Since you are writing about option pricing , I would like to offer a true story about options pricing and volitility.
The still widely used option pricing model "Black Scholes" is still widely used
today to price options.
One of the developers Myron Scholes ,and Robert merton won the 1997
Nobel Prize for Economics for their work on this pricing model with subjects such as constant volatility, lognormal distribution, stocks that move like Gas Molecules?, heat diffusion (for finance?) etc.
This is a classic case of math gone wrong. The math is correct but the application has been shown to be a disaster in the real world.There is no theoretical basis for Black Scholes to OPTION PRICING.

The basic idea is volatility reversion to the mean. Scholes fund" LTCM,LongTerm Captitol Mgmt lost Hundreds of millions of dollars from
arbitrage. The fund closed and they opened another in 2000.

Black-Scholes option pricing model had nothing to do with the collapse of LTCM. They were highly leveraged in Russian debt and then Russia defaulted on all of it.

Actually it did. the fund was set up to test the volatiltiy theory. They received a huge amount of money to start that fund . as the situation worsened they reasoned, (based on their models) that it all would revert and it didnt. You are correct about the market they were in. They were using an arbitrage strategy expecting various prices to converge and they didnt. The underlying theory
is what caused them to stay in and wait for what"Normally" happened ,
and it didnt. Thnis happened over a 2 month period. They had plenty of time to react but they didnt. Black=Scholes prices an option in a way that isnt in line with reality. The good news is you can profit from it.
Just a quick example. If you take a bell shaped curve or triangle drawing and draw a horizontal line through it so that you have the same point in the upside curve and downside curve and those points of intersection represent
the same price in theup curve as the down curve. Very basically speaking Black Scholes prices those points the same . But the underlying stock is in an uptrend on the left and downtrend on the right. Black scholes does not account for the price action, only volatility. Ill leave the rest for you to make your own assumptions, but traders who are actually making money with options are mostly fading black scholes and looking at the underlying trend of the stock.

They started another fund that made money for a while b ut i heard it was in trouble as well once again, prior to the recent un pleasentness.

Here is the actual money lost by the fund. The russian situation was not the deInvestment Loss

Russia and other emerging markets $430 million
Directional trades in developed countries (such as shorting Japanese bonds) $371 million
Equity pairs trading $286 million
Yield-curve arbitrage $215 million
Standard & Poor's 500 stocks $203 million
High-yield (junk bond) arbitrage $100 million
Interest swaps $1.6 billion
Equity volatility bets $1.3 billion *******

The volatility bets were the biggest losers and were based on the models developed by scholes.
LTCM's mistakes were made fatal by massive leverage and lack of liquidity. If not for their huge leverage, LTCM could have survived these mistakes, or at least survived without such breathtaking losses. So while the mistakes themselves did not have to be catastrophic, it is interesting to consider how LTCM's "world view" contributed to their losses. At the heart of LTCM's trading strategies were two core beliefs:

"The academic view is that the fluctuations (volatility) of a given stock and, in fact, the entire stock market follows a random course. The most articulate expression of this arguments can be found in Professor Burton Malkiel's book A Random Walk Down Wall Street. According to this view, volatility is distributed in a bell curve (a so called "log normal" distribution), just as people's height and weight are distributed in a bell curve. The larger the movement away from the mean (the center of the bell curve), the larger the movement in the stock price and the greater the potential risk. If volatility falls in a bell curve, risk can be estimated. The calculation of volatility assumes that the way a given security or set of securities has acted in the past will reflect the way they will act in the future. Since the past is known, the future can be modeled. "

"Markets are perfectly efficient. The actions of market traders will price securities correctly. A "mispriced" security will be returned to its proper price by the market. This is sometimes referred to as "perfect market theory". Markets may be out of balance at some point in time, but they will always move back toward balance. "

These assumptions are generally true in an un eventful market with no crisis or major changes, but reality is another issue as we are seeeing right now in the markets.
Most high profile traders like George Soros discount market academics because the market doesnt behave in a linear fashion . Bottom line the volatility theories behind ltcm trading is the same that developed Black-scoles pricing. doesnt work

I've been out of school for a while and dont really feel like looking this stuff up so i may be off a little bit, but their assumption that prices are mean reverting wasn't necessarily wrong ASSUMING that you have an infinte supply of capital which is not practical in the real world. As the speads widened in those 2 months LTCM had to liquidate assets to keep up with their margins calls. Many of the assets that they owned were illiquid resulting in an inability to meet margin calls resulting in the fall of LTCM.

You seem very knowledgeable about this, but i dont think that black scholes takes into account default risk, does it? It also doesn't account for extremely improbable devistating events such as the subprime crisis or the dot com bubble like you mentioned. The book "the Black Swan" talks about this and i've been meaning to read it.

A couple of points:

LCTM had to have the leverage they did to get high enough returns. The inefficiencies in the market were just not large not to make an acceptable return without high leverage. In effect LCTM could not have survived with less leverage either.

Black-Scholes formula was previously known (Thorp, Bachelier). The credit given to Black/Scholes/Merton was for the derivation of the formula through continuous arbitrage/dynamic hedging.

Yes the book Black Swan talks about these random unforseeable events that
can wipe out years of profits by defying the "Lawsof Nature" as it were.
The author has made the mistake of trading his ideas as well as he statrted a funded that continually bought way out of the money options that were "Waiting" for that out lier event. He went Down, waiting.
The volatility model works in general in the "Long tERM" whatever that is,
but the market continues to offer surprises year in and year out. The one lesson that is talked about among a handful from the ltcm event is that the underlying price of a vehicle and what it is doing matters. Sounds so simple yet these guys were trading complex volatility models that didnt really monitor price. If you see a trend developing in a stock and buy an option
and the stock moves in your favor by 15-20%, you will gain far more than if
the volatility increases 15-20%. good luck

I understand what you are saying but aren't they very connected in the sense that the higher the volitility the greater the chance of large price moves either up or down, and that was the point of the volitility model?

I understand what you are saying but aren't they very connected in the sense that the higher the volitility the greater the chance of large price moves either up or down, and that was the point of the volitility model?

No, stocks can make sustained moves without large changes in volatility.
The volatility model is more about reversion

The press release from the 1997 Nobel Prize awarded for Black/Scholes formula together with recent events supports the OP contention.

http://nobelprize.org/nobel_prizes/e...997/press.html
Robert C. Merton and Myron S. Scholes have, in collaboration with the late Fischer Black, developed a pioneering formula for the valuation of stock options. Their methodology has paved the way for economic valuations in many areas. It has also generated new types of financial instruments and facilitated more efficient risk management in society....

A new method to determine the value of derivatives stands out among the foremost contributions to economic sciences over the last 25 years....

Black, Merton and Scholes thus laid the foundation for the rapid growth of markets for derivatives in the last ten years. Their method has more general applicability, however, and has created new areas of research - inside as well as outside of financial economics. A similar method may be used to value insurance contracts and guarantees, or the flexibility of physical investment projects.

Maybe Sklansky should have won instead.

The article is extremely simplistic even for 1980...
So I don't really see the point...
Since writing "Options Valuation For Dummies"...
Is akin to publishing "Neurosurgery For Dummies".

Since options are designed for hedging to slash risk/volatility... or to lock in profits.... what would REALLY be interesting... is an adaptation of options for WSOP and Major poker tournaments. For all the name players... and then for everyone in the money... there would be some sort of option or "contract for difference" trading on each players final finish in real-time.

Someone should set up a web site... develop the "2+2 Poker Options Exchange" infrastructure... and have the capital to back it up. Poker Pros would the first to use the Poker Options Exchange, pooling risk via a respected 3rd Party (replacing dodgy verbal agreements)... and fans would provide liquidity by betting on winners/losers.

Since there is an almost desperate need to lay off risk in the poker economy... a "Poker Options Exchange" might be very profitable... since there would be relatively large bid/ask spreads and, therefore, high margins.

Of course, "insider trading" would start instantly...
Just like in every other financial market.

LTCM, Amaranth Advisors, Victor Niederhoffer, and others have had big blow ups with Leveraged plays that are high accuracy -Low risk to reward ratio
trading. They all trade well most of the time but then the big loss comes that takes them down.
Accuracy isnt as important as riskto reward. If you have a 7-1 risk to reward
and expect small losses you dont have to be right that often to show a profit. Something to think about to adapting to the pokerworld in terms of style of play.

Redman,

I thought your idea about a poker players option exchange was intriguing. The credit risk involved and the large risk of players trying to 'game' the system would probably make it completely unworkable in the real world. That's probably why the sports books in vegas don't touch it either. Well that plus a complete lack of interest outside the poker community who wins which tourney. It was fun to ponder anyway...