Remembering Marco

Lixin Wu: “We should celebrate his life. A life with numerous contributions to quantitative finance and beyond and a life that enriched numerous others’, including mine.”

I was introduced to Marco in 1997, not long after he rose as a figure in quantitative finance. A year later, I came to the Courant Institute at NYU for sabbatical leave, working primarily with Marco as a visiting scholar. We produced two joint papers during my stay there and remained friends ever since.

I stumbled into quantitative finance (QF) around 1996, and soon took on the challenge of consulting an investment bank in Hong Kong on the pricing and risk management of convertible bonds. The conversion right has been modeled as a Parisian option, a soft-barrier option which is either knocked in or knocked out when the excursion time of an asset price or an index beyond a certain level exceeds a specified limit. The pricing of Parisian options had been an open challenge for a while, and it was cracked around 1996 by Marc Yor, a top French probabilist of the time. As a person trained in applied partial differential equations (PDE), I found the language in Yor’s solution to be hardly comprehensible, so I turned to Marco for help. Marco seemed to be well aware of the issue, and he threw me one sentence that led to an alternative solution: “The soft-barrier feature can be priced as a knocked-in option.” Based on that understanding, we developed a PDE model and lattice-tree methodology to price general Parisian options as well as convertible bonds. After we finished this piece of work, Marco said, “I will not work on exotic options again,” which has turned out to be the case. I gathered that exotic options were not challenging or interesting enough to him.

As someone, not a hundred percent devoted to academics, I was trying to find a quant job in the banking industry. My timing, however, was poor: in late 1998, there was global financial distress triggered by the Ruble crisis, which caused severe losses to many investment banks, so they became eager to fire rather than hire. When Marco learned of my intention, he poured cold water on it. “You are a thinker; why do you want to go there?” he said. Having no other choice, I buried my head in work on a credit contagion model, which describes how the deterioration of the credit worthiness of a bigger economy drags down that of a smaller economy. Such credit contagion occurred during the Ruble crisis in the Brady bond markets, the sovereign debt market of South America where Marco came from. Proudly, we presented a new model to the credit markets. Yet our contributions are less known as most citations have gone to Jarrow and Yu (2001), a paper with a similar model published in the same year as ours. Nonetheless, it was my first experience working with market data, during which I learned a lot from Marco.

Trained as an applied mathematician with perhaps the strongest background in applied probability, Marco had been very productive in several areas of applied mathematics. Quantitative finance only appeared to be an even more friendly territory that allowed him to show his muscle. His growing reputation enabled him to invite a slew of academic and industrial speakers, some with big names, to his weekly seminar at NYU. From time to time, I witnessed intense intellectual exchanges between him and his guests or colleagues and his relentless efforts to push the boundary forward. Yet the other side of Marco was a warm-hearted and candid personality, such that academic juniors like me were just as comfortable to learn and perform. Benefitting from such an enriching environment, I was able to uplift my skills and knowledge to a higher level in a short time. I accomplished more and got tenured soon after my sabbatical leave.

I think of Marco as a maverick in the QF community. He was regarded as a bigshot by the community; however, he had kept one arm’s distance from the Bachelier Finance Society, which is likely the largest association of QF people. He was also not keen to publish in top-tier journals in either finance or mathematical finance. He stood out as a practitioner and an informed investor in the QF community. He had run his own hedge fund with employees, a sign of investment success. Almost all his research was motivated by challenges in the financial markets, the derivatives sector in particular. The spectrum of his research outputs was amazingly broad, including, but not limited to, uncertain volatility models for option pricing, minimum-entropy calibration of pricing models, weighted Monte-Carlo methods for derivatives pricing, credit risk modeling, and credit derivatives pricing, volatility smiles, high-frequency trading, variance and volatility derivatives, leveraged ETF pricing and big data finance. His dynamic model for hard-to-borrow stocks, a topic in market microstructure, earned him the Quant of the Year in 2010. In addition, he was one of the very few academics who was frequently interviewed and sought out for expert opinions on issues of common interest, like central clearing, market transparency, the Dodd-Frank act, tax evasion, QF education, etc. In his prime, he was undoubtedly one of the top guns in quantitative finance.

I am saddened by Marco’s early departure, but I feel more strongly that we should celebrate his life. A life with numerous contributions to quantitative finance and beyond and a life that enriched numerous others’, including mine.

May Marco rest in peace


Avellaneda, M., & Wu, L. (1999). Pricing Parisian-style options with a lattice method. International Journal of Theoretical and Applied Finance.

Avellaneda, M., & Wu, L. (2001). Credit contagion: Price cross-country risk in Brady debt markets. International Journal of Theoretical and Applied Finance.