks moving average model. Assume that you think, that the following GARTH model is a good description of the volatility process: 'tot=WV+rater + go to-1 - where you expect the long term variance to be V = (0.

04) = 0. 0016 .In addition, you 2 '2 assume that your estimate of the initial variance for the first period is 0 1 = (0. 04) = 0. 0016 .

2 Question 2. B Estimate the three parameters y , a , of the GARTH model by minimizing the ARMS, and report the corresponding standard deviation estimate for the first "out-of-sample" weekly return o ( ROR) . Question 2. C Assume normally distributed returns and estimate the three parameters y , a , of the GARTH model using maximum likelihood. Test if the estimated value of is significantly different from zero.Assume that Just before week 53 starts, you observe prices of options with an underlying asset equal to the one you are trying to predict the volatility for.

For a European call option with one year to maturity, with a price of the underlying asset equal to 100, and with an exercise price equal to 100, you observe an option price equal to 12. 37. You can assume a yearly rissoles interest rate equal to 0. 02. Assume that the standard Black-Schools-assumptions (including no dividends) are correct.

Question 2 a Determine an estimate AT ten standard volatile AT ten return Tort week 53, o ( ROR ) , based on the observations of the option price. Page 3 of 5 Exercise 3: Option pricing (25%) To signal dynamic leadership, the CBS-management has decided to "go public" and list Jobsharers at a newly created stock exchange, First South. To secure profit for the new stock holders, it has been decided to offer the employees at CBS "employee stock options" to boost incentives. It turns out that the employees prefer American put- options, which is accepted by the CBS-management, who sees an opportunity to show creative leadership.You have the following information about the employee stock options: Price of CBS-stocks: Exercise price: Time to maturity (years) Interest rate (yearly) Volatility parameter 5 5 5 0.

05 0. 5 Assume that the Black-Schools assumptions are a good approximation of the situation. Question 3. Determine the value of one employee stock option using a 5 period binomial grid.

After having realized the unfortunate incentives caused by the new employee stock option scheme, the CBS-management regrets its decision to accept put options.In order to make all employees exercise their put options right away and thereby re-establish good incentives, the CBS-management shows generous leadership and resets the exercise price of the options to 7. Question 3. B Determine the new value of an employee stock option, and show the exercise policy explicitly in a grid.

Question 3. Determine the lowest possible exercise price that would make the (rational) employees exercise their put options immediately after having received the options.Finally, the CBS-management decides to show intelligent leadership, and hires an external consultant who has passed the course Financial Models in Excel. The consultant suggests normal European type call options. In addition, to keep incentives right for the entire period, the consultant suggests to add some call options which have their exercise price determined by the stock price after three years.

(And no exercise before maturity). Question 3. Use 100 Monte-Carlo paths to price a 5-year call option, which will have its exercise price set equal to the CBS-stock price after 3 years.Page 4 of 5 Exercise 4: Performance evaluation (25%) Assume you are an Investor Interested In two stock Investment Tunas, Yuan A Fund B.

The table below shows the past six years returns of the two funds and the relevant market index: t 1 234 56 Market Index -0. 20 0. 30-0. 20 0.

30-0. 20 0. 30 Fund A -0. 24 0. 30-0.

20 0. 26-0. 22 0. 28 Fund B -0. 37 0.

44-0. 31 0. 38-0. 34 0. 41 Question 4.

A Assume that you don't own any stocks, and that you only want to invest n one of the two funds.Calculate, based on the historical data, two relevant key- figures, and conclude shortly (in text) if one of the two funds has performed better than the other. Assume in the following that you own a well-diversified stock portfolio with a return equal to the market index. Question 4. B You consider whether it would be profitable to add Fund A, Fund B, or both of them to your portfolio.

Calculate for each fund the relevant key-figure that shows if you should include the given fund in your portfolio or not. Conclude shortly (in text) on the result: Should you include Fund A, Fund B, OTOH of them, or none of them?Question 4. C You want to add one and only one of the two funds, Fund A and Fund B, to your portfolio. Hence, you want to rank the two funds against each other. Calculate the relevant key-figure. Conclude shortly (in text) on the result: Which of the two funds should be preferred? Or are they equally good to add? Question 4.

D Perform the necessary calculations in order to be able to conclude shortly (in text), for each fund, if the stock picking and market timing abilities of the fund are positive, negative or neutral. Page 5 of 5