You are considering several investment strategies involving the following financial instruments:

• Company XYZ's shares with current stock price = $200 per share.
• Call option on XYZ's share with an exercise price = $210, option price = $6, and expires in 1 year.
• Put option on XYZ's share with an exercise price = $190, option price = $4, and expires in 1 year.

Note: Assuming a one-year investment horizon, the end-of-the-year net payoff (profit & loss) associated with the investment strategies below will depend on the value of Company XYZ's share in one-year time (t = 1), which is uncertain.

Required

a) Given the uncertainties over Company XYZ's share price in one-year time (t = 1), simulate (tabulate) and plot (graphically) the end-of-the-year potential net payoff (profit & loss) associated with the following investment strategies: (i) long stock strategy; (ii) long call strategy; (iii) short call strategy; (iv) long put strategy; and (v) short put strategy.

b) Similarly, simulate and plot the end-of-the-year potential net payoff for an investor with a combined "short call and short put" strategy. What is the investor speculating on using this investment strategy?

c) Consider an investor that owns 10,000 Company XYZ's shares (with a total value = 10,000 * 200 = $2 million), who is worried about the decline in the value of his/her portfolio if there is a crash in the stock market. Discuss in detail how the investor can manage this risk using the derivative instruments given above. Also, simulate and plot the investor's combined net payoff from hedging his portfolio position with the above derivative instrument.