Sunday, August 31, 2008

Decomposing Option Price for Imperfections – Smile, Skew, “Abnormal” Distribution

Currently, it is very rare to see options trading at the Black Scholes price. The reason for this can be classified as:
* Market anticipation of future volatility
* Volatility of volatility effects (which results in the volatility skew or smile), and
“Imperfections” of actual returns distribution

All these are fitted into the fitting parameter which is volatility.

In identifying underpriced options, the above effects should be removed from the implied volatility and residual volatility should be compared with the historic volatility. When doing this, things to consider is that the effects of vvol is not present for ATM options, thus, theirs price reflects more of anticipatory and adjustments for the distributions imperfections.

Imperfections in the distribution results in the distribution’s moments diverting from the normal distribution. These can be modeled using moment fitting techniques where one option is decomposed into a basket of BSOPM options at different vols. The de composition can take the following form:
* Fit a kernel to the distribution and get the basket for the imperfection effects plus the normal BSOPM effects
* Subtract the BSOPM priced option to get a zero weight basket which has the pure imperfection effects
* From the observed price of an ATM option subtract the above to get the price component of the anticipator vol. effects
* The deference between the ATM and options at the other strike with the same term is the risk of volatility effect

NB: in a basket all the option parameters should reflect the modeled option except for the implied volatility which is the fitting parameter.

Best regards, Suminda Sirinath Salpitikorala Dharmasena

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Tuesday, August 26, 2008

Attribution Analysis and Exposures

A portfolio will contain a certain asset mix. The exposure of a portfolio to these classes can be determined by weight of such investment. The market factors can be separated from the asset selection skills using attribution analysis. Such selection could be influenced by various factors like economic indicators, certain revenue drives, etc. which do not have the asset as an element like in an index. In such cases the factor exposures can be determined by regression analysis.

--
Thanking you.
Best regards,
Suminda Sirinath Salpitikorala Dharmasena B.Sc. (Hon.) Comp. & I.S., Lon.

The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honours the servant and has forgotten the gift. - Albert Einstein

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Attribution Analysis and its Link to Information Coefficient and Alpha

Hi,

The Information Ration (IR) is a measure of the information captured in the portfolio. The IR changes with the weights within an asset class, which is the same thing that that creates Alpha. The Information Coefficient (IC) is the information capture of the portfolio. Therefore, IC is directly proportional to IR and Alpha.

Attribution Analysis deals with separating and attributing the return due to asset allocation and asset selection. The returns would have an asset allocation component plus the individual asset selection component. This excess returns is a result of information capture and would lead to an IR deviating from 0 as well as such an Alpha.

Please be good to share your thoughts on this.

Best regards, Suminda Sirinath Salpitikorala Dharmasena

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THIS COMMUNICATION OR ANY OTHER POSTS IN THIS BLOG OR ANY BLOG MAINTAINED BY THE AUTHOR DOES NOT CONSTITUTE INVESTMENT ADVICE OR COUNSEL OR SOLICITATION FOR INVESTMENT IN ANY SECURITY.

No Frills Attribution Analysis with Overlaps and Sub Categories

Hi,

Attribution analysis becomes problematic when:

  • Overlap in asset classifications
    • Industry and company size (Individual Sector and Large, Mid, Small, Micro Cap classification)
    • Industry and market (Individual Sector and market like US, EU, Asia, etc.)
  • Main classification classes and sub classes are included
    • Sector sub sector
    • Market industry (E.g. US Stocks and sector S&P SPDR)

In the latter case the broader classifications exposure to the sub classification can be worked out. The portfolios exposure to the sub classification will be the sub classifications exposure to the broader classification scaled by the portfolio’s exposure to the broader classification. When there are overlaps things are not that straight forward though.

When there is an overlap, things become more tedious. In this case the exposure to each classification and the overlapping subset needs to be computed separately and the final analysis would have the individual exposures minus the sub exposures.

Broader analysis would be advantages and more informative despite the need of adjustments.

Simple summary of the process:

  1. Identify portfolio’s asset class exposure attributed returns - Portfolio’s exposure to asset classes simply by the weight or a market weighted index of the asset classes
    1. If the market weighted approach is used, certain part of excess returns are attributed to asset allocation among the asset classes
  2. Identify the asset classes exposure to its sub classifications
    1. Part of excess returns identified in 1 when a market weighted index is used can be attributed to this sub classification
    2. Adjustments mentioned above need to be applied.
  3. Any remaining excess returns are attributed to the individual stock selection

The exposure to each classification can be minimized to reduce the downside due to market fluctuations but such exercise should be combined with at least static hedging since these relationships would breakdown on adverse market events. If dynamic hedging is used the re adjustment frequency should be low and the hedge ratio should be selected such that it is greater than or equal for a static hedge and less than or equal to delta neutral hedge paying head to the other Greeks and the cost of hedging vs. the maximum loss the hedging would bound.

Please be good to share your thoughts on this.

Best regards, Suminda Sirinath Salpitikorala Dharmasena

Blogger Profile: http://www.blogger.com/profile/03835227536866539389

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Sunday, August 24, 2008

Attribution Analysis and Exposures

A portfolio will contain a certain asset mix. The exposure of a portfolio to these classes can be determined by weight of such investment. The market factors can be separated from the asset selection skills using attribution analysis. Such selection could be influenced by various factors like economic indicators, certain revenue drives, etc. which do not have the asset as an element like in an index. In such cases the factor exposures can be determined by regression analysis.

--
Thanking you.
Best regards,
Suminda Sirinath Salpitikorala Dharmasena B.Sc. (Hon.) Comp. & I.S., Lon.

The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honours the servant and has forgotten the gift. - Albert Einstein

My Profile: http://www.linkedin.com/in/sirinath
http://www.facebook.com/profile.php?id=842840093
http://www.blogger.com/profile/03835227536866539389

(c) Suminda Sirinath Salpitikorala Dharmasena. All rights reserved.

This message is subjected to the standard disclaimer: http://sirinath1978m.googlepages.com/standarddisclaimer.

Monday, August 04, 2008

Normality Assumption in VaR Calculated Using Mote Carlo Simulation

Hi,

Subjectively, the VaR is conservative if the minimum value of the portfolio is bounded. The values are more accurate if the Gamma is +ve.

Best regards, Suminda Sirinath Salpitikorala Dharmasena

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