Wednesday, January 23, 2013

Finding useful quant finance research papers

While a lot of the academic research effort around mathematical finance does not add much value toward actual trading, the few enlightening literature are definitely worth digging for. So here are some means to finding great research papers.

Quality research documents usually come in PDF format, so putting this in the search term filters out a whole lot of trivial, inadequate writings. By the way, I find Foxit PDF reader much more efficient compared to the Adobe version.

Good schools
Some schools whose research papers I’ve found very interesting and practical include:

Specific researchers
It is unfortunate that some PhD researchers have absolutely no clue of how the real world operates; I have met a few of these guys throughout the years and have become increasingly conscious of the research qualities with respect to the writers. Here is a couple of researchers I constantly look up:

Concise math
It is a usual tendency for some academics to make their papers as complex as humanly possible to hopefully imply rigorousness and aptitude. It does not always work. From my experience so far, if the paper is filled with incredibly arcane formulas that cannot be verified easily, the content is usually not worth the time for the market practitioner.

Brute force volume
When it comes down to it, volume is still required to find the gems out of an ocean of quantitative finance grads looking to impress somebody. I currently spend at least an hour each day going over any research material around traded products. This is what it takes.

Tuesday, January 15, 2013

Since we can only delta hedge at finite intervals due to transaction cost constraints, return distribution of an option trade is still relatively volatile. Expected return volatility can be expressed in quantitatively.

Getting a feel for return volatility
Here is an example 100 realized returns from a short option position, -\$1,000vega, with the ending realized vol = implied so the EV~ 0, delta hedged once a week. (Volatility Trading, Sinclair)

We can see that even if the trader is correct with future realized vol, luck still plays a large factor without a large number of trades (Law of Large Numbers).

Quantitative estimate of return volatility

Derman and Kamal gave the answer in "When you can not hedge continuously..."

where
K = vega
N = number of delta hedges

Friday, January 4, 2013

Options Deltas, Probability of expiring ITM

Delta is different from the probability of an option expiring In The Money (ITM); and here is the surprisingly simple mathematical proof.

According to Black Scholes,

where

σ = implied volatility
T = time to expiration

Since σ and T are positive values, and that N(x) is a monotonically increasing function, it is logical that
which then means
and we can see that the probability of a call expiring in the money must be less than its delta. The same logic applies to put options as well.

*The above also explains why delta of ATM calls are usually a bit greater than 0.5.

From the math, it is apparent that this difference between delta and P(ITM) varies with respect to volatility and time to expiration, and becomes significant with far dated options in volatility contango.

Wednesday, January 2, 2013

Excel data analysis 7.0 Realized Vol Smile

Here we look at estimating the volatility smile (AKA Vol Skew) off realized vol. This gives the trader a point of reference while initiating a trade based on the current implied vol smile.

Data

Underlying: NDX (Nasdaq100 Index)
I am using the end of day adjusted values from Yahoo Finance.

On deriving realized vol, see this earlier post (Excel Data Analysis 3.0)

Moving Realized Vol Smile

For this example I've used the last 6 months of realized vol against NDX values in a Scatter Plot.
X- Axis: NDX values
Y- Axis: 20-day Realized Volatility

Quadratic Regression gave the best fit/model, having the highest R-squared at 0.53

There it is.

On running a Quadratic Regression in Excel