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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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)....
View Full Document

{[ snackBarMessage ]}

Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online