AEM4210_assignment5_Sol

AEM4210_assignment5_Sol - AEM 4210 Derivatives and Risk...

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AEM 4210 Derivatives and Risk Management Spring Semester 2010 Homework Assignment 5 Suggested Solutions This assignment is due in class on Friday, April 30, 2010. Total 150 points. Question 1: Covereds and Straddles This worksheet is designed to investigate the payoffs to covered calls and straddles. The initial hedge positions are taken in time period 1 (column 1). Then it shows the value of the hedge across time with random futures starting in column 2 through column 12. Random futures prices are generated using a uniform random number generator that can change by hitting the F9 key (hit the F9 key now to see). As prices progress from month 2 through month 12 the results in rows 24 and higher provide the net hedge position at each month. 1) Using the futures price as the x axis (from column 2-12) and covered call and covered put (row 35,36) on the Y axis prepare an XY graph (like that shown below but please add labels). Hit the F9 key and observe the graph. Select, cut and paste an interesting graph. Discuss the graph in the context of covered puts and calls. Make sure you provide an explanation of a covered call and covered put and the interesting characteristics of its payoff. 1

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Covered Put The selling or writing of a put option while being short an equivalent amount in the underlying security Covered put pay off is identical to selling a naked call Max Profit = Premium Received - Commissions Paid Max profit is limited, achieved when price of underlying <= Strike Price of Short Put (below 10 on the graph ,profit = 0.2876) Max Loss can be infinite Covered Call The selling or writing of a call option against a long position in the underlying stock Covered call payoff is identical to selling a naked put Max Profit is limited, achieved when price of underlying >= Strike Price of Short Call (above 10 on the graph, profit = 0.2876) Max Loss achieved when price of underlying = 0 2) Repeat question 1 for bottom straddles and top straddles. Bottom Straddle The buying of a call and a put with the same strike price The payoff is like a V shape 2
The maximum profit is unlimited as long as price of underlying increases The maximum loss is when price of underlying = strike price (in this case, when k=10, loss = -0.5752) Top Straddle The selling of a call and a put with the same strike price The payoff is like an upside- down V The maximum profit is limited, achieved when price of underlying = strike price (in this case, when k=10, profit = 0.5752) The maximum loss is unlimited 3) Repeat question 1 for synthetic long and synthetic short Synthetic long The selling of a put and buying of a call at the same strike price The payoff increases as price of underlying increases The maximum profit is unlimited Profit achieved when price of underlying > strike price of long Call + net premium paid The maximum loss achieved when price of underlying = 0 Synthetic short 3

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The selling of a call and buying of a put at the same strike price The payoff decreases as price of underlying increases
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