Your firm is offering a new type of exotic equity option. The

expiration date of the option is two periods from now. The

option is not initially specified to be a put or a call. Instead,

the owner makes this choice after one period. Once the

choice is made, the option can be exercised at any time. For

example, if after one period the owner chooses for the new

exotic option to be a put, it would at that time become

identical to an ordinary American put with one period

remaining until expiration.

A customer has asked for a quote for an option of this type

on GameGo Inc. stock with a strike price of $K=$$$100\mathrm{.}00.$

The current price of GameGo Inc. stock is $S=$$$100\mathrm{.}00$ per

share, and over each period the stock price evolves as shown

on the tree below. The risk$-$neutral probability of an up move

is $0\mathrm{.}50.$ The stock does not pay dividends, and the interest

rate is $5\mathrm{.}00\%$ per period $($simple compounding$).$

Let $C(S,n)$ and $P(S,n)$ be the values of American calls

and puts when the stock price is $S$ and there are $n$ periods to

go$.$

A$.$ What is the value of $C(155\mathrm{.}00,1)$ and $P(155\mathrm{.}00,1)?$

$C(155\mathrm{.}00,1)$

$P(155\mathrm{.}00,1)$

B$.$ What is the value of C$(55\mathrm{.}00,1)$ and P$(55\mathrm{.}00,1)?$

C$(55\mathrm{.}00,1)$

P$(55\mathrm{.}00,1)$

C$.$ What is the lowest price your firm could charge and still break even?