Which trading position is created by short straddle and long strangle

This is an assignment that focuses on demonstrating which trading position is created by short straddle and long strangle. The paper also requires a working, final profit and loss diagram.

Which trading position is created by short straddle and long strangle

Your task, as the recently recruited PWC’s Quant Analyst, is to provide a thorough analysis of the following parts:
(1)    Firstly, the price of a non-dividend paying stock is $29, its volatility is 30%, and the risk free rate for all maturities is 5% per annum.
Construct a table showing the relationship between profit/loss and stock prices.  Select only one strategy, depending on your group selection.
table in the attachment below
(1)    Secondly, three options (put) on a stock have the same expiration date and exercise prices of $55, $60 and $65.  The option prices are $13, $15 and $18.  Demonstrate for which range of prices would a butterfly spread lead to a loss.  Show clearly your workings.

(2)    Thirdly, assuming that the strike price in a straddle is half way between the two strike prices in a strangle, demonstrate which trading position is created by combining a short straddle with a long strangle, when both have the same time to maturity?  Clearly show your working and final profit and loss diagram.
Although it’s a take home assignment, just be aware that plagiarism is a form of cheating.  The penalty for plagiarism is a mark of zero and possible expulsion from the unit and/or course of study.
For those aiming a higher grade in the project, you should be able to demonstrate your finance skills through various concepts learnt through the course.  Your work experience can add value as well, if appropriate.

Maximum number of students per group: 6
Grade Allocation: 25% of your total course grade.  There will be 15% allocated for the report and also 10% allocated for presentation.