hw1sol

# hw1sol - Introduction to derivatives Fall 2011 BUSI 588...

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Unformatted text preview: Introduction to derivatives, Fall 2011 BUSI 588, Homework 1 solutions Homework 1 solutions 1. (*) The problem is close enough to the Rinconete case that I shall briefly sketch the calcula- tions below. The spreadsheet with the solutions has further details. (a) The payoffs from each strategy are discussed in turn. I let S T denote the value of the underlying asset at maturity. Consider the following trading strategies: i. The cost of the portfolio is- . 80 + 0 . 85 = +0 . 05, i.e. we get more money from the put than from the call. The payoffs are S T- 25 no matter what happens to the underlying asset. The profits are therefore S T- 24 . 95, i.e. the trading strategy yields positive profits if and only if S T > 24 . 95. ii. The cost of the portfolio is- . 80 + 0 . 10 =- . 70. The payoffs are 0 if S T < 25 (both options are out-of-the-money); S T- 25 if S T ∈ (25 , 27 . 5) (the long call is in- the-money); and 2 . 5 if S T > 27 . 5 (both options are in-the-money). The profits are therefore positive as long as S T- 25- . 70 = S T- 25 . 7 > 0, or if S T > 25 . 7. iii. The cost of the portfolio is- . 90 + 0 . 15 =- . 75. The payoffs are 0 if S T > 25 (both options are out-of-the-money); 25- S T if S T ∈ (22 . 5 , 25) (the long put is in- the-money); and 2 . 5 if S T < 22 . 5 (both options are in-the-money). The profits are therefore positive as long as 25- S T- . 75 = 24 . 25- S T > 0, or if S T < 24 . 25. (ii) The first two strategies get positive profits for high values of S T , so they can be considered bullish, whereas the last one yields positive profits for low values of S T , so it can be fairly labelled bearish. 2. (*) LNUX’s stock is currently trading for \$4.59. There are puts and calls traded on LNUX. In particular, you know that a call option with a strike of \$4.25 which matures one year from today is trading in the market for \$0.85. The risk-free rate is 5% (in annual terms). (a) If there are no arbitrage opportunities then the put-call parity must hold, i.e. P = C- S + K (1 + r f ) T = 0 . 85- 4 . 59 + 4 . 25 1 . 05 = 0 . 3076 (b) If the put were trading at 0.20 then it would be “cheap” (relative to the other securities)....
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hw1sol - Introduction to derivatives Fall 2011 BUSI 588...

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