differential equations
1. Find the expected price that someone would pay for a 6 month European call option contract with a strike price of $50 on a stock that is currently trading at $45,with =0.07
time steps.We can findt by noting thatt=
2. Find the expected price for a 6 month European call option contract with similar parameters to the one from question 1,but try the current price of $50,and another one at $55.Use about 10,000 sample trajectories for each. Comment on what you notice with these two options,in relation to the current price and strike price. 3. Check your solutions for 1 and 2 with the exact values from the Black-Scholes equation given below: c(s=1---3-1--2
d=d=ovT
Where the parameters are the ones from the model above,and the xis the cumulative distribution function for the standard normal probability distribution, given by: x= e2dx V2n You can look up these values using software,or use the sheet linked in Blackboard 4. For each of the options you priced in number 1 and 2,plot a histogram of the final prices for each of the 10,000 trajectories.Attach them with the project,and write a few sentences about what you notice for each of them 5. For each of the options you priced in number 1 and 2,plot a histogram of the payoffs for each of the 10.000 trajectories.Attach theTrm with the project and write a few sentences about what you notice for each. 6.Try increasing and decreasing the strike price,K,with the same starting price. You should see that by increasing the strike price there is a decrease in the present value of the option.Why do you think that is? 7. Try changing and a.What do these appear to do to the pricing? What do they do to the underlying stock?