- The Wharton School of the University of Pennsylvania
- New York University
- University of St. Gallen - Swiss Institute of Banking and Finance
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.
Google filetype:pdf
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
Return volatility, option trades
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
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..."
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
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.
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
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
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