Discrete Time Models in Finance. HOMEWORK 3. Due April 10, 2019
金融类Assignment代写 Please write a pledge that homework solutions represent your own work and that you did not copy solutions from the work of other students.
Please write a pledge that homework solutions represent your own work and that you did not copy solutions from the work of other students.
1.Matlab option model. Download from courseworks matlab option model files BlackScholesStocks.m and BlackScholesGraph.m and put them in the same directory. BlackScholesStocks.m contains the function that calculates the Black Scholes price for options on nondividend paying stocks. BlackScholesGraph.m is a script that makes a graph of option price as a function of stock price. Type at Matlab prompt 金融类Assignment代写
and the script will be executed and the graph will appear. Now modify the file BlackScholesStocks.m so that the function now calculates the price of options on stocks paying continuous dividends at a rate q.
Modify the file BlackScholesGraph.m so that it now plots graph of a call with the same parameters as before but with the dividend yield q=5.5% and the new strike price 11.5. Submit printouts of code and graph.
2 Download matlab Brownian motion model from the courseworks. 金融类Assignment代写
Modify it to a constant elasticity of variance model with starting value Xo=30, growth rate µ = 0.064 and volatility σ = 0.15, a=1.3 and 4,000 trajectories. Check that the code works. Try out 50,000 trajectoriesSubmit the code printout and the graph printout. For a=0.75, a=1, a=1.25 calculate in code the average and the standard deviation of the value of the process at time t=1 and time t=0.5.
3.Using arbitrage arguments explain why the price of an American call option on a stock paying no dividends should be the same as the price of a corresponding European call. Why American calls on a nondividend paying stock should not be exercised early.
4.Why when the stock pays dividends the argument of the problem No.3 can not be used. Give a numerical example (choosing x, k, r, T −t, σ) in which it is obvious (without any formulas) that American put price on a nondividend paying stock is larger then the corresponding European put price.
5.What are the parameters affecting prices European and American calls and puts. How do the prices change when one of the parameters changes with all the others remaining the same?
6.Suppose that we have three European puts with strikes 55, 60, and 65 and the same maturity 1 year. Their prices are 6.75, 9.00, 11.00. Is it possible to do an arbitrage? If so, create the strategy. If not, explain why.
7.Create a spreadsheet modeling trajectories of geometric Brownian motion starting at 100 with growth rate 2.5 percent (it is also risk free rate) and volatility 30 percent. Make a spreadsheet that calculates 金融类Assignment代写
European call maturing in 1 year with strike 100 on a non-dividend paying stock using Monte-Carlo method and using 20,000 trajectories with 250 steps per year in each trajectory. Compare Monte-Carlo price with 20,000 trajectories to a theoretical model price. Calculate with 50,000 trajectories. Compare Monte-Carlo price with 50,000 trajectories to theoretical model price.
8.Do the same thing as problem 7 but now assuming instead of nondividend paying stock stock having 1% continuous dividend yield. (Growth rate would be r-q =1.5%=2.5%-1%) 金融类Assignment代写
9.Create Matlab code doing the same thing as problems 7 and 8. Compare Matlab and spreadsheet results.
10.Suppose that current stock price is 100 $. Its annualized volatility is 30 % and return 10 % i.e. we assume that the stock price follows dXt = 0.10 Xt dt+0.30 Xt dWt. Write the probability density function for the stock in 1 year and in 2 years.