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Graph the portfolio profit as a function of stock price

Task: The price of a stock is $50. The price of a one-year European put option on the stock with a strike price of 42 is quoted as $8 and the price of a one-year European call option on the stock with a strike price of 58 is quoted as $6.

Question 1: Suppose that an investor buys 100 shares (one round lot), shorts 1 call option contract (covering one round lot or 100 shares), and buys one put option contract (covering one round lot or 100 shares). Construct a table showing the investor's profit or loss as a function of the stock price. To do this, construct an array (a column in Excel) of stock prices from 20 to 80 in increments of 1. Then use adjoining columns to calculate the stock and option payoffs (one column for each position). Then calculate the stock and option profits by adding/subtracting the initial cash flows. Then add the profits from the three positions (stock, put, call). Finally, use Excel to graph the portfolio profit (y-axis) as a function of stock price (x-axis).

Question 2: Suppose that an investor buys 100 shares (one round lot), shorts 2 call option contracts (covering 2 round lots or 200 shares), and buys 2 put option contracts (covering 2 round lots or 200 shares). Construct a table showing the investor's profit or loss as a function of the stock price. Graph the portfolio profit as a function of stock price. With respect to risk and return, how does this position differ from the position described in Q1?

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## Q : Calculate the implied volatility of the call option

Q1: Use Derivagem to calculate the implied volatility of the call option. Q2: Use put-call parity to estimate the no arbitrage price of a December 117 put.