Using the data from the oil futures used in homework $1,$ answer the following questions: $($please provide your MATLAB code and results$)1-$ Using the daily data on crude oil futures prices, try to price American options with $1-$ month and $3-$month time to maturity on crude oil futures using $1,2,30$ and $365$ step binomial trees. $2-$ Do the same practice to price European options on crude oil futures using binomial trees. $3-$ Repeat the pricing of European options on crude oil futures using Black model. $4-$ Do you need to repeat the pricing of both put options and call options? $($Hint: what do we know about the relationship between the prices of American and European calls?$)5-$ What is the trend in prices, using binomial trees, when you increase the number of steps from $1$ to $365?$ Do you think the price you got from binomial trees converges to Black$$s prices when you increase the number of steps? $6-$ Plot the time$-$series of the prices of each type of options through time. $7-$ Calculate the Delta of options using both Black model and binomial trees. $8-$ Plot the time$-$series of Delta of the options. $9-$ Using the Delta from Black model and the futures data, form a Delta$-$Neutral portfolio of options and futures at each day. $($Hint: you need to have a portfolio consisting of $1$ unit of futures contract and X unit of options contract. You should solve for X to achieve the goal of Delta$-$Neutrality$)10-$ Plot the time$-$series of the value of the delta neutral portfolio through time.