Welcome to John Crosby's
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I work as a quantitative analyst in the City of London for Grizzly Bear Capital. My main area of expertise is in financial economics and finance. More specifically, I am interested in the carry trade, international risk sharing and the pricing, hedging and risk-management of complex derivatives (across all asset classes) as well as in related fields such as commodities and foreign exchange markets and the measurement of risk and risk premia.

My email address (in anti-spam format) is: johnc2205 xx yahoo yyy com where there are no spaces and where xx = “at” and yyy = “dot”.

A brief profile:

John gained a first class honours degree in Applied Mathematics and Theoretical Physics at Girton College, Cambridge University before going on to study Electrical Engineering at University College, Oxford University. He began his career by trading fx options. He then moved to Monis (formerly London Business School Financial Software) where he researched and wrote their pricing libraries for a very wide range of exotic options as well as co-writing their three-factor Convertible bond model, which captured stochastic equity prices, interest-rates and default risk. He has then worked at First Chicago, Barclays Capital, Lloyds TSB Financial Markets and UBS where he has been responsible for developing advanced models for pricing and risk-managing a wide-range of complex derivatives. John is best known for publishing a number of papers on the subject of pricing commodity derivatives using a multi-factor jump-diffusion model and for being a co-author of the Carr-Crosby fx options model.

John is a visiting Professor of Finance in the Centre for Economic and Financial Studies in the Department of Economics at Glasgow University / Glasgow University Adam Smith Business School.

John is also an invited lecturer on the M.Sc. course in Mathematical Finance in the Mathematical Institute at Oxford University (link here).

Outside of finance, his main interests are sport (he is a keen runner and cyclist and regularly goes to the gym) and history. He is also a reasonably proficient speaker of Russian.

Erdos number = 4 (Paul Erdos -> Endre Csaki -> Marc Yor -> Peter Carr -> Crosby).

Einstein number = 3 (Albert Einstein -> Hans von Engel -> John Allen -> Crosby).

Recent published papers:

A multi-factor jump-diffusion model for commodities” published in Quantitative Finance March 2008 Vol. 8 No. 2 p181-200. Copyright Taylor and Francis. This is a preprint of an article whose final and definitive form has been published in Quantitative Finance 2008 [copyright Taylor & Francis]; Quantitative Finance is available online at informaworldTM; A link to the published version can be found here: www.informaworld.com/smpp/title~content=g790757349~db=all

Commodity options optimised” published in Risk magazine May 2006 p72-77 (courtesy of Incisive Media). Was also reprinted in Energy Risk magazine in May 2007.

Pricing a class of exotic commodity options in a multi-factor jump-diffusion model” published in Quantitative Finance August 2008 Vol. 8 No. 5 p471-483. Copyright Taylor and Francis. This is a preprint of an article whose final and definitive form has been published in Quantitative Finance 2008 [copyright Taylor & Francis]; Quantitative Finance is available online at informaworldTM; A link to the published version can be found here: www.informaworld.com/smpp/title~content=g901732526~db=all

Valuing inflation futures contracts” published in Risk magazine March 2007 p88-90 (courtesy of Incisive Media).

Convexity adjustments in inflation-linked derivatives” published in Risk magazine September 2008 p124-129 (courtesy of Incisive Media). Was also reprinted in Asia Risk magazine in Nov 2008. This is joint work with Dorje Brody and Hongyun Li of Imperial College, London. The preprint version of this paper, which contains more explicit formulae for zero-coupon inflation swaps with delayed payment and period-on-period inflation swaps with delayed payments, can be found “here”.

A class of Levy process models with almost exact calibration to both barrier and vanilla fx options” published in Quantitative Finance 2010 Vol. 10 No. 10 p1115-1136. Copyright Taylor and Francis. This is a preprint of an article whose final and definitive form has been published in Quantitative Finance 2010 [copyright Taylor & Francis]; Quantitative Finance is available online at informaworldTM; A link to the published version can be found here: http://www.informaworld.com/smpp/title~db=all~content=g928681098~tab=toc This is joint work with Peter Carr of the Courant Institute, New York University and Bloomberg.

There is also an on-line supplement to the last paper which contains some addition information about the implementation of the model.

An on-line supplement to "A class of Levy process models with almost exact calibration to both barrier and vanilla fx options"” This is joint work with Alan Ambrose and Peter Carr.

Approximating Levy processes with a view to option pricing” published in International Journal of Theoretical and Applied Finance Feb 2010 Vol. 13 No. 1 p63-91 2010 [copyright World Scientific Publishing Company]. A link to the published version can be found here: www.worldscinet.com/ijtaf/13/1301/S02190249101301.html. This is joint work with Nolwenn Le Saux and Aleksander Mijatovic of Imperial College, London.

There is also a “spreadsheet” which contains in tabular format some of the results contained in sections 4 and 5 of the last paper. This is joint work with Nolwenn Le Saux and Aleksander Mijatovic.

Optimal hedging of variance derivatives” Optimal hedging of variance derivatives; published in The European Journal of Finance 2014 Vol. 20 No. 2 p150-180. A link to the published version can be found here: http://www.tandfonline.com/toc/rejf20/20/2

Exact Pricing of Discretely-Sampled Variance Derivatives (2013). Journal of Business Management and Applied Economics. This is a slightly shortened version of Variance derivatives: Pricing and convergence (see below).

Relation between higher order co-moments and dependence structure of equity portfolios” published in Journal of Empirical Finance 2017 Vol. 40 No. 1 p101-120. This is joint work with Mario Cerrato, Minjoo Kim and Yang Zhao (Glasgow University Adam Smith Business School).

Works in progress:

Why do UK banks securitize” Why do UK banks securitize? (2015). This is joint work with Mario Cerrato, Moorad Choudhry and John Olukuru. Submitted for publication.

The Joint Credit Risk of UK Global-Systemically Important Banks” The Joint Credit Risk of UK Global-Systemically Important Banks (2017). This is joint work with Mario Cerrato, Minjoo Kim and Yang Zhao (Glasgow University Adam Smith Business School). Submitted for publication.

No Good Deals - No Bad Models” No Good Deals - No Bad Models (2013). This is joint work with Nina Boyarchenko (Federal Reserve Bank of New York), Mario Cerrato (Glasgow University Adam Smith Business School) and Stewart Hodges (Cass Business School). BEST PAPER AWARD. This paper won a best paper award at the French Finance Association meeting in Lyon in May 2013 (out of 240 papers actually presented and many hundreds more originally submitted).

Risk sharing in international economies and market incompleteness” Risk sharing in international economies and market incompleteness (2015). This is joint work with Gurdip Bakshi (Smith School of Business, University of Maryland) and Mario Cerrato (Glasgow University Adam Smith Business School). This paper has been accepted for the AMERICAN FINANCE ASSOCIATION meeting in San Francisco, USA, January 2016.

Working papers:

Commodities: A simple multi-factor jump-diffusion model” (2005). This was essentially an earlier (and longer) version of “A multi-factor jump-diffusion model for commodities”. Compared to the latter, this paper contains some additional results and examples but is less “polished”.

Variance derivatives: Pricing and convergence” Variance derivatives: Pricing and convergence (2011). This is joint work with Mark Davis of Imperial College London. A slightly shorter version of this paper, entitled Exact Pricing of Discretely-Sampled Variance Derivatives, is forthcoming in Journal of Business Management and Applied Economics.

Other:

In the summer of 2007, Hongyun Li of Imperial College, London did her M.Sc. dissertation project, which I co-supervised, on the subject of inflation derivatives. Hongyun is now a Ph.D. student in the Department of Mathematics at Imperial College. A copy of her M.Sc. dissertation can be found here: “Convexity adjustments in Inflation-linked derivatives using a multi-factor version of the Jarrow and Yildirim (2003) model” (with permission of Hongyun Li).

In the summer of 2008, Nolwenn Le Saux of Imperial College, London did her M.Sc. dissertation project, which I co-supervised, on the subject of Levy processes. A copy of her M.Sc. dissertation can be found here: “Approximating Levy processes by a hyperexponential jump-diffusion process with a view to option pricing” (with permission of Nolwenn Le Saux).

In the summer of 2009, Komal Shah of Imperial College, London did her M.Sc. dissertation project, which I supervised, on the subject of using saddlepoint approximations for pricing options. A copy of her M.Sc. dissertation can be found here: “Saddlepoint approximations for pricing options” (with permission of Komal Shah).

In the summer of 2010, Blandine Stehle of Imperial College, London did her M.Sc. dissertation project, which I co-supervised, on the subject of methodologies for obtaining faster Greeks from Monte Carlo simulations. A copy of her M.Sc. dissertation can be found here: “Proxy scheme and automatic differentiation: Computing faster Greeks in Monte Carlo simulations” (with permission of Blandine Stehle).

Teaching at Glasgow University:

Lecture on convertible bond arbitrage strategies for the M.Sc. and Ph.D. courses in Finance / Financial Economics in the Department of Economics, Glasgow University / Glasgow University Adam Smith Business School can be found here: “Convertible bond arbitrage strategies

Lecture on caps, floors and 3 m LIBOR futures contracts for the M.Sc. and Ph.D. courses in Finance / Financial Economics in the Department of Economics, Glasgow University / Glasgow University Adam Smith Business School: “Caps, floors and 3 m LIBOR futures contracts

Lecture on variance swaps and volatility derivatives for the M.Sc. and Ph.D. courses in Finance / Financial Economics in the Department of Economics, Glasgow University / Glasgow University Adam Smith Business School: “Variance swaps and volatility derivatives

Teaching at Oxford University:

Lecture on the practicalities of pricing exotic derivatives for Module 3 of the M.Sc. course in Mathematical Finance in the Mathematical Institute, Oxford University can be found here: “Practicalities of pricing exotic derivatives

Lecture on an introduction to jump and Levy processes for Module 4 of the M.Sc. course in Mathematical Finance in the Mathematical Institute, Oxford University can be found here: “Introduction to jump and Levy processes

Below are some (anonymous) comments made by Oxford University students about my lectures:

"I liked these lectures very much".
"Nice lectures, well explained and presented".
"John was a fascinating speaker and I hope he continues to give lectures at Oxford".
"Probably the best lecture so far. Good combination of theory and practice. Well appreciated extra mini-lecture on interplay between risk neutral and real world measures".

Conference presentations:

I have been an invited speaker at a number of university seminars and practitioner conferences around the world. A list of recent (and soon-to-given) talks can be found “here”.

A selection of some of the presentations I have given can be downloaded below.

A multi-factor jump-diffusion model for Commodities” Presentation given at the Centre for Financial Research, Cambridge University, 7th October 2005.

Pricing exotic energy and commodity options in a multi-factor jump-diffusion model” Presentation given at the Risk Magazine Derivatives Summit in Monte Carlo, 6th June 2006.

Pricing Commodity Hybrid Derivatives” Presentation given at the Marcus Evans 2nd Annual Hybrid Products conference in London, 16th February 2007.

Commodity and Commodity Hybrid Derivatives” Presentation given at the Risk South Africa conference in Cape Town, South Africa, 15th March 2007.

Fx and cross-currency options modelling with Levy processes time-changed by other Levy processes” Presentation given at the ICBI Global Derivatives conference in Paris, 23rd May 2007.

A class of Levy process models with almost exact calibration to both barrier and vanilla fx options” Presentation given at the ICBI Global Derivatives conference in Paris, 21st May 2008.

Approximating Levy processes by a hyperexponential jump-diffusion process with a view to option pricing” Presentation given at the Workshop on spectral and cubature methods in Finance and Econometrics in June 2009. “Graphs and figures here

Optimal hedging of variance derivatives” Presentation given at Baruch College, City University of New York in November 2010.

Variance derivatives and estimating realised variance from high-frequency data” Presentation given at Columbia Business School in November 2010.

Links:

I sometimes get asked by people, with M.Sc. or Ph.D. degrees in maths, physics, engineering or related disciplines, what is the best way to become a quant. My best suggestion is as follows:
Go to Mark Joshi’s website (www.markjoshi.com) where he has provided a guide to getting a job as a quant which is both witty and informative.

Disclaimer:

This web-site is my personal web-site. It is not affiliated with or endorsed by institutions for which I work or I have previously worked.