
Basic Option Strategies, Part 2 - Options Pricing - karamazov
https://www.datanitro.com/blog/2012/11/19/Options2/
======
ezl
I really like that you guys are doing this.

Former options guy myself and was thinking about doing some similar writeups
on options pricing.

i like the graphs of you drew of the strips with different times to
expiraiton. One thing that is generally counterintuitive for people is how
there is translation of the graph on the x axis over time (theta and carry
rates).

also generally, I think introducing black scholes is good, but doesn't really
"stick" for most people for a while. it takes a while to develop an intuition
about the components of "C = SN(d1) - KN(d2)" means.

I think teaching these intuitions would really sit well for the HN crowd. Also
explaining option pricing as the value of the cash flows of the hedge
portfolio with constant or regular hedging (like physics, start with
assumptions like GBM, zero transaction cost, no bid-ask spread -- then if you
ever feel like it later, address how hedge strategies can dramatically change
option pricing). Natenberg does a simplied version of this.

Also, Cox Ross Rubenstein is a great way to teach euro AND american options --
just change the rules at each node to get different rules and you can
demonstate convergence to Black Scholes with the right parameters.

~~~
daleroberts
Do you think there is a market for teaching this? I've taught a couple of
courses on this stuff "professionally" and have been debating for a while if I
should create some nice online course on the topic.

~~~
ezl
I suspect there is some interest, but I don't know is the market is big enough
to justify creating the materials solely for profit.

As other comments have noted, there are already exhaustive guides on the
subject and they are very good. I think the key would be to have a very
different approach to it specifically, teach intuitions, not technical
details.

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confluence
Imagine a drunk man walking down a dark, rainy road one night after his car
breaks down. He gets out, and begins a "random" walk along the road, looking
for help. Neither you (the trader), nor he (the stock), can see anything -
it's raining, and it's dark. The man stumbles along the road and your job is
to predict his future path, and in return, you get paid money.

A lot of money.

Here's the problem: the guy is both drunk and blind (and probably just a
little stupid) - he can't see anything and hence his movements are erratic.
How in the hell can you predict where this idiot is going to end up? You have
bills to pay, derivatives to price and insurance to sell. So you latch onto
the closest thing that'll work - volatility (anchoring bias).

You use his volatility and assume that, dependant upon his past movements, and
in turn his apparent level of drunkenness, you can, more or less, predict the
possible range of his future random walk. This is a very useful model for
predicting where he will be within the next 30 seconds. It works very well,
and you make a lot of money.

It feels good.

Now you become confident. You start projecting it out just that little bit
further, putting on more precise predictions with tighter spreads, and
levering up your bets - because, of course, everyone else is competing with
you and driving down your alpha. You have now mistaken past movement for the
actual risk of movement - they are not the same thing.

Unfortunately for you, of course, the man has broken down on the edge of a
steep cliff. He continues his random walk, blissfully unaware of his impending
doom. You continue your bets on his volatility. I mean, why wouldn't you?
You're king of the fucking world after all - in fact, not only are you rich,
but you also have a Nobel Prize in Economics from a Swedish Bank!

Oops - too late. Your man has just fallen off the cliff, and you, and your
savings, along with him. You yell inefficient markets, beta sucks balls, VAR
is a trap, the CAPM is a lie and modern portfolio theory is fucking stupid.
The last thing we hear, before that final, brutal, resounding thud is the
faint line: "It was all a fucking lie."

You have just met real risk. It has not been a pleasant experience. Welcome to
the real world.

~~~
actionbrandon
This doesn't really make sense, or have much to do with options trading,
pricing, or theory. Kind of a cool narrative, though.

~~~
confluence
I disagree with your first two points.

It has everything to do with it. It also makes sense.

~~~
actionbrandon
Professional options traders prey on ineffiecent markets, never curse them.
Beta and CAPM literally have nothing to do with options trading, pricing, or
theory. VAR, like all models, is a trap. Options traders would know this; they
are ingrained with a deep distrust of models since they forced to use them all
day every day and understand their appropriate uses and limitations. It would
be unreasonable to expect any serious options trader to blame her model or
worse, "all of it", for failure.

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photon137
Suggestion: In practice, for stock-options, volatility is strike-dependent ie
implied volatility has a skew (lower strikes have higher implied volatility -
the leverage effect). Also, the volatility is dependent on time to expiry of
the option.

Also, as I've mentioned in the HN thread for your previous article, single-
name stock options which are exchange-traded have an American exercise type.
The valuation of these cannot be done using Black-Scholes if they are (a)
long-dated (ie time to expiry is quite long) or (b) they are deeply in the
money/out of money or (c) have an underlying which has a significant dividend
yield (in which case you'd want to own the stock rather than the option).

Puts behave different than calls if the exercise-style is American (puts have
a limited upside - so you wouldn't wait too long if the underlying stock has
fallen far enough - your payoff is not likely to be larger).

You may want to discuss this and option greeks the next time.

~~~
karamazov
We're getting there - implied volatility and greeks will be in the next post.

Thanks for the suggestions!

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gfodor
The bible on this subject, fyi:

[http://www.amazon.com/Options-Futures-Other-Derivatives-
Edit...](http://www.amazon.com/Options-Futures-Other-Derivatives-
Edition/dp/0131499084/ref=pd_vtp_b_3)

~~~
jakarta
Options Volatility by Natenberg is much better:

[http://www.amazon.com/Option-Volatility-Pricing-
Strategies-T...](http://www.amazon.com/Option-Volatility-Pricing-Strategies-
Techniques/dp/155738486X)

~~~
actionbrandon
This one is the best:

[http://www.amazon.com/Dynamic-Hedging-Managing-Vanilla-
Optio...](http://www.amazon.com/Dynamic-Hedging-Managing-Vanilla-
Options/dp/0471152803)

The first thirty or so pages offer the most intuitive introduction to vanillas
I've read. The middle is must read, and the end gets into exotics if that's
your fancy.

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drinkzima
The math looks off on the 50% vol 30 day option. No way a $50-strike option on
a stock at $25 would be pricing at $20. Unless you mean 50% non-annualized
vol, which would not be very conventional.

~~~
karamazov
You're right, the numbers were off. They're fixed now.

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tikhonj
I really like this series of posts--it's a great introduction to options.

The little aside in one of the notes made me curious: what _is_ the logic
behind trading options on their expiry date? I can't think of any obvious
reason to do that, but I'm not terribly experienced with finance. That's why
I'm curious about it, I suppose.

~~~
ezl
good q, tikhonj.

a lot of people DON'T trade options on their expiration day. Even
marketmakers, whose job is to provide liquidity in the name often shy away
from it or demand high premia.

historically, retail investors sometimes closed out their positions on
expiration day instead of exercising. this might sound weird, but some people
have weird portfolio restrictions so its occasionally sensible.

also, for some equities, there are big events that happen to coincide with
expirations. If you have an opinion on a big event (lets say AAPL options are
expiring and you think there's going to be a huge announcement), it lets you
buy expiring options for virtually no volatility premium.

also: people like gambling. buying cheapie out-of-the-money options is kind of
like buying a lottery ticket. I've seen them hit (saw a guy take home a
5million dollar win one wednesday morning for a $6k lottery ticket he bought
on the close on tuesday)

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daleroberts
I think the author of the article hasn't really grasped the concept of option
pricing. You are not calculating an 'expected value'.

The whole point of the theory is there is a correspondence between a 'no-
arbitrage argument' and calculating an expectation under the 'risk-free'
measure. The mathematical operation of expectation E is only a tool. This link
between no-arbitrage and martingale theory is called the 'Fundamental Theorem
of Asset Pricing'.

There is a nice (basic) explanation of this idea in the book by Baxter and
Rennie "Financial Calculus" where they compare the 'expected value' approach
of a bookmaker and the 'no-arbitrage' approach.

For a more advanced explanation, you can have a look at the book by Delbaen
and Schachermayer (2006).

~~~
karamazov
Of course you're calculating an expected value. If the expected value of an
option isn't its price, what is it?

The no-arbitrage argument is another way of looking at it, but the two methods
are equivalent. In particular, if the expected value of an option is higher
than its price, you should buy the option - and if it's lower, you should sell
it.

With just one transaction this would be statistical arbitrage rather than pure
arbitrage, but if option prices regularly differed from the option's expected
value, stat arb would be a fine strategy.

~~~
daleroberts
The key point you are glossing over is: under what probability measure?

You are calculating an expected value in the sense of 'mathematical operation
E' under some measure not in the sense of 'I expect the price to be...'

I don't want to pick a fight or anything, your product datanitro looks nice
and it's cool you are writing articles on the topic.

Where did you learn this stuff from?

~~~
karamazov
Sorry if my comment came across harshly, I didn't intend it to.

By expected value, I mean the price as you'd calculate it with a risk-neutral
valuation based on some model of the underlying security.

For example, if you have a model that says an option is worth $4, and it's
selling for $2, you should buy it if you're confident in your model. If you
can do this repeatedly on a bunch of independent options you'll make money in
the long run (assuming your model is correct and you're placing a large enough
number of bets relative to the probability of making money on an individual
option).

I learned this with a combination of practical experience, self-study, and
coursework.

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debacle
I feel like this could have been longer. Volatility is really the only way
options make money, no matter what your position is. Is volatility going to be
covered in later parts as well?

~~~
karamazov
I'll talk about implied volatility in the next part. What parts do you think
need more explanation?

~~~
debacle
I think a discussion of measuring and predicting volatility, and how
volatility varies based on the class of asset would be useful. Someone who
invests but doesn't know a lot about options probably doesn't have the respect
for volatility that an options trader does.

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brisance
I'm going to get flamed for this, but promulgating Black-Scholes as the
"standard way" to price options is a little misleading. A better choice of
word would be "conventional", but that's also inexact because the BSM is
broken, since BSM makes a lot of unrealistic assumptions for the model to
work. The point is that there is no One True Pricing Model... the price is
what the market thinks the value is. Too many people who should know better
get it all mixed up, with disastrous effects.

~~~
cjlars
It's not really flame-worthy because you're mostly right. I do however, think
Black-Scholes is an appropriate starting point for options theory, even if
it's not used a ton in practice. Without some sort of framework, you're
effectively lost. I doubt many people could realistically develop any sort of
options based strategy (besides simple leveraged long / short of the
underlying) without a deep inside-and-out understanding of the BSE. The reason
being not that you need to use it to calculate anything, but because it lays
out a straightforward conceptual model of how various greeks interact with
each other.

Of course, understanding the shortfalls of it are equally important. But the
same could be said of DCF, P/E or any other valuation method.

~~~
daleroberts
Yes, Black-Scholes is a good benchmark model, i.e., something to compare other
models to. For example, through the implied volatility surface.

