Submitted by: Submitted by lordteo
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Pages: 3
Category: English Composition
Date Submitted: 04/17/2010 10:12 AM
options, futures and other derivatives
EXAM
You will find six questions but you must only solve two questions. Each question is graded on 10 points. Book and slides are allowed.
Question 1
You are asked to determine the number of calls and puts with exercise price of $45 that must be sold to have a delta neutral reverse straddle that gives you an initial cash flow of $4,000. Find the number of contracts of each type of option that satisfies these requirements. Assume that the theoretical value is $2.74 for the call and $2.19 for the put, and that the option deltas are 0.568 for the call and –0.447 for the put.
Question 2
In a two-period, two-state world, an asset with a current price of $200 can either rise in value by 24 percent or fall by 20 percent each period. The risk-free rate of interest is 6 percent per period (continuously compounded). A put option written on the asset has an exercise price of $210.
• Determine the possible put prices at expiration.
• What is the put option's current price
• If the observed market price of the put is 19, how would you exploit this mispricing? Give details and show the arbitrage profit in details for all branches of the tree
Question 3
Suppose you observe the following prices for European puts and calls (expiring in one year) on UConn Inc:
| |P|
| |r|
| |i|
| |c|
| |e|
| |s|
|x|c|puts |
| |a| |
| |l| |
| |l| |
| |s| |
|4|$|$1.71 |
|0|1| |
| |5| |
| |.| |
| |0| |
| |0| |
|5|$|$4.00 |
|0|8| |
| |.| |
| |3| |
| |6| |
Suppose the current price of UConn is $50 per share and the stock will pay a dividend (for sure) at the end of one year. Find the interest rate per year and the dividend implicit in these prices.
Question 4
Explain what an arbitrageur would do in the following cases, and how (giving detailed numbers) his arbitrage strategy would have no liabilities at...