Friday, August 26, 2011

Dynamic Hedging by Nassim Taleb (Book Review)

Dynamic Hedging by Taleb is one of the most practical books I've gone through around option trading and associated risk management. Without having to explore specifics, Taleb explains logic applied for various derivative trading philosophies going from market making to higher moment trades such as correlation, leptokurtosis betting achieved via option spreads. Here are some of the book's key points I have found practical.

Black Scholes Merton vs. real world option trading

The BSM option pricing model makes a number of false assumptions regarding market behavior:

source: Maxi-Pedia
1) Constant volatility. The most significant assumption is that volatility, a measure of how much a stock can be expected to move in the near-term, is a constant over time. While volatility can be relatively constant in very short term, it is never constant in longer term. Some advanced option valuation models substitute Black-Schole's constant volatility with stochastic-process generated estimates.

2) Efficient markets. This assumption of the Black-Scholes model suggests that people cannot consistently predict the direction of the market or an individual stock. The Black-Scholes model assumes stocks move in a manner referred to as a random walk. Random walk means that at any given moment in time, the price of the underlying stock can go up or down with the same probability. The price of a stock in time t+1 is independent from the price in time t.

3) No dividends. Another assumption is that the underlying stock does not pay dividends during the option's life. In the real world, most companies pay dividends to their share holders. The basic Black-Scholes model was later adjusted for dividends, so there is a workaround for this. This assumption relates to the basic Black-Scholes formula. A common way of adjusting the Black-Scholes model for dividends is to subtract the discounted value of a future dividend from the stock price.

4) Interest rates constant and known. The same like with the volatility, interest rates are also assumed to be constant in the Black-Scholes model. The Black-Scholes model uses the risk-free rate to represent this constant and known rate. In the real world, there is no such thing as a risk-free rate, but it is possible to use the U.S. Government Treasury Bills 30-day rate since the U. S. government is deemed to be credible enough. However, these treasury rates can change in times of increased volatility.

5) Lognormally distributed returns. The Black-Scholes model assumes that returns on the underlying stock are normally distributed. This assumption is reasonable in the real world.

6) European-style options. The Black-Scholes model assumes European-style options which can only be exercised on the expiration date. American-style options can be exercised at any time during the life of the option, making american options more valuable due to their greater flexibility. 

7) No commissions and transaction costs. The Black-Scholes model assumes that there are no fees for buying and selling options and stocks and no barriers to trading.

8) Liquidity. The Black-Scholes model assumes that markets are perfectly liquid and it is possible to purchase or sell any amount of stock or options or their fractions at any given time.

One of the most important lessons from Taleb and Espen Haug, is that one must learn to understand and remedy the weaknesses of applied mathematical models to have a shot at controlling risk and thereby make money.

Fair value estimations   

Options on equities, exchange rate futures, and etc. utilize different fair value calculations. It is then intuitive that monitoring real time option price deviations from fair value could offer a robust theoretical edge for the trader.

Arbitrage and Arbitrageurs

Despite an academic belief of "risk-free-ness" of arbitrage means, nothing is in real markets. Taleb discusses risk management around option arbitrage strategies. This main involves liquidity, leverage management, stopping times and etc.

Volatility and Correlation

Taleb discusses several alternative means to estimate historical volatility and correlation for more practical, accurate measurements. Mainly, instead of standard deviations, we could simply look at absolute returns.

Over all, I can't believe it took me so long to get and read this book. It's rare to find a book on quantitative trading that's actually practical in nature, Dynamic Hedging is one of them.

Thursday, August 18, 2011

Paul Wilmott on Volatility "Arbitrage"

The video uploader here lectures around Paul Wilmott's theory of exploiting deviations between implied and actual volatilities. 
As much as some may call this trade an arbitrage, actual markets do not offer certainty in net profit at the end of each trade. 

Implied vol doesn't always follow actual, sometimes it feels the other way around. I don't have the exact stats.

Theta is the main issue for long vol positions. An accurate estimate for the average cost of theta before vol hits target is required for realistic PnL.

To get a true sense of expected return each trade, actual cost of potentially dynamic delta hedging, associated transaction costs must be estimated accurately. So we might be left with only the long volatility side being likely profitable over time.

There's also the issue of stopping time, it sometimes takes a while for implied volatility to converge with actual/historical, so if there's need to roll positions over expiration dates, that means more expenses.

There's still money to be made off this logic, it's just not THAT easy given Wall St. competition today is filled with math PhDs.

Quick correction for the last comment about determinism of this theory,
... Getting rid of the dX part makes the randomness go away, you're left with a deterministic equation. 

Sunday, August 14, 2011

Meredith Whitney Interview on stock valuations and her life on Wall St.

She was one of the few bold personnel in 2007 who pointed out the looming 2008 credit crisis.

"A truly talented woman, gives her insight on the Economy and Her personal Biography."

Friday, August 12, 2011

About credit rating agencies

Despite the possibly naive simplicity, it's still funny.

Tuesday, August 9, 2011

Municipal Credit Examined (Full Disclosure)

Discussion around municipal bond credit conditions today, and associated risk management.

Monday, August 8, 2011

Number crunching vs. Fundamental Events

I have an algorithm that suggested bearish near term future for the VIX last week, and... the S&P lowered US credit rating on Saturday. Intuitively, volatility is expected to rise for a while. How long til the dust settles? That is probably the answer everyone's looking for.

So this brings up a very important idea, that math alone isn't enough to squeeze a profit out of the markets consistently over time. While the numbers show that DOW is undervalued with respect to its yield vs treasury bonds, it still does not mean a rally in the next week is likely considering the increasingly alarming US federal and municipal credit concerns.

Today, I can genuinely appreciate how hedge funds like Ray Dalio's Bridgewater operate, making precision decisions off macro economics, likelihood of future crowd behavior. Sometimes it requires both quantitative and qualitative methods for more robust decisions.

Tuesday, August 2, 2011

Popular Applied Math. Skills on Wall St.

Came across this at Christian Marks.

... Wall Street has begun quietly and aggressively recruiting proof theorists and recursion theorists for their expertise in applying ordinal notations and ordinal collapsing functions to high-frequency algorithmic trading

An ordinal notation system is used to name each ordinal in a certain initial subsequence of the countable ordinals; such systems have recently been applied by elite trading operations to the parameterization of families of trading strategies of breathtaking sophistication. Ordinal notation high-frequency trading algorithms, also called ordinal arbitrage systems, pit their strategies against similar algorithmic opponents on electronic exchanges for a few fleeting seconds, during which thousands of trades are executed, including exploratory trades that test the strategies of opposing human and machine traders.

The monetary advantage of the current strategy is rapidly exhausted after a lifetime of approximately four seconds–an eternity for a machine, but barely enough time for a human to begin to comprehend what happened. The algorithm then switches to another trading strategy of higher ordinal rank, and uses this for a few seconds on one or more electronic exchanges, and so on, while opponent algorithms attempt the same maneuvers, risking billions of dollars in the process. The elusive and highly coveted positions for proof theorists on Wall Street, where they are known as trans-quantitative analysts, have not been advertised, to the chagrin of executive recruiters who work on commission. Elite hedge funds and bank holding companies have been discreetly approaching mathematical logicians who have programming experience and who are familiar with arcane software such as the ordinal calculator. A few logicians were offered seven figure salaries, according to a source who was not authorized to speak on the matter.

Set Theory is Ph.D material. Game theory is postgrad as well, and is probably also a necessity to accomplish the above. Is it really necessary to learn all this to make money? Probably not. At the same time, Wall St. technology and application of advanced mathematics are growing so rapidly that it would likely become necessary to understand these concepts to go toe to toe on the institutional level.

Here's a research paper applying a Set Theory based algorithm to trade Indian stocks for a positive expectancy.