Assignment a. (2 -5 pages) Collect historical data for these three US treasury yields proxies: ^FVX (5 years yield), ^TNX (10 years yield), ^TYX (30 years yield). Focus on the years 2000 -2020. Describe (in short) the changes in these three over the years. Is there a positive or a negative correlation between the three? Explain. Choose three dates ( i.e 2000, 2005, 2010, 2015, 2020, etc.). For each draw the yield curve using only these three proxies. Explain what happened to the curve, and which bond (i.e 5 years, 10 years or 20 year) was more profitable than the other two – • between the first date t o the second date • between the second date to the third date b. (2 -5 pages) Provide a binomial model example (create this example with numbers) for two periods, in which the current value (time 0) of the underlying asset is 1,000, and the high value of th e underlying asset in period one is 1,200. Describe the tree, including Qu, Qd and the interest rate. Show the tree for a C(1,300) and a P(1,300) assuming the options are European options. For each node – write the intrinsic value and the time value. Show the tree for a C(1,300) and a P(1,300) assuming the options are American options. Assume now that the underlying asset is the asset value of a firm, for which the current value of the debt is 700. What is the yield to maturity on the debt? What is th e maximal return for the equity holders? 3 c. (2 -5 pages) “SPY” is an ETF following the S&P500, considered to a proxy for the “market portfolio”. Go to one of the financial sites and gather information (current information, could be at any point of time du ring the defined 72 hours of the exam): SPY price, a price of a CALL option with an exercise price of 345 a price of a PUT option with the same exercise price and for the same expiration date. You can choose any expiration date. Check if the PCP holds for these options’ prices. Use B&S calculator (appears in many financial sites and also given in the course site) to find estimated values for these Greeks: Delta, Gamma, Vega, Theta. Note: you should change the relevant parameter and see the effect on the option’s price, and by that to estimate the value for the Greek. Suggest a strategy using these two Call and Put options for which Delta is positive and Vega is positive. Explain your choice. If there is not any strategy fulfill ing the requirements – explain why. Suggest a strategy using these two Call and Put options for which Delta is negative Vega is zero. Explain your choice. If there is not any strategy fulfilling the requirements – explain why. Suggest a strategy using these two Call and Put options for which the value (price) of this strategy is negative, the strategy’s value is positively correlated with the VIX, and Delta is negative. Explain your choice. If there is not any strategy fulfilling the requirements – expl ain why.
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