Finance Derivative

    graph profit diagrams for several trading strategies. Compute the profit of the strategy at maturity with respect to different realizations of the stock price in the future and plot the profit diagram (stock price on x-axis; profit on y-axis) of the strategy. a. Buying a Straddle: Buy a call with an exercise price of $25 for a price of $3.15 and buy a put with an exercise price of $25 for $1.25. b. Writing a Strangle: Sell a call with an exercise price of $80 for a price of $4.75 and sell a put with an exercise price of $65 for $7.85. c. Buying a bull spread: Buy a call with an exercise price of $45 for a price of $12.30 and sell a call with an exercise price of $55 for $8.70. d. Buying a butterfly spread with calls: Buy a call with an exercise price of $35 and a price of $6.20. Sell two calls with an exercise price of $40 and a price of $4.50. Finally, buy one call with an exercise price of $45 and a price of $3.75. e. Writing a butterfly spread with puts: Sell a put with an exercise price of $120 and a price of $8.50. Buy two puts with an exercise price of $130 and a price of $11.90. Finally, sell one put with an exercise price of $140 and a price of $22.60. 2. Building a Binomial Tree in EXCEL with Market Data: This problem walks you through the process of building a binomial tree in EXCEL and using it to price options. In addition, you will use actual market data to estimate the market parameters that you need to do this (i.e., the risk-free rate and standard deviation of returns). In this problem, we will download price data for Amzaon.com, build a binomial tree of Amazon’s stock price, and finally you will price put and call options on the underlying AMZN stock using that tree     b. Compute the UP and DOWN factors for a binomial model with weekly price changes (i.e., ∆t = 1/52). Be sure to use the annualized standard deviation. Also compute the risk-neutral probability of an UP move. Let’s use the 12-month Treasury rate as the riskfree rate so that everyone is doing the same thing. (We should use the weekly rate, but the entire short-end of the yield curve is so close to zero that it hardly matters which maturity we use). c. Build a 16-week binomial tree for AMZN (this will take you from October 27 to February 16). The standard way to represent a binomial tree in EXCEL is to have each column represent a date (step). An UP move is a represented as the column directly to the right and on the same row. A DOWN move is represented as the column directly to the right and down one row. As you move across the spreadsheet the columns will grow one row longer with each step. AMZN closed at $1,100.95 on October 27. d. Price a 16-week call option on AMZN with a strike price of $1160. Use backward induction and risk-neutral valuation to work your way back to today’s call price. In EXCEL, build a second tree. Start by filling in the last column (step 16); these are the payoffs at maturity that correspond to the stock prices in the last column in the stockprice tree you built in part c. (Hint: just use a formula like =max(price-1160, 0) where price references the appropriate cell from the last column of part c.) Work back one column at time, copy and pasting the risk-neutral valuation formulas. As a benchmark, the AMZN Feb 1160 call was selling for $39.38 on October 27. e. Price a 16-week put option on AMZN with a strike price of $1000. As a benchmark, the AMZN Feb 1000 put was selling for $20.50 on October 27.