Appeared in VitalLaw - Wolters Kluwer - October 4, 2024

Appeared in VitalLaw - Wolters Kluwer - February 20, 2024

Appeared in Law360 - August 17, 2021

Appeared Pratt’s Journal of Bankruptcy Law - February/March 2021

Appeared in Wolters Kluwer – July 31, 2020

Appeared in Law360 – Jan 2019 – was presented at the Chicago Bar Association in April 2019

bitcoin.com – April 2018

Appeared in Law360

With Heng Sun, Guowen Han and Jiping Guo (Risk Magazine, March 2009) 

Pdf Version

With John Hiatt, published in Swiss Derivatives Review July 2007

With Kumar Kakumanu and Moorad Choudhry, published in Derivatives Use, Trading and Regulation (DUTR Volume 11, Number 1) June 2005

Published in StructuredNotesOnLine.com, December 2004

pre-conference summit at the ICBI Global Derivatives and Risk Management Conference, 2003 - with multiple authors. Published in Quantitative Finance, August 2003 

Many financial institutions are profoundly interested in modeling the credit risk of various counter-parties. Traditional models rely on the stock price and stock volatility combined with  knowledge of the company's financial structure. In this paper, we show that using just two option implied volatility numbers even without knowledge of the company's financial structure   gives better results. Thus the paper connects two seemingly disjoint markets: the equity options market and the credit derivatives market. Published in Journal of Credit Risk, Volume 1, Number 1,  Winter 2004/2005

Analysis of hedge funds on a historical basis is often misleading. Past returns look very high and the risks very small. There are risks in these funds that historical analysis can not account for. Many funds impose a "lock up". The investor can not withdraw capital from the fund for a pre-specified time (perhaps a year). There is a "liquidity premium" that must be accounted for. In this paper, we show how to calculate the liquidity premium.
Has been published in Risk Magazine , April 2003

The process of “pinning” is frequently mentioned in stock traders' lore, but its effect upon the price of an option is not well understood. Some traders believe that on days when equity options expire (typically the third Friday of a given month), many stocks seem to close near a multiple of $5. In this paper, we give statistical evidence for the existence of pinning and develop an option-pricing model that incorporates this phenomenon. We conclude that, near expiration, there is a discrepancy between the Black-Scholes price of an option and the price of an option whose underlying stock has a higher than normal probability of being pinned. We analyze the various cases (e.g., when the pinned price is cheaper than the Black-Scholes price) and provide intuition for the price discrepancies.

Published in Risk Magazine , December 2001

When valuing basket options of foreign currency, a major question is estimating the correlation matrix. In this paper, we shall use entropy as a means of choosing the correlation matrix which a. Matches the implied volatility of the basket option, b. Resembles the historical correlation matrix and c. Makes as few other assumptions as possible.

Published in Derivatives Use Trading and Regulation , Vol. 7, No. 3, (2001)

Japanese reset convertibles have received some notoriety after the well publicized losses at the Union Bank of Switzerland  (see for example “UBS to upgrade its derivatives losses to $421m”, Financial Times, January 31, 1998).

In this paper, we discuss several advanced issues relating to Japanese “style” convertible bonds. The convertible bonds, issued by several Japanese and Taiwanese issuers (among others) have some unique features.

This paper will also mention two more interesting items relating to non-reset convertibles:

• The duration of a convertible bond.
• How correlation impacts convertible securities

In this paper, we describe the Weather Derivatives market., weather options, how to price and hedge them and more.

Using numerical integration to value these options.  (Published in Risk Magazine April 1993)

A primer on contingent premium options.

Using multi-factor trees to price convertible bonds.

Interview with the El Pais newspaper about Exotic Options.

How parallel computation was used to speed up some financial algorithms  (Risk Magazine April 1992)

Double barrier options and the "box trade"

Interview with the Wisconsin Sentinel newspaper

Interview with Bill Falloon about the Compound Options issued by Banker's Trust Canada  (Risk Magazine, July 1994)

Analysis of Structured Notes  : (Risk Magazine Cover Story, December  1994)