Re Put, Calls:
Yes, a put is an option, ie the option to put the stock in someone else's hand (the option writer), at a prearranged price.
A call is the option to call the stock from someone (the option writer) at a prearranged price.
Both of these options require the prepayment of a premium (to the option writer) for the privilege to have the ability to put and call.
They are derivatives since their values are derived from the underlying stock (or currency, commodity, etc).
They are used to speculate and hedge.
If you think a stock will go up, you buy a call option, and make a profit by exercising your option in the future.
If you don't agree, ie stock will remain flat, you could write a call option contract, ie get the premium from a sucker who thinks the stock will be going up.
If it does not rise, then you keep the premium.
If you think a stock will go down, you buy a put option and sell the stock at a higher price than the decline price.
Likewise, if you don't agree, and think stock will remain flat or increase, you write the put option for the premium.
Secondary markets are available for the options themselves. Ie. 90% of the options traded are never exercised, they are just sold back to the writers. Their value is based on the difference between the exercise price and the underlying asset (stock).
BA Mathematics, UC Berkeley
Certificates in CPA and EA preparation, College of San Mateo
CMA I 420, II 470
FAR 91, AUD Feb 2015 (Gleim self-study)