## Contact

- +44 (0)20 7040 8630
- +44 (0)20 7040 8630
- gianluca.fusai.1@city.ac.uk

## Postal address

106 Bunhill Row

London

EC1Y 8TZ

United Kingdom

## About

### Overview

Gianluca is a Reader in Mathematical Finance. He holds a PhD in Finance from Warwick Business School, an MSc in Statistics and Operational Research from the University of Essex and a BSc in Economics from Bocconi University. His research interests focus on Financial Engineering, Numerical Methods for Finance, Portfolio Selection, and Energy Markets. He has published extensively on these topics in Mathematical Finance, Finance and Stochastics, Quantitative Finance, Journal of Banking and Finance, Journal of Computational Finance, Risk, Annals of Applied Probability and the International Journal of Theoretical and Applied Finance. Gianluca has co-authored the textbook ‘Implementing Models in Quantitative Finance’ (Springer Finance) and has worked as a consultant in the public and private sectors. Gianluca also currently holds a position in Financial Mathematics at the Università del Piemonte Orientale.

### Qualifications

- BSc in Economics, Bocconi University, unknown
- MSc in Statistics and Operational Research, University of Essex, United Kingdom
- PhD in Finance, Warwick Business School, United Kingdom

### Languages

French and Italian.

### Expertise

#### Primary topics

- Commodities
- Risk Management
- Mathematical & Quantitative Methods
- Simulation Methods
- Financial Engineering
- Futures & Options
- Asset Pricing
- Mathematical Finance
- Quantitative Finance
- Derivatives
- Fixed-Income Investments
- Investment Theory
- Bond Markets
- Risk Modelling

## Research

Deafault risk premium

Counterparty Credit Risk

Interest rate modelling and pricing of swaptions

Commodity markets and pricing of basket and spread options

### Research topics

#### Credit Risk and Counterparty Risk

Counterparty Credit Risk (CCR) is the risk that the counterparty of an OTC deal will default before the maturity of the contract. The Credit Value Adjustment (CVA) tries to measure the expected loss due to missing the remaining payments

#### Model Risk in Derivative Pricing

How calibration error can affect the reliability of exotic derivative prices

#### Default Risk Premium

How to estimate a corporate structural model, by using data from credit and stock market, and reconstruct the dynamics of the market value of assets and debt, and the default boundary, for a sample of non-financial firms

#### Efficient Pricing of Basket Options

Closed form lower and upper bounds on the prices of basket options for a general class of continuous-time financial models.

#### Efficient Pricing of Swaptions

Efficient pricing of European-style swaptions for a wide class of interest rate models

## Research students

### Anna Maria Gambaro

**Attendance: **Jan 2014 – present, full-time

**Thesis title: **Swaption Pricing in Multifactor Affine Models

**Role: **1st Supervisor

### Angela Loregian

**Attendance: **Jan – Dec 2013, full-time

**Thesis title: **Multivariate Levy Models

**Role: **1st Supervisor

### Raffaele Corvino

**Attendance: **Oct 2012 – present, full-time

**Thesis title: **Credit RiskCredit Risk

**Role: **1st Supervisor

### Ruggero Caldana

**Attendance: **Jan 2009 – Dec 2012, full-time

**Thesis title: **Interconnecting Power Markets and Derivative Pricing

**Role: **1st Supervisor

## Publications

- Fusai, G. and Kyriakou, I. (2016).
**General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options.***Mathematics of Operations Research*,*41*(2), pp. 531–559. doi:10.1287/moor.2015.0739.

### Books (2)

- Roncoroni, A., Fusai, G. and Cummins, M. (2015).
*Handbook of Multi-Commodity Markets and Products Structuring, Trading and Risk Management.*John Wiley & Sons. ISBN 978-0-470-74524-3. - Fusai, G. and Roncoroni, A. (2008).
*Implementing Models in Quantitative Finance: Methods and Cases.*Springer. ISBN 978-3-540-22348-1.

### Chapters (12)

- Gambaro, A.M., Caldana, R. and Fusai, G. (2018).
**Accurate pricing of swaptions via lower bound.***International Series in Operations Research and Management Science*(pp. 183–208). - Ballotta, L., Fusai, G. and Marena, M. (2016).
**Introduction to Default Risk and Counterparty Credit Modelling.**In Kaminski, V. (Ed.),*Managing Energy Price Risk*(pp. 683–754). Riskbook. ISBN 978-1-78272-209-0. - Fusai, G. and Ballotta, L. (2016).
**Introduction to Portfolio Value-at-Risk.**In Kaminski, V. (Ed.),*Managing Energy Price Risk*(pp. 641–682). Riskbook. - Marena, M., Fusai, G. and Longo, G. (2015).
**Asian Options: Payoffs and Pricing Models.**In Roncoroni, A., Fusai, G. and Cummins, M. (Eds.),*Handbook of Multi-Commodity Markets and Products Structuring, Trading and Risk Management*John Wiley & Sons. ISBN 978-0-470-66250-2. - Fusai, G., Marena, M. and Quaglini, C. (2015).
**Pricing Commodity Swaps with Counterparty Credit Risk: The Case of Credit Value Adjustment.**In Roncoroni, A., Fusai, G. and Cummins, M. (Eds.),*Handbook of Multi-Commodity Markets and Products Structuring, Trading and Risk Management*Wiley. ISBN 978-0-470-74524-3. - Ballotta, L. and Fusai, G. (2015).
**A Quick Review of Distributions Relevant in Finance with Matlab Examples.**In Roncoroni, A., Fusai, G. and Cummins, M. (Eds.),*Handbook of Multi-Commodity Markets and Products: Structuring, Trading and Risk Management*(pp. 967–967). John Wiley & Sons. ISBN 978-0-470-74524-3. - Ballotta, L. and Fusai, G. (2015).
**An introduction to stochastic calculus with Matlab examples.**In Roncoroni, A., Fusai, G. and Cummins, M. (Eds.),*Handbook of Multi-Commodity Markets and Products: Structuring, Trading and Risk Management*(pp. 557–557). John Wiley & Sons. ISBN 978-0-470-74524-3. - Fusai, G. (2010).
**Corridor Options.**In Cont, R. (Ed.),*Encyclopedia of Quantitative Finance (4 Volumes)*Wiley. ISBN 978-0-470-05756-8. - Fusai, G. (2010).
**Lookback Options.**In Cont, R. (Ed.),*Encyclopedia of Quantitative Finance, (4 Volumes)*Wiley. ISBN 978-0-470-05756-8. - Fusai, G., Marena, M. and Recchioni, C. (2009).
**Levy Processes and Option Pricing by Recursive Quadrature.**In Hurlington, C.W. (Ed.),*Chapter in book Economic Dynamics: Theory, Games and Empirical Studies*ISBN 978-1-60456-911-7. - Fusai, G. (1998).
**Introduction to Brownian Motion and its Financial Applications.**In Erzegovesi, L. (Ed.),*Financial Engineering: Principles and applications in the debt and currency markets*(pp. 104–116). - Fusai, G. (1993).
**The Term Structure of Interest Rates and Mathematical and Statistical Appendix.**In Erzegovesi, L. (Ed.),*Forward and Futures on bond*Il Sole 24h Libri.

### Conference papers and proceedings (8)

- Ballota, L., Fusai, G., Kyriakou, I., Pouliasis, P. and PAPAPOSTOLOU, N. (2017).
**Non-parametric and semi-parametric modelling of weather variables and cost-revenue analysis of ski resort establishments.***The 3rd Symposium on Quantitative Finance and Risk Analysis (QFRA 2017)*15-16 June, CORFU, GREECE. - Fusai, G., Germano, G. and Marazzina, D. (2012).
**Pricing Credit Derivatives in a Wiener-Hopf Framework.***6th CSDA International Conference on Computational and Financial Econometrics (CFE 2012)*1-3 December, Oviedo, Spain. - Marena, M., Marazzina, D. and Fusai, G. (2008).
**Option pricing, maturity randomization and grid computing.***IPDPS 2008 - 22nd IEEE International Parallel and Distributed Processing Symposium*14-18 April, Miami, Florida, USA. - Fusai, G., Goia, A. and May, C. (2004).
**Functional Regression Tools for Peak Loading Forecasting.***CLADAG 2005 - Conferenza della CLAssification and Data Analysis Group of the Italian Statistical Society*6 Jun 2005 – 8 Jun 2005, Parma. - Fusai, G., Longo, G., Marena, M. and Vulcano, A. (2002).
**Probabilistic Techniques for Contingent Claims Evaluation.***International Conference on Computational Finance*Auronzo di cadore. - Fusai, G. and Tagliani, A. (1999).
**Discretely Sampled Asian Options - Part I: The Model and the Numerical Analysis.***XXIII Amases Conference (The Italian Association of Mathematics Applied to Economic and Social Sciences)*8-11 September, Universita della Calabria. - Fusai, G. (1996).
**Term Structure and Inflation Targeting.***XX AMASES Conference (Italian Association of Mathematics Applied to Economic and Social Sciences))*5-7 September, Urbino. - Fusai, G. (1992).
**An Observation on Two Moment Decision Models and Expected Utility Maximization.***XVI Amases Conference (Associazione per la matematica applicata alle Scienze economiche e Sociali)*10-13 September, Treviso.

### Journal articles (37)

- Phelan, C.E., Marazzina, D., Fusai, G. and Germano, G. (2018).
**Fluctuation identities with continuous monitoring and their application to the pricing of barrier options.***European Journal of Operational Research*,*271*(1), pp. 210–223. doi:10.1016/j.ejor.2018.04.016. - Ballotta, L., Fusai, G. and Marazzina, D. (2018).
**Integrated Structural Approach to Credit Value Adjustment.***European Journal of Operational Research*,*Forthcoming*. doi:10.1016/j.ejor.2018.07.026. - Phelan, C.E., Marazzina, D., Fusai, G. and Germano, G. (2018).
**Hilbert transform, spectral filters and option pricing.***Annals of Operations Research*pp. 1–26. doi:10.1007/s10479-018-2881-4. - Gambaro, A.M., Caldana, R. and Fusai, G. (2017).
**Approximate pricing of swaptions in affine and quadratic models.***Quantitative Finance*,*17*(9), pp. 1325–1345. doi:10.1080/14697688.2017.1292043. - Caldana, R., Fusai, G. and Roncoroni, A. (2017).
**Electricity forward curves with thin granularity: Theory and empirical evidence in the hourly EPEXspot market.***European Journal of Operational Research*,*261*(2), pp. 715–734. doi:10.1016/j.ejor.2017.02.016. - Gambaro, A.M., Casalini, R., Fusai, G. and Ghilarducci, A. (2017).
**Quantitative assessment of common practice procedures in the fair evaluation of embedded options in insurance contracts.***Insurance: Mathematics and Economics*. doi:10.1016/j.insmatheco.2017.10.005. - Fusai, G., Germano, G. and Marazzina, D. (2016).
**Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options.***European Journal of Operational Research*,*251*(1), pp. 124–134. doi:10.1016/j.ejor.2015.11.027. - Caldana, R., Fusai, G., Gnoatto, A. and Grasselli, M. (2016).
**General closed-form basket option pricing bounds.***Quantitative Finance*,*16*(4), pp. 535–554. doi:10.1080/14697688.2015.1073854. - Caldana, R., Cheang, G.H.L., Chiarella, C. and Fusai, G. (2015).
**Correction: Exchange Option under Jump-diffusion Dynamics.***Applied Mathematical Finance*,*22*(1), pp. 99–103. doi:10.1080/1350486X.2014.937564. - Ballotta, L. and Fusai, G. (2015).
**Counterparty credit risk in a multivariate structural model with jumps.***Finance, Revue de l'Association Française de Finance*,*36*(1), pp. 39–74. - Ballotta, L., Fusai, G. and Marazzina, D. (2015).
**Integrated Structural Approach to Counterparty Credit Risk with Dependent Jumps.***SSRN Electronic Journal*. doi:10.2139/ssrn.2706416. - Sesana, D., Marazzina, D. and Fusai, G. (2014).
**Pricing exotic derivatives exploiting structure.***European Journal of Operational Research*,*236*(1), pp. 369–381. doi:10.1016/j.ejor.2013.12.009. - Caldana, R. and Fusai, G. (2013).
**A general closed-form spread option pricing formula.***Journal of Banking and Finance*,*37*(12), pp. 4893–4906. doi:10.1016/j.jbankfin.2013.08.016. - Fusai, G. (2013).
**Asian options with jumps.***Argo Newsletter: New Frontiers in Practical Risk Management,*,*1*(1), pp. 47–56. - Fusai, G. and Potgieter, L. (2013).
**Cutting EdgE Sovereign Credit Risk in a Hidden Markov Regime- Switching Framework. Part 2.***Journal of Financial Transformation*,*38*. - Potgeiter, L. and Fusai, G. (2013).
**Sovereign credit risk in a hidden Markov regime-switching framework. Part 1: methodology.***Journal of Financial Transformation*,*37*, pp. 99–109. - Fusai, G., Marazzina, D., Marena, M. and Ng, M. (2012).
**Z -Transform and preconditioning techniques for option pricing.***Quantitative Finance*,*12*(9), pp. 1381–1394. doi:10.1080/14697688.2010.538074. - Fusai, G., Marazzina, D. and Marena, M. (2011).
**Pricing Discretely Monitored Asian Options by Maturity Randomization.***SIAM Journal on Financial Mathematics*,*2*(1), pp. 383–403. doi:10.1137/09076115X. - Goia, A., May, C. and Fusai, G. (2010).
**Functional clustering and linear regression for peak load forecasting.***International Journal of Forecasting*,*26*(4), pp. 700–711. doi:10.1016/j.ijforecast.2009.05.015. - Fusai, G., Marazzina, D. and Marena, M. (2010).
**Option pricing, maturity randomization and distributed computing.***Parallel Computing*,*36*(7), pp. 403–414. doi:10.1016/j.parco.2010.03.002. - Green, R., Fusai, G. and Abrahams, I.D. (2010).
**The wiener-hopf technique and discretely monitored path-dependent option pricing.***Mathematical Finance*,*20*(2), pp. 259–288. doi:10.1111/j.1467-9965.2010.00397.x. - Fusai, G. and Meucci, A. (2008).
**Pricing discretely monitored Asian options under Lévy processes.***Journal of Banking and Finance*,*32*(10), pp. 2076–2088. doi:10.1016/j.jbankfin.2007.12.027. - Fusai, G., Marena, M. and Roncoroni, A. (2008).
**Analytical pricing of discretely monitored Asian-style options: Theory and application to commodity markets.***Journal of Banking and Finance*,*32*(10), pp. 2033–2045. doi:10.1016/j.jbankfin.2007.12.024. - Fusai, G., Roncoroni, A. and Marena, M. (2008).
**A Note on the Analytical Pricing of Commodity Asian-Style Options under Discrete Monitoring.***Journal of Banking and Finance*,*32*, pp. 2033–2045. - Green, R., Abrahams, I.D. and Fusai, G. (2007).
**Pricing financial claims contingent upon an underlying asset monitored at discrete times.***Journal of Engineering Mathematics*,*59*(4), pp. 373–384. doi:10.1007/s10665-007-9176-0. - Fusai, G. and Recchioni, M.C. (2007).
**Analysis of quadrature methods for pricing discrete barrier options.***Journal of Economic Dynamics and Control*,*31*(3), pp. 826–860. doi:10.1016/j.jedc.2006.03.002. - Atkinson, C. and Fusai, G. (2007).
**Discrete extrema of Brownian motion and pricing of exotic options.***The Journal of Computational Finance*,*10*(3), pp. 1–43. doi:10.21314/JCF.2007.174. - Fusai, G., Abrahams, I.D. and Sgarra, C. (2006).
**An exact analytical solution for discrete barrier options.***Finance and Stochastics*,*10*(1), pp. 1–26. doi:10.1007/s00780-005-0170-y. - Fusai, G. (2006).
**Grid Based Full Portfolio Revaluation for VaR Computation.***Proceedings of Science 1st International Workshop on Grid Technology for Financial Modeling and Simulations*. - Fusai, G. (2004).
**Pricing Asian options via Fourier and Laplace Transforms.***Journal of Computational Finance*,*7*(3). - Fusai, G. and Meucci, A. (2003).
**Assessing Views.***Risk Magazine*,*13*(3). - D’Amico, M., Fusai, G. and Tagliani, A. (2002).
**Valuation of exotic options using moments.***Operational Research*,*2*(2), pp. 157–186. doi:10.1007/BF02936326. - Fusai, G. and Tagliani, A. (2002).
**An Accurate Valuation of Asian Option using Moments.***International Journal of Theoretical and Applied Finance*,*5*(2), pp. 147–69. - Fusai, G., Tagliani, A. and Sanfelici, S. (2002).
**Practical Problems in the Numerical Solution of PDE's in Finance.***Rendiconti per gli Studi Economici Quantitativi*,*2001*, pp. 105–132. - Fusai, G. and Luciano, E. (2001).
**Dynamic value at risk under optimal and suboptimal portfolio policies.***European Journal of Operational Research*,*135*(2), pp. 249–269. doi:10.1016/S0377-2217(01)00039-X. - Fusai, G. and Tagliani, A. (2001).
**Pricing of Occupation Time Derivatives: Continuous and Discrete Monitoring.***Journal of Computational Finance*,*5*(1), pp. 1–37. - Fusai, G. (2000).
**Corridor options and arc-sine law.***Annals of Applied Probability*,*10*(2), pp. 634–663. doi:10.1214/aoap/1019487359.

### Report

- Fusai, G., Amerio, E. and Vulcano, A. (2003).
**Pricing of Implied Volatility Derivatives.**University of Warwick.

### Theses/dissertations (3)

- Fusai, G.
**GARCH Models and Volatility Forecast in the Option Market.**(Master's Thesis) - Fusai, G.
**Inflation Targeting and Term Structure of Interest Rates.**(PhD Thesis) - Fusai, G.
**Applications of Laplace Transform for Evaluating Occupation Time Options and Other Derivatives.**(PhD Thesis)

### Working papers (5)

- Ballotta, L. and Fusai, G. (2018).
**Tools from Stochastic Analysis for Mathematical Finance: A Gentle Introduction.** - Alizadeh, A.H., Adland, R. and Fusai, G. (2017).
**A New Ship Valuation Model based on Spread Option Pricing Approach.** - Ballotta, L. and Fusai, G. (2017).
**A Gentle Introduction to Value at Risk.** - Ballotta, L., Fusai, G. and Marena, M. (2016).
**A Gentle Introduction to Default Risk and Counterparty Credit Modelling.** - Loregian, A., Ballotta, L. and Fusai, G. (2015).
**Multivariate LLvy Models by Linear Combination: Estimation.**

### Other (8)

- Fusai, G. and Santoli, M. (2011).
**Bounds for pricing Asian options under non-Gaussian dynamics.** - Fusai, G. (2011).
**Estimation Risk and Value at Risk Computation.** - Fusai, G., Germano, G. and Marazzina, D. (2011).
**Fast option methods via Wiener-Hopf technique.** - Fusai, G., Billi, M. and Bedendo, M. (2011).
**Implicit costs in the Italian retail market of structured bonds.** - Fusai, G. and Zanotti, G. (2011).
**New Efficient Frontier: can structured products really improve the risk return profile?** - Fusai, G., Sesana, D. and Marazzina, D. (2011).
**Pricing Exotic Derivatives under CEV process Exploiting Structure.** - Fusai, G., Atkinson, C. and Marena, M. (2011).
**Pricing Hybrid Products via Fourier Transforms.** - Fusai, G., Longo, G. and Marina, M. (2006).
**Value at Risk: A Comparison between Delta-Gramma Approximation and MC Simulation using a Grid Architecture.**

## Professional activities

### Consultancy

**BNP Paribas Calyon Italia**(Private Sector) (Jan 2010 – Dec 2012)

Construction of a complete engine for calibration, simulation and pricing of complex hybrid financial products.

### Editorial activity (7)

**Finance Research Letters**, Referee, 2015 – present.**European Journal of Operations Research**, Referee, 2014 – present.**Journal of Banking and Finance**, Referee, 2013 – present.**Journal of Futures Markets**, Referee, 2012 – present.**Operations Research**, Referee, 2011 – present.**Quantitative Finance**, Referee, 2011 – present.**Mathematical Finance**, Referee, 2008 – present.

### Events/conferences (19)

**Bachelier World Conference, July 2016, New York.**New York (2016).

Paper: General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options

Author: G. Fusai

Co-authors: I. Kyriaokou**Energy and Commodity World Conference.**(Conference) Paris (2016).

Paper: A Structural Model for CVA computation with wrong way risk

Author: L. Ballotta

Co-authors: Fusai, G.; Marazzina, D.- (Seminar) Banca IMI, Milan (2015). Invited speaker.

Paper: A Structural Model for CVA computation with wrong way risk

Author: Fusai G. (invited)

Co-authors: L. Ballotta and D. Marazzina - (Seminar) Nomura Centre for Mathematical Finance, Department of Mathematics, Oxford University (2015). Invited speaker.

Paper: A Structural Model for CVA computation with wrong way risk

Author: Fusai G.

Co-authors: L. Ballotta and D. Marazzina **Quant 12 Workshop, 26-27th November 2015.**(Conference) EMLYON Business School, Lyon, France (2015). Invited speaker.

Paper: A Structural Model for CVA computation with wrong way risk

Author: Fusai G.

Co-authors: L. Ballotta and D. Marazzina**2014 Conference - 8th Conference in Actuarial Science & Finance.**(Conference) Samos, Greece (2014).

Paper: General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options

Author: Kyriakou I.

Co-authors: Fusai G.**2014 Conference - 2014 Conference - Bachelier Finance Society, 8th World Congress.**(Conference) Brussels, Belgium (2014).

Paper: Pricing Basket Options in non-Gaussian models

Author: Caldana R.

Co-authors: Gnoatto, A. , Fusai G., Grasselli, M.**Summer School on Risk Management.**(Conference) Rome (2014). Invited speaker.

Paper: Counterparty Credit Risk with Jumps

Author: Fusai G.

Co-authors: Laura Ballotta**2014 Conference - Financial Engineering and Banking Society (FEBS) Conference.**(Conference) University of Surrey, UK (2014).

Paper: Multivariate L evy models by linear combination: estimation

Author: Loregian A.

Co-authors: Fusai G., Ballotta L.**2014 Conference - Bachelier Finance Society, 8th World Congress.**(Conference) Brussels, Belgium (2014).

Paper: Counterparty credit risk in a multivariate structural model with jumps

Author: Ballotta L.

Co-authors: Fusai G.**Financial Engineering Workshops.**(Conference) Cass Business School (2013). Organising Committee.- (Seminar) Prometeia, Bologna (2013). Invited speaker.

Paper: A Structural model for CVA computation with wrong way

Author: Fusai G

Co-authors: Laura Ballotta **Workshop in honor of Erio Castagnoli's 70th birthday.**(Workshop) Universita L. Bocconi, Milano (2013). Invited speaker.

Paper: Estimation risk and option pricing: Why to use the Black-Scholes formula

Author: Fusai G.

Co-authors: Marco Materazzi**2013 Conference - 3rd International Conference of the Financial Engineering and Banking Society (FEBS).**(Conference) Paris, France (2013).

Paper: Counterparty credit risk in a multivariate structural model with jumps

Author: Ballotta L.

Co-authors: Fusai G.**2013 Conference - 30th International Conference of the French Finance Association (AFFI).**(Conference) Lyon, France (2013).

Paper: Counterparty credit risk in a multivariate structural model with jumps

Author: Ballotta L.

Co-authors: Fusai G.**Counterparty credit risk and credit valuation adjustment: Quantitative and regulatory framework.**(Conference) Cass Business School (2013). Chair and Organising Committee.**XIV Workshop on Quantitative Finance.**(Conference) Rimini (2013). Organising Committee.**6th CSDA International Conference on Computational and Financial Econometrics (CFE 2012).**(Conference) Oviedo, Spain (2012).

Paper: Pricing credit derivatives in a Wiener-Hopf framework

Author: Fusai G

Co-authors: D. Marazzina and G. Germano- (Conference) Marburg University, Germany (2011). Invited speaker.

Paper: New Efficient Frontier: can structured products really improve the risk return profile?.

Author: Fusai G.

Co-authors: G. Zanotti

### Media appearance

**Cass Business School's Fusai on commodity risk return-trade offs.**(2012)*www.automatetrader.net*(website).