I've come across the below question which has no answers to it and I was hoping someone could provide some help. I know it quite a long question and I appreciate any help with this.
An investment bank Markup Int., has oﬀered to sell you a hybrid security where the payoﬀ is based on the price of RIO TINTO common stock (RIO). The hybrid matures in one year.
On the maturity date, the owner of the hybrid may either choose to receive the face value of 100 dollars (AUD), or may convert the note into RIO common stock
(1) If the price of RIO is less than or equal to 130 and the owner chooses to convert the hybrid and receive RIO stock, each hybrid converts into 1 share of RIO common stock.
(2) If the price of RIO is greater than 130 and the owner chooses to convert, each note converts into 130/S shares of RIO common stock, where S is the price of RIO on the maturity date of the note.
The owner of the note is not required to convert, so she will do so only if the RIO common stock she receives by converting is worth more than the face value of $100.
There are no other cash ﬂows (ie the note does not pay interest and RIO will not pay any dividends during the next year.
The current price of RIO is 100 per share, and the current price of a zero-coupon bond paying $100 in one year is 95. Standard European call and put options are available with strike prices of 100, 110, 120, and 130 and one year until expiration. The prices of the options are shown in the table below.
'Strike Call Put
100 14.25 9.25
110 10.00 14.50
120 7.00 21.00
130 4.75 28.25
(a) Sketch the payoﬀs of the note as a function of the stock price on the maturity date. (b) Find a portfolio that replicates the payoﬀs of the note. (c) What is the proper current market value of the note?