Help with question 4,5,6 please

Option Pricing 1. The sample tree you got has 2 steps. Current stock price is $100. Annual volatility o is 20%. Now make this tree have 3 steps instead of 2. In order to keep the annual volatility the same while increasing the number of steps, the 3-step tree should have upward movement as u = pO/T/N, where e is exponential, o is annual volatility, T is time to maturity, and N is number of steps. The downward movement should be d = e ) -GT/N Calculate the price of call option with a strike price of $95 using your 3-step tree. Risk-free rate is 3% and the option has 1 year to maturity. 2. Create a binomial tree with 4 steps. Other conditions are the same as 1. What is the price of call option with a strike price of $95? 3. How does the option price change by number of steps? Draw a graph to show the pattern. The x-axis of the graph should be number of steps and the y-axis of the graph should be the call option price. The format (not the actual value) is something like this: Call Option Price 6 4 2 0 2 steps 3 steps 4 steps 5 steps 6 steps Option Price To draw the graph, get the option price for 2, 3, 4, 5, 6 steps. 4. Now keeping the other conditions the same, change the annual volatility to 25%. Use the 6-step tree you created above. What is the price of the call option with strike price $95? What can you infer about the relationship between call option price and volatility? 5. There is a put option on the same stock, with strike price $95 and 1 year to maturity. The annual volatility o of the underlying stock is 20%. Risk-free rate is 3%. Use the 6-step tree to get the price of the put option. 6. Now calculate the price of the same put option when annual volatility increases to 25%. What can you infer about the relationship between put option price and volatility? 7. Create a Black-Scholes calculator with Excel. Calculate the price of a call option with strike price $95 and 1 year to maturity. Stock price is currently $100 and annual volatility is expected to be 20%. Risk-free rate is 3%. Is this number similar to the call option price from the 2-step tree? How about the price from the 6-step tree? 8. Create a Monte Carlo simulation of call option pricing with Excel. Stock price is currently $100, and stock price at maturity will be determined by log-normal distribution. In this case, you can create a random pick of stock price at maturity by calculating, S(T) = S(0).el( " - *)T+0VT]. - S(T) is stock price at maturity, S(0) is current stock price, ris risk-free rate, o is annual volatility, T is time to maturity, and e is a random pick from normal distribution. To generate the random number e, use Excel function norm.s.inv(rand()). Report the average of 100 cells, 500 cells, and 2000 cells. Which value would be closer to the Black-Scholes price in the previous question? Option Pricing 1. The sample tree you got has 2 steps. Current stock price is $100. Annual volatility o is 20%. Now make this tree have 3 steps instead of 2. In order to keep the annual volatility the same while increasing the number of steps, the 3-step tree should have upward movement as u = pO/T/N, where e is exponential, o is annual volatility, T is time to maturity, and N is number of steps. The downward movement should be d = e ) -GT/N Calculate the price of call option with a strike price of $95 using your 3-step tree. Risk-free rate is 3% and the option has 1 year to maturity. 2. Create a binomial tree with 4 steps. Other conditions are the same as 1. What is the price of call option with a strike price of $95? 3. How does the option price change by number of steps? Draw a graph to show the pattern. The x-axis of the graph should be number of steps and the y-axis of the graph should be the call option price. The format (not the actual value) is something like this: Call Option Price 6 4 2 0 2 steps 3 steps 4 steps 5 steps 6 steps Option Price To draw the graph, get the option price for 2, 3, 4, 5, 6 steps. 4. Now keeping the other conditions the same, change the annual volatility to 25%. Use the 6-step tree you created above. What is the price of the call option with strike price $95? What can you infer about the relationship between call option price and volatility? 5. There is a put option on the same stock, with strike price $95 and 1 year to maturity. The annual volatility o of the underlying stock is 20%. Risk-free rate is 3%. Use the 6-step tree to get the price of the put option. 6. Now calculate the price of the same put option when annual volatility increases to 25%. What can you infer about the relationship between put option price and volatility? 7. Create a Black-Scholes calculator with Excel. Calculate the price of a call option with strike price $95 and 1 year to maturity. Stock price is currently $100 and annual volatility is expected to be 20%. Risk-free rate is 3%. Is this number similar to the call option price from the 2-step tree? How about the price from the 6-step tree? 8. Create a Monte Carlo simulation of call option pricing with Excel. Stock price is currently $100, and stock price at maturity will be determined by log-normal distribution. In this case, you can create a random pick of stock price at maturity by calculating, S(T) = S(0).el( " - *)T+0VT]. - S(T) is stock price at maturity, S(0) is current stock price, ris risk-free rate, o is annual volatility, T is time to maturity, and e is a random pick from normal distribution. To generate the random number e, use Excel function norm.s.inv(rand()). Report the average of 100 cells, 500 cells, and 2000 cells. Which value would be closer to the Black-Scholes price in the previous