Category: Financial Markets

Efficient binomial model

view,1060/tag_ids~986,550,1115/request_format~json A consolidated, efficient and practical model for American options with discrete dividends

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The binomial model for pricing American option is well developed with a tremendous volume of research on the topic.  The original model does have several shortcomings which have been addressed by improvements and modifications.

However majority of the research has focused on independently analyzing one particular area or issue with the model, for example convergence, accuracy of greeks and handling of discrete dividends.

While each of these issues have several reasonable independent solutions, the goal of this paper is to construct one consolidated model that is efficient and accurate. The various models that fix single issues cannot be blindly “stitched” together without possible unintended affects.

Several approaches mentioned below, in particular while addressing the discrete dividend issue, rely on a large number of iterations.  The definition of efficiency is a practical model, that can be used in real time trading and risk applications to calculate options value, greeks and implied volatilities fast.

In this paper, the consolidated model developed will address several issues and suggest a practical, efficient and accurate model.

Click here to download the paper. Consolidated Binomial Model RJ 2015

Factors detrimental to growth of options in India

The Indian options market is touted as a very large, liquid options market. The reality however is that the Indian options market is extremely skewed with a vast majority of the liquidity and volumes only in NIFTY options. The single stock options market remains without depth and liquidity and has not grown as would be expected from a mature market.
Stock options are a very important tool for both investment and portfolio hedging and are actively used by investors and market participants globally. Access to stock options enables investors to mitigate stock specific risk as opposed to simply broad market systematic risk by the use of Index options.
The lack of growth of stock options in India can be partially attributed to certain regulatory factors. This paper discusses these factor and offers suggestions on change.

I presented this paper to SEBI via a brokers association in India as well as discussed this with the exchanges several years ago.  However nothing came of it. I do expect this will be resolved in the years to come.

The full paper can be viewed here:

Factors detrimental to the growth of Stock options for hedging and investing


Volatility surfaces for risk and OCC portfolio margin

Calculating the current implied volatility of an option or the entire options chain of listed options is quite straightforward. However the use of these implied volatilities in risk measurements has varying implications.  This article studies how different volatility surface methods can result in very different stress risk calculations for an equity options portfolio. Furthermore is shows the impact on portfolio margin calculations. Several years ago, Customer Portfolio Margin was introduced for equity options positions.   The margin calculations are performed by The Options Clearing Corp (“OCC”) using their TIMS methodology. The methodology is stress test based, where each underlying is shocked by various percentage moves, typically about 8% for indices and 15% for single stocks.  The worst case loss for each underlying is calculated and aggregated using some aggregation logic.

Since it is stress test based the implied volatility surface used to perform the simulations plays an important part in the results.  For many years the OCC followed a methodology of cleansing options closing prices to ensure no arbitrage conditions occurring and they employed certain volatility surface corrections to ensure reasonable stress tests.However in mid 2014 the OCC changed their methodology, and the volatility surfaces are no longer smoothed.  The result of this has been deterioration in the portfolio margin results in some cases.  The margin requirements for many deep out the money options jumped dramatically, simply due to the implied volatility used for them bring exorbitantly high.  Lack of smoothing retains the “kinks” in the volatility surface in the stress calculations – resulting in many cases where further out of the money options have greater margin requirement than strikes closer to the money.  Thus certain long call or long put spreads were actually being assessed as requiring margin, which should never be the case. Such irregularities in the portfolio margin calculations are disturbing as many firms rely on the accuracy and consistency of the calculation from the OCC.

Link to the full research article is below

Volatility surfaces for Risk and OCC margin

What Ails Market risk management – March 2008

I wrote this article back in early 2008, before the financial crisis.  It appeared in Wilmott magazine in April/May 2008.

The article explores some of the shortcomings in the market risk analysis practice at most financial institutions.  It presents several ideas on how to improve the actual process of producing market risk numbers.  It is focused on the practical aspects of market risk managemen


Looking back at this article in the post-2008 world,  it highlighted several issues that really came to light after the crisis – in particular the use of too short a historical lookback for VaR and stress tests, the importance of the outliers in a VaR PL distribution (now use of CVaR is common)  and the need to incorporate more risk factors.

The link to the article is below:

What ails market risk management