Â鶹´«Ã½ÉçÇøÈë¿Ú

Professor of Finance Carol Alexander shares her interests in mathematical and quantitative finance, including crypto assets and non-fungible tokens (NFTs). Carol was ranked 2nd in the top 50 female quantitative analysts on Wall Street in 2022 by think tank Rebellion Research. For the full article please go to our latest Research Review. 

Becoming interested in crypto assets 

My first research was in algebraic number theory and game theory. But after the global stock market crash of 1987, I started to establish consultancies in financial econometrics, risk management and mathematical finance.  

I initially focused on market risk analysis, but gradually moved away from this topic because, in the final analysis, risk managers have virtually no power to shape behaviour in financial markets. Chief Risk Officers are ignored because they have no seat on the board, and financial asset prices (hence also income inequality within and between economies) are increasingly driven by misguided, even corrupt, practices from large US political and financial institutions.  

The 2008 banking crisis projected the world into an unsustainable cycle of dumping our debts on future generations. My disgust that this type of capitalism is being sustained by traditional financial institutions propelled me down the rabbit hole of listening to hours of videos about bitcoin (the crypto) and Bitcoin (the blockchain – a record-keeping technology). That was in 2017, and everything else followed from there.   

We need to teach less traditional finance  

It is a huge challenge to keep abreast of all the innovations in decentralised finance (De-Fi) that are completely reinventing the financial markets of today. We need to teach less traditional finance, because it is dying out in practice, and to introduce more modules about the original and rapid developments being led mainly by young computer scientists, entrepreneurs and other participants in decentralised autonomous organisations.  

Pioneering a method to measure NFT rarity 

NFTs use blockchain technology to verify ownership of a unique digital asset such as your identity, a piece of virtual land or a digital designer watch for your avatar. In virtual and augmented realities, an NFT takes the place of a real-world asset (RWA) such as a painting or – if it is a specific type of NFT called a personal profile picture (PFP) token – a persona.  

The most valuable PFPs are those that are deemed ‘special’ in some way. Buthow do you measure specialness within an NFT collection like Bored Apes or CryptoPunks? My research with , Lecturer in Finance, found that the various metrics currently used to measure the so-called ‘rarity’ of NFTs can give vastly different results. A particular token might be considered extremely rare by one model but very common by another. And all existing rarity models are (almost always) mathematically incorrect. No wonder NFT markets are collapsing: nobody knows the right price because they don’t know how ‘rare’ a token is.  

Measuring rarity is an exciting but highly challenging problem in combinatorial algebra. After putting the problem to Dr Peter Williams, a retired Â鶹´«Ã½ÉçÇøÈë¿Ú mathematician, we are pioneering a universal method to measure NFT rarity correctly.We regard this as important research towards a new economic theory of value for virtual worlds.  

Sharing knowledge and expertise 

I give TV interviews, keynote talks and podcasts, and am frequently quoted in the financial press. contains a regular blog as well as free lecture notes, videos and other learning resources on quantitative finance and financial risk management, which are useful for practitioners and academics as well as students. is designed to offer free access to learning for the younger generation, especially those in countries that struggle to provide resources to students.  

Back to the Business School blog

Image credit .