newbie question about options

[poker1O1]

I have a good understanding of the stock market with exception to options. i honestly dont know understand them at all. can someone please explain. ty.

[OrangeCat]

A good overview:
http://www.investopedia.com/university/options/

Options on futures:
http://www.orionfutures.com/opts.htm#terms

Options as used for employees:
http://money.howstuffworks.com/question436.htm

If you really want to get into it, here is an online tutorial:
http://www.cboe.com/LearnCenter/Tutorials.aspx#Basics

[cwsiggy]

McMillan's books are also good

[GeorgeF]

1) The only real use of options is when you have a large gain but you do not wish to trigger taxes by selling. You can insure your gains by purchasing options. If it were not for taxation, much fewer options would be sold as people would just sell their positions. All other options tranactions are gambling or by people that cannot sell for other reasons.

2) People that sell you the options are 'sharps' and they are not doing it because they want you to be rich.

3) Try your local business library (it's free). It might be worth your while to go to buy a finance 101 text, perhaps last years from ebay or what ever. Their may even be an online course worth the effort.

4) Stocks are actually options. They are an option on the value of a company exceeding it's liabilities (debts).

5) Just for fun you might take buy an option for a few hundred $ (cost to you of 1 option = 100 x listed price) on a 2007 option and watch what happens over the next few years.

6) Good luck you will need it.

[edtost]

[ QUOTE ]
The only real use of options is when you have a large gain but you do not wish to trigger taxes by selling.

[/ QUOTE ]

there are many reasons one would want to purchase various types of derivative securities.

in fact, this sentence was so dumb and displayed such a fundamental misunderstanding of derivitaves markets that i stoppped reading; i hope (for the sake of the forum) your post didnt get any worse.

[GrunchCan]

[ QUOTE ]
i hope (for the sake of the forum) your post didnt get any worse.

[/ QUOTE ]

It did.

[ QUOTE ]
4) Stocks are actually options. They are an option on the value of a company exceeding it's liabilities (debts).

[/ QUOTE ]

Wrong. In fact, this doesn't even make any sense.

There are 2 kinds of options: calls and puts. I’ll describe call options now, and puts in a moment.

When you buy a call option, you buy a contract that gives you the right to buy a specified stock at a specified price on or before a specified date. The stock is called the “underlying,” the prearranged price is called the “strike price,” and the specified date is the “expiration date.”

This contract is not free – it comes at a price that is at least loosely based on a “theoretical value” for that contract. For example, as I type this IBM stock is trading at $89.96 per share on the NYSE. IBM call contracts with a strike price of $80 (giving the contract owner the right to buy IBM stock at $80.00), and an expiration date in July are going for $12.30 per share on the CBOE. If you were to buy the contract and exercise at that same moment, you would end up owning 1 share of IBM stock but you would have paid a total of $92.30 for it ($80 for the strike price + $12.30 for the option itself).

That doesn’t mean options are bad – they have their place. In fact, there are lots of professional traders who do nothing but trade options.

There are also put options. They are the same as call options, with 1 difference. Instead of being a contract to buy stock at a specified price, put options are a contract to sell stock at a specified price. Everything else is the same.

You can either buy or sell options. If you sell an option, you don't have to own one first. You can just write up your own options contract and sell it in the marketplace. This is different than the stock market. In the stock market, there are X shares of ABC company that traders buy & sell amongst themselves. But in the options market, contracts come in to and go out of existance all the time.

Options aren’t for everyone, but it is absolutely incorrect to suggest that they have no place in a diversified investment portfolio. And it is wrong to imply that anyone trying to sell you an option is trying to rip you off. I haven’t given you enough information to be able to trade in options profitably – or even safely. Options could carry a great deal of risk. It would be a very bad idea for anyone reading this to execute options trades if the extent of your options knowledge is this post. You could lose your shirt. I'm serious - you could really get in to serious trouble if you don't know what you are doing. Much more trouble than just buying & selling stocks.

[GeorgeF]

"there are many reasons one would want to purchase various types of derivative securities."

Name some, silly boy. Options (and all forms of insurance) are used by people who have more risk than they are compfortable with but cannot simply stop the activity they are engaged in. People buy homeowners insurance because they cannot face the risk of a fire, but cannot sell the home as they need a place to live. They sell the risk to insurers that are better able to manage the risk.

People buy stock options because they have a position that has more risk than they are comfortable with but they cannot sell, usually to avoid capital gains tax, or because they are company officers.

As to stocks being an option that is finance 101. A company has debt. Management has an option keep the business going or hand over the business the debt holders, that is the option. The option has a strike price of the debt amount. The excersise date depends on the cash burn rate. That is why a company like EXAS swings around so much. The stock no longer has an infinite excersize date.

[edtost]

[ QUOTE ]
Name some, silly boy. Options (and all forms of insurance) are used by people who have more risk than they are compfortable with but cannot simply stop the activity they are engaged in. People buy homeowners insurance because they cannot face the risk of a fire, but cannot sell the home as they need a place to live. They sell the risk to insurers that are better able to manage the risk.

[/ QUOTE ]

yes, hedging risk is ONE possible use of options, but you're telling me you can't think of a derivitave position that's (for example) long volatility? options can also be used to circumvent margin requirements, as they are (in general) inherantly leveraged positions.

[GrunchCan]

[ QUOTE ]
Name some, silly boy.

[/ QUOTE ]

Montage. Theoretical pricing imbalances. There's 2 that have nothing to do with hedging stock positions. Want more?

[poker-penguin]

What on earth is montage?

[GrunchCan]

[ QUOTE ]
What on earth is montage?

[/ QUOTE ]

Some options are traded on more than one exchange at the same time. In fact, there are 5 options exchanges in the US, and many (most?all?) options are traded on all 5. Every now and then the same exact option is traded on one exchange for one price and another exchange for another price. This opens up a profit opportunity. All you have to do is buy it on the exchange where its being sold for less and turn around and sell it on the other exchange where its trading higher. Insta-profit. This imbalance between exchanges is called montage. (mon-tazh)

[Paluka]

[ QUOTE ]
[ QUOTE ]
What on earth is montage?

[/ QUOTE ]

Some options are traded on more than one exchange at the same time. In fact, there are 5 options exchanges in the US, and many (most?all?) options are traded on all 5. Every now and then the same exact option is traded on one exchange for one price and another exchange for another price. This opens up a profit opportunity. All you have to do is buy it on the exchange where its being sold for less and turn around and sell it on the other exchange where its trading higher. Insta-profit. This imbalance between exchanges is called montage. (mon-tazh)

[/ QUOTE ]

I an options market maker on of the exchanges. I've never heard this term.

[GrunchCan]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
What on earth is montage?

[/ QUOTE ]

Some options are traded on more than one exchange at the same time. In fact, there are 5 options exchanges in the US, and many (most?all?) options are traded on all 5. Every now and then the same exact option is traded on one exchange for one price and another exchange for another price. This opens up a profit opportunity. All you have to do is buy it on the exchange where its being sold for less and turn around and sell it on the other exchange where its trading higher. Insta-profit. This imbalance between exchanges is called montage. (mon-tazh)

[/ QUOTE ]

I an options market maker on of the exchanges. I've never heard this term.

[/ QUOTE ]

What is the term for what I am describing?

[GrunchCan]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
What on earth is montage?

[/ QUOTE ]

Some options are traded on more than one exchange at the same time. In fact, there are 5 options exchanges in the US, and many (most?all?) options are traded on all 5. Every now and then the same exact option is traded on one exchange for one price and another exchange for another price. This opens up a profit opportunity. All you have to do is buy it on the exchange where its being sold for less and turn around and sell it on the other exchange where its trading higher. Insta-profit. This imbalance between exchanges is called montage. (mon-tazh)

[/ QUOTE ]

I an options market maker on of the exchanges. I've never heard this term.

[/ QUOTE ]

Sorry, I'm a dork. The term I meant was arbitrage not montage. Duh.

[mrbaseball]

[ QUOTE ]
In fact, there are 5 options exchanges in the US

[/ QUOTE ]

In fact there are 6. CBOE, AMEX, ISE, PSE, PHLX, and BOX. BOX (Boston options exchange) is fairly new though so I guess that's the one you missed.

[ QUOTE ]
Every now and then the same exact option is traded on one exchange for one price and another exchange for another price

[/ QUOTE ]

I can assure you this almost never happens. Ocassionally but not often enough to make any money on. It is very very rare.

[J_V]

People that start posts like this don't want links. They want someone to explain options to them in 1-2 minutes so that they can get their options knowledge on par with their acute understanding of stocks.

I'll help him out.


An option is the right but not the obligation to buy a stock at your excercise price. If that's not right, who cares.

[eastbay]

[ QUOTE ]
[ QUOTE ]
What on earth is montage?

[/ QUOTE ]

Some options are traded on more than one exchange at the same time. In fact, there are 5 options exchanges in the US, and many (most?all?) options are traded on all 5. Every now and then the same exact option is traded on one exchange for one price and another exchange for another price. This opens up a profit opportunity. All you have to do is buy it on the exchange where its being sold for less and turn around and sell it on the other exchange where its trading higher. Insta-profit. This imbalance between exchanges is called montage. (mon-tazh)

[/ QUOTE ]

Isn't that arbitrage?

eastbay

[GrunchCan]

[ QUOTE ]


Isn't that arbitrage?

eastbay

[/ QUOTE ]

Yea, I'm a dork. I corrected myself above.

[Recliner]

[ QUOTE ]
People that start posts like this don't want links. They want someone to explain options to them in 1-2 minutes so that they can get their options knowledge on par with their acute understanding of stocks.

I'll help him out.


An option is the right but not the obligation to buy a stock at your excercise price. If that's not right, who cares.

[/ QUOTE ]

That's only a call, what about a put option? Which is the right to sell a stock at the strike price. If you really don't care if anything you post is correct then why bother posting?

[Rotating Rabbit]

Yes, the holder of a put option has the right to sell at the exercise price K.

You can have 'american style' options which allow you to exercise at any time up to the expiry time, and 'european style' that allow you to exercise only AT the expiry time.

An american call is worth the same as a european call provided there are no dividends to be paid.

This is not the case for a put option for all interest rates >0.

[crazy canuck]

An american call is worth the same as a european call provided there are no dividends to be paid.


This is not true. In fact under the Black Scholes framework the price of an american option (call or put) can't even be expressed analytically, i.e. there is no formula for it.

[Rotating Rabbit]

You're mistaken.

Sure, an american option cannot be expressed analytically (thats what discrete approximation models are for) but an american call is the same as a european call under geometric brownian motion, the assumption for BS. Its never preferable to exercise an american call before its expiry.

e.g. S(t) = price of security at time t. If an american call (Price C,Strike K,Expiry T) is in the money, at time t1 say, t1<T, you can exercise and realise a time-T gain of:

[S(t1)-K]e^r(T-t1)

If instead you sell short at T1, stick the funds S(t1) into a bank paying continuously compounded interest at rate r (as above), then at time T buy the stock at the minimum of K and S(T) with the bank money you have a time-T gain of:

S(t1)e^(T-t1) - min {K, S(T)}

which is greater. So its never preferable to exercise early, thus its the same expected value as its european sibling, under Black-Scholes and its assumptions.

[Your Mom]

[ QUOTE ]
[ QUOTE ]
What on earth is montage?

[/ QUOTE ]

Some options are traded on more than one exchange at the same time. In fact, there are 5 options exchanges in the US, and many (most?all?) options are traded on all 5. Every now and then the same exact option is traded on one exchange for one price and another exchange for another price. This opens up a profit opportunity. All you have to do is buy it on the exchange where its being sold for less and turn around and sell it on the other exchange where its trading higher. Insta-profit. This imbalance between exchanges is called montage. (mon-tazh)

[/ QUOTE ]

Arbitrage, I think, is what he is talking about.

[jason1990]

Just a point that might be of interest to some. The value of the call option when it is exercised is h(S(t)), where

h(x)=max{x-K,0}.

This function is convex and has h(0)=0. These two properties are all one needs in order to conclude that it is never optimal to exercise the option before expiry. Notice that the corresponding function for the put is still convex, but it is not 0 at 0.

[jason1990]

[ QUOTE ]
There are 2 kinds of options: calls and puts. I’ll describe call options now, and puts in a moment.

[/ QUOTE ]
In theory, any function of the stock history up to the time of expiry can be regarded as an option. So, in practice, are these more "exotic" options not bought or sold very often?

[crazy canuck]

These two properties are all one needs in order to conclude that it is never optimal to exercise the option before expiry.

This is wrong. Somtimes it is correct to exercise an option early. If it wouldn't be correct, then it would be easy to price american options.

[jason1990]

[ QUOTE ]
These two properties are all one needs in order to conclude that it is never optimal to exercise the option before expiry.

This is wrong. Somtimes it is correct to exercise an option early. If it wouldn't be correct, then it would be easy to price american options.

[/ QUOTE ]
Let me just repeat myself:

[ QUOTE ]
Just a point that might be of interest to some. The value of the call option when it is exercised is h(S(t)), where

h(x)=max{x-K,0}.

This function is convex and has h(0)=0. These two properties are all one needs in order to conclude that it is never optimal to exercise the option before expiry. Notice that the corresponding function for the put is still convex, but it is not 0 at 0.

[/ QUOTE ]
Nowhere did I contradict the fact that "somtimes it is correct to exercise an option early." So what are you saying?

[crazy canuck]

Nowhere did I contradict the fact that "somtimes it is correct to exercise an option early." So what are you saying?

Exercising before expiry means exercising early.

[jason1990]

[ QUOTE ]

Nowhere did I contradict the fact that "somtimes it is correct to exercise an option early." So what are you saying?

Exercising before expiry means exercising early.

[/ QUOTE ]
I said:

[ QUOTE ]
it is never optimal to exercise the option before expiry.

[/ QUOTE ]
This means:

[ QUOTE ]
it is never optimal to exercise the option early.

[/ QUOTE ]
What is "the option" in this context? It is an American call option. So I am saying:

[ QUOTE ]
it is never optimal to exercise the American call option early.

[/ QUOTE ]
This is a fact and I am offering up an explanation for it, which shows conditions under which the same conclusion can be drawn for certain other options as well.

[crazy canuck]

it is never optimal to exercise the American call option early.

Yes it is.

I'm sure there is a simpler explanation, but this will do:

American option pricing (http://finance.bi.no/~bernt/gcc_prog/algoritms_v1/algoritms/node24.html)


[ QUOTE ]
To do their approximation, BAW decomposes the American price into the European price and the early exercise premium

[/ QUOTE ]

If it would be never optimal to exercise the option early the early exercise premium would be zero.

[Paluka]

[ QUOTE ]

it is never optimal to exercise the American call option early.



[/ QUOTE ]

This is absolutely false.

[jason1990]

I thought it was clear from the context of the thread what I was talking about. Apparently it wasn't. I am talking about an American call option without a continuous payout. The link you have provided is for an American call option with a continuous payout.

If you would like to see a proof of the fact I mentioned, you may see Proposition 14.3 on page 245 of "Stochastic Calculus and Financial Applications" by J. Michael Steele.

[jason1990]

[ QUOTE ]
[ QUOTE ]

it is never optimal to exercise the American call option early.



[/ QUOTE ]

This is absolutely false.

[/ QUOTE ]
Earlier in this section of the thread, Rotating Rabbit pointed out that

[ QUOTE ]
An american call is worth the same as a european call provided there are no dividends to be paid.

[/ QUOTE ]
This is the context in which I was making my comment and in this context, it is absolutely true.

(By the way, I'm simply making a mathematical claim here for the benefit of those that find it interesting. I am not making any claims about the "real world" of finance, if that's what you're referring to.)

For a rigorous formulation of my claim and a proof of it, you can see the reference I gave in my previous post.

[crazy canuck]

I'm not talking about real world option prices either.

Have you read the link I posted?

First sentence:

We now discuss an approximation to the option price of an American option on a commodity having a continuous payout


So according to your claim the American option price should be the same as European option price.

I don't care whatever book it is in, your claim is wrong.

[jason1990]

[ QUOTE ]
Have you read the link I posted?

First sentence:

We now discuss an approximation to the option price of an American option on a commodity having a continuous payout

[/ QUOTE ]
Did you read the post I posted?

Second sentence:

I am talking about an American call option WITHOUT a continuous payout.

[ QUOTE ]
So according to your claim the American option price should be the same as European option price.

[/ QUOTE ]
For the kind of American call option I'm talking about, yes this is true. The prices are the same.

[ QUOTE ]
I don't care whatever book it is in, your claim is wrong.

[/ QUOTE ]
I gave you the book reference so you could read the proof for yourself. As a professional mathematician whose research area is stochastic analysis and mathematical finance, I can assure you that what I'm claiming is the absolute truth. If you choose not to believe it or choose not to try to better understand exactly what it is I'm claiming, then I suppose that's your business.

[crazy canuck]

You said in your first post:


h(x)=max{x-K,0}.

This function is convex and has h(0)=0. These two properties are all one needs in order to conclude that it is never optimal to exercise the option before expiry. Notice that the corresponding function for the put is still convex, but it is not 0 at 0.



No, as you said yourself these properties are not enough.

Yes, there are options for which there is no early exercise premium (like probably the example in your book), but in GENERAL the claim is not true.

In fact even if an option has non continuous payout, early exercise can be optimal. For example find a simple example of binomial option pricing.

Maybe you forgot to mention continuous stock price and some other conditions too?

[jason1990]

Whatever. This is just silly now. My original post was a reply to Rotating Rabbit, who was explicitly talking about an American call option without any payoff rate (continuous or otherwise) other than the terminal payoff, in a Black-Scholes model using geometric Brownian motion.

You obviously either didn't read the thread carefully enough, or you don't have enough interest in it to discern the context for yourself. Frankly, this is not worth my time.

If you have any genuine interest in learning more about the theorem I mentioned about options of this kind that are defined as convex functions of the stock price, then you'll have to PM me, because I'm not going to bother with this thread anymore.

[Rotating Rabbit]

Hi Jason. Indeed he's not read my answer properly, I clearly stated that there were exceptions (e.g. dividend payments continuous or otherwise etc).

When you say the value of the call option (at s(t) = x):

h(x) = max {x - K, 0}

I presume you mean the payoff (ie not including cost) as opposed to the value.

If you dont mind, I'm very interested to know the gist of why max{s(t)-K, 0} being convex and passing the origin implies its an increasing function of t (and why max{K-S(t), 0} i.e. the put with coordinate (s(0),K) , is different)?

[jason1990]

Hi Rabbit. Thanks for the PM. So here's the idea. Our stock is simple geometric Brownian motion S(t). Our bond is simple exponential growth b(t). Assume h is convex with h(0)=0. Then for all p between 0 and 1, we have

(*) h(px) <= ph(x) + (1 - p)h(0) = ph(x).

Now, let M(t)=h(S(t))/b(t), let F_t be the Brownian filtration, and let Q be the equivalent martingale measure under which the discounted stock price D(t)=S(t)/b(t) is a martingale. Then

E_Q[M(t+s) | F_t] = E_Q[h(S(t+s))/b(t+s) | F_t]
= b(t)^{-1} E_Q[h(S(t+s))b(t)/b(t+s) | F_t]
>= b(t)^{-1} E_Q[h(S(t+s)b(t)/b(t+s)) | F_t]

by (*). Since h is convex, Jensen's inequality gives

E_Q[h(S(t+s)b(t)/b(t+s)) | F_t]
>= h(E_Q[S(t+s)b(t)/b(t+s) | F_t])
= h(b(t)E_Q[S(t+s)/b(t+s) | F_t])
= h(b(t)E_Q[D(t+s) | F_t])
= h(b(t)D(t))
= h(S(t)),

where we have used the fact that D is a Q-martingale. Putting these two facts together gives

E_Q[M(t+s) | F_t] >= b(t)^{-1}h(S(t)) = M(t),

so M is a Q-submartingale. Hence, by optional sampling, if T is expiry and tau is any stopping time with tau<=T, then

(**) E_Q[h(S(T))/b(T)] >= E_Q[h(S(tau))/b(tau)].

By the martingale pricing formula, the price of this option is

sup E_Q[h(S(tau))/b(tau)],

where the sup is taken over all stopping times tau<=T; and the optimal exercise time is the stopping time which achieves this supremum. Therefore, by (**), we see that the optimal exercise time is simply T, the time of expiry.

In terms of arbitrage, let's see if I remember this correctly. As the seller of the option, suppose I use the same hedging portfolio I would use if it were a European option. Then my initial investment is

V(0) = E_Q[h(S(T))b(0)/b(T)]

and my wealth at time t will be

V(t) = E_Q[h(S(T))b(t)/b(T) | F_t]
= b(t)E_Q[M(T) | F_t].

If the buyer exercises at time tau, then my wealth will be

V(tau) = b(tau)E_Q[M(T) | F_tau]
>= b(tau)M(tau) = h(S(tau)).

So I will have enough to cover him, plus a possible surplus.

Edit: There is a b(0) missing in at least one place above. So let's just assume b(0)=1.

[Rotating Rabbit]

Well thankyou for this Jason. I'm not fluent enough in martingales to have been able to derive this myself. I'd previously been trying to think of a way of adapting the security/bond hedging european-call pricing argument to find a price. I note your edit I would normally assume b(0) is 1 anyway unless its someone being particularly annoying /images/graemlins/smile.gif

Its interesting to me that weak-convexity is so powerful even when the functions dont even have continuous first derivatives.

There's probably a paper in here somewhere for someone looking at concave utility functions and american calls conbined, if it hasnt already been examined in detail.

[jason1990]

[ QUOTE ]
There's probably a paper in here somewhere for someone looking at concave utility functions and american calls conbined, if it hasnt already been examined in detail.

[/ QUOTE ]
Are you a researcher? If you discover an open research problem related to this, I would definitely be interested in reading about it.

[edtost]

holy crap. someone posted somehting intelligent in this forum.

im pretty sure this is the first time ever.

[Glenn]

Lol, yes! You would think that when something intelligent regarding options touched this forum they would mutually annihilate in a burst of energy.