Case $10$

OPTIONS CASE

General Synergistics is an emerging leader in the development of bioengineering technology.

Since its stock is relatively volatile and draws a large amount of investor interest, the firm has

recently been listed on the Chicago Board of Options Exchange $($CBOE$),$ and put and call options

on the firm$$s stock are now being traded. The listing has generated a lot of interest among the

firm$$s senior managers, but only a few of them have a good understanding of what options are

and how they work.

As a service to the firm$$s senior managers, General Synergistics$$ chief financial officer,

Rex Moncrief, plans to hold a seminary on the basic of option theory and valuation. Mr$.$

Moncrief has asked you, a newly hired financial analyst, to make the presentation. To help you

get started, Moncrief has supplied you with the following set of questions. See if you can answer

them.

$1.$ What is an option?

$2.$ Suppose General Synergistics, which is currently trading at $$28,$ has $3-$month put and call

options with a striking price of $$25.$ The call option currently sells for $$4\mathrm{.}50$ per share while

the put option costs $$1\mathrm{.}50$ per share.

$(1)$ What is the minimum number of shares in a stock option contract?

$(2)$ Is the call option in or out of the money? What about the put option?

$3.$ Again consider General Synergistics$$ call option with a $$25$ striking price. The following

table contains historical values for this option at different stock prices:

Stock Price Call Option Price

$$25$ $ $3\mathrm{.}00$

$307\mathrm{.}50$

$3512\mathrm{.}00$

$4016\mathrm{.}50$

$4521\mathrm{.}00$

$5025\mathrm{.}50$

$(1)$ Create a table which shows $($a$)$ stock price, $($b$)$ striking price, $($c$)$ expiration value, $($d$)$

option price, and $($e$)$ the premium of option price over expiration value.

$4.$ In $1973,$ Fischer Black and Myron Scholes developed the Black$-$Scholes Model $($OPM$).$

$(1)$ What assumptions underlie the OPM?

$(2)$ Write out the three equations that constitute the model.

$(3)$ What is the value of the following call option according to the OPM?

Stock price $=$ $$28\mathrm{.}00$

Exercise price $=$ $$25\mathrm{.}00$

Time to expiration $=3$ months

Risk$-$free rate $=5\%$

Stock return variance $=0\mathrm{.}38$

$5.$ What impact does each of the following call option parameters have on the value of the

option?

$(1)$ Current stock price

$(2)$ Exercise price

$(3)$ Option period

$(4)$ Risk$-$free rate

$(5)$ Stock return variance