problem 1:

We consider the US put price to exercise $ 50 and expiring in a year, written on ZZR stock. ZZR does not pay dividends and is traded at $ 13 in the market. Knowing that the interest rate is 10%, and that it is optimal to exercise this option early: a) What is the price of a put with the same characteristics but a strike price of $ 55? b) What is the maximum price of the $ 50 strike price call? 

Problem # 2

VVS stock is now trading at $ 33 and does not pay dividends. A European put expiring one year on VVS and exercise price $ 35 is currently worth $ 2.10. The annual risk-free interest rate is by 10%. What is the price of a European call with identical characteristics?

Problem # 3

Express the position of a shareholder using puts

Problem 4:

Consider a large number of private companies headquartered in different locations across United States. Some of these companies are located in central areas (urban areas or financial centers like New York City, Boston, etc.) and the other part of these companies is located in remote areas (rural areas). Suppose all of these companies are planning to become publicly traded. Discuss in detail whether the geographic location of these businesses could influence the level of undervaluation associated with the IPO underpricing of these companies?