# Recent Publications

**A multiple curve Lévy swap market model.**Preprint (2020) (with Chr. Gerhart and E. Lütkebohmert) (pdf)**Variable annuities in a Lévy-based hybrid model with surrender risk.**Quantitative Finance 20 (5) (2020), 867–886 (with L. Ballotta, Th. Schmidt and R. Zeineddine) (pdf)

The Version of Record of this manuscript has been published and is available in Quantitative Finance 20 (5) (2020) (doi: 10.1080/14697688.2019.1687929)**Multiple curve Lévy forward price model allowing for negative interest rates.**Mathematical Finance 30 (1) (2020), 167–195 (with Chr. Gerhart and Z. Grbac) (pdf)**Hybrid Lévy models: Design and computational aspects.**Applied Mathematical Finance 25 (5–6) (2018), 533–556 (with M. Rudmann) (pdf)

The Version of Record of this manuscript has been published and is available in

Applied Mathematical Finance 25 (5-6) (2018) http://www.tandfonline.com/

(doi: 10.1080/1350486X.2018.1536523)**A multiple-curve Lévy forward rate model in a two-price economy.**Quantitative Finance 18 (4) (2018), 537–561 (with Ch. Gerhart) (pdf)

The Version of Record of this manuscript has been published and is available in Quantitative Finance 18 (4) (2018) (doi:10.1080/14697688.2017.1384558)**A Lévy-driven asset price model with bankruptcy and liquidity risk.**In From Statistics to Mathematical Finance. D. Ferger, W. G. Manteiga, T. Schmidt and J.-L. Wang (eds.), Springer (2017), pp. 387–416 (with P. Bäurer) (pdf, doi:10.1007/978-3-319-50986-0 )**Valuation in illiquid markets.**Procedia Economics and Finance 29 (2015), 135–143 (pdf)**Option pricing and sensitivity analysis in the Lévy forward process model.**In Innovations in Derivatives Markets, K. Glau, Z. Grbac, M. Scherer, and R. Zagst (eds.), Springer (2016), pp. 285–313 (with M'hamed Eddahbi and Sidi Mohamed Lalaoui Ben Cherif) (pdf)**Computation of Greeks in LIBOR models driven by time-inhomogeneous Lévy processes.**Applied Mathematical Finance 23 (3) (2016), 236–260 (with M'hamed Eddahbi and Sidi Mohamed Lalaoui Ben Cherif) (doi:10.1080/1350486X.2016.1243013)**Portfolio theory for squared returns correlated across time.**Probability, Uncertainty and Quantitative Risk 1 (1), 1–36 (2016) (with D. B. Madan) (pdf, SSRN, doi:10.1186/s41546-016-0001-4)

The original publication is available at Springer link.**Bid and ask prices as non-linear continuous time G-expectations based on distortions.**Mathematics and Financial Economics 8 (3) (2014), 265–289 (with D. B. Madan, M. Pistorius and M. Yor) (pdf)**Modeling risk weighted assets and the risk sensitivity of related capital requirements.**The Journal of Risk 16 (2) (2013), 3–23 (with D. B. Madan and W. Schoutens) (pdf)**A simple stochastic rate model for rate equity hybrid products.**Applied Mathematical Finance 20 (5–6) (2013), 461–488 (with D. B. Madan, M. Pistorius and M. Yor) (pdf)**Two price economies in continuous time.**Annals of Finance 10 (2014), 71–100 (with D. Madan, M. Pistorius, W. Schoutens and M. Yor) (pdf)**Discrete tenor models for credit risky portfolios driven by time-inhomogeneous Lévy processes.**SIAM Journal on Financial Mathematics 4 (1) (2013), 616–649 (with Z. Grbac and T. Schmidt) (pdf)**Fourier based valuation methods in mathematical finance.**In Quantitative Energy Finance, F. Benth, V. Kholodnyi, and P. Laurence (eds.), Springer (2013), pp. 85–114 (pdf)**Dealing with complex realities in financial modeling.**Current Science 103 (6) (2012), 647–649 (with D. B. Madan) (pdf)**Variational solutions of the pricing PIDEs for European options in Lévy models.**Applied Mathematical Finance 21 (5) (2014), 417–450 (with K. Glau) (pdf)**Capital requirements, the option surface, market, credit and liquidity risk.**Preprint, University of Freiburg (2011) (with D. B. Madan and W. Schoutens) (pdf)**Pricing to acceptability: with applications to valuation of one's own credit risk.**The Journal of Risk 15 (1) (2012), 91–120 (with T. Gehrig and D. B. Madan) (pdf)**On correlating Lévy processes.**The Journal of Risk 13 (1) (2010), 3–16 (with D. B. Madan) (pdf)**The distribution of returns at longer horizons.**In Recent Advances in Financial Engineering 2010, M. Kijima, C. Hara, Y. Muromachi, H. Nakaoka, K. Nishide (eds.), World Scientific (2011), pp 1–18 (with D. B. Madan)**Correlations in Lévy interest rate models.**Quantitative Finance 11 (9) (2011), 1315–1327 (with M. Beinhofer, A. Janssen and M. Polley) doi:10.1080/14697688.2010.542299**Rating based Lévy LIBOR model.**Mathematical Finance 23 (4) (2013), 591-626 (with Z. Grbac) (pdf)**Unbounded liabilities, capital reserve requirements and the taxpayer put option.**Quantitative Finance 12 (5) (2012), 709–724 (with D. B. Madan) (pdf)**Analyticity of the Wiener–Hopf factors and valuation of exotic options in Lévy models.**In Advanced Mathematical Methods for Finance, G. Di Nunno and B. Øksendal (eds.), Springer (2011), pp 223–245 (with K. Glau and A. Papapantoleon) (pdf)**Mathematik und die Finanzkrise.**Spektrum der Wissenschaft 12/09 (2009), 92–100**Maximally acceptable portfolios.**In Inspired by Finance. The Musiela Festschrift, Y. Kabanov, M. Rutkowski, T. Zariphopoulou (eds.), Springer Verlag (2014), pp 257–271 (with. D. B. Madan) (pdf)**Generalized hyperbolic models.**In Encyclopedia of Quantitative Finance, R. Cont (ed.), John Wiley & Sons Ltd. (2010), pp 833–836 (pdf)

The definitive version is available at John Wiley & Sons, Inc.**Jump processes.**In Encyclopedia of Quantitative Finance, R. Cont (ed.), John Wiley & Sons Ltd. (2010), pp 833–836 (pdf)

The definitive version is available at John Wiley & Sons, Inc..**Hedge fund performance: sources and measures.**International Journal of Theoretical and Applied Finance 12 (3) (2009), 267–282 (with D. B. Madan) (pdf)**On pricing risky loans and collateralized fund obligations.**The Journal of Credit Risk 5 (3) (2009), 1–18 (with H. Geman and D. B. Madan) (pdf)**Short positions, rally fears and option markets.**Applied Mathematical Finance 17 (1-2) (2010), 83-98 (with D. B. Madan) (pdf)**Analysis of Fourier transform valuation formulas and applications.**Applied Mathematical Finance 17(3) (2010), 211–240 (with K. Glau and A. Papapantoleon) (pdf)

Author Posting. (c) 'Taylor & Francis', 2009. This is the author's version of the work. It is posted here by permission of 'Taylor & Francis' for personal use, not for redistribution. The definitive version was published in Applied Mathematical Finance, January 2010. doi:10.1080/13504860903326669**Esscher transform and the duality principle for multidimensional semimartingales.**The Annals of Applied Probability 19 (2009), 1944–1971 (with A. Papapantoleon and A. N. Shiryaev) (pdf)**Advanced credit portfolio modeling and CDO pricing.**In Mathematics – Key Technology for the Future, W. Jäger and H.-J. Krebs (eds.), Springer (2008), pp 253–280 (with R. Frey, E. A. von Hammerstein) (pdf)**Jump-type Lévy processes.**In Handbook of Financial Time Series, T. G. Andersen, R. A. Davis, J.-P. Kreiß, T. Mikosch, Springer Verlag (2009), pp 439–455 (pdf)**Mathematics in financial risk management.**Jahresbericht der Deutschen Mathematiker Vereinigung 109 (2007), pp. 165–193 (with R. Frey, M. Kalkbrener, L. Overbeck) (pdf)**Sato processes and the valuation of structured products.**Quantitative Finance 9 (1) (2009), 27–42 (with D. B. Madan) (pdf)**Calibration of Lévy term structure models.**In Advances in Mathematical Finance: In Honor of D. B. Madan, M. Fu, R. A. Jarrow, J.-Y. Yen, and R. J. Elliott (eds.) Birkhäuser (2007), pp. 147–172 (joint with W. Kluge) (pdf)**On the duality principle in option pricing: semimartingale setting.**Finance and Stochastics 12 (2) (2008), 265–292 (with A. Papapantoleon, A. N. Shiryaev) (pdf)

The original publication is available at Springer link.**The Lévy swap market model.**Applied Mathematical Finance 14 (2) (2007) 171–196 (with J. Liinev) (pdf)

This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. The definitive version was published in Applied Mathematical Finance, Volume 14 Issue 2, May 2007. doi:10.1080/13504860600724950.**The Lévy Libor model with default risk.**Journal of Credit Risk 2 (2) (2006) 3–42 (with W. Kluge, P. J. Schönbucher) (pdf)**A cross-currency Lévy market model.**Quantitative Finance 6 (2006) 465–480 (with N. Koval) (pdf)

This is an electronic version of an article published in Quantitative Finance Vol 6 No. 6 (2006) 465–480. Quantitative Finance is available online at: Taylor & Francis Online doi:10.1080/14697680600818791.**Symmetries in Lévy term structure models.**International Journal of Theoretical and Applied Finance 9 (6) (2006) 967–986 (with W. Kluge and A. Papapantoleon (pdf)**Symmetries and pricing of exotic options in Lévy models.**In Exotic option pricing and advanced Lévy models, A. Kyprianou, W. Schoutens, P. Wilmott (eds.), Wiley (2005), pp. 99–128 (with A. Papapantoleon) (pdf)**Valuation of floating range notes in Lévy term structure models.**Mathematical Finance 16 (2006) 237–254 (with W. Kluge) (pdf)**Exact pricing formulae for caps and swaptions in a Lévy term structure model.**Journal of Computational Finance 9 (2) (2006) 99–125 (with W. Kluge)**Equivalence of floating and fixed strike Asian and lookback options.**Stochastic Processes and Their Applications 115 (2005) 31–40 (with A. Papapantoleon) (pdf)**The Lévy Libor model.**Finance and Stochastics 9 (2005) 327–348 (with F. Özkan)**Lévy term structure models: no-arbitrage and completeness.**Finance and Stochastics 9 (2005) 67–88 (with J. Jacod, S. Raible)**Generalized hyperbolic and inverse Gaussian distributions: limiting cases and approximation of processes.**In Seminar on Stochastic Analysis, Random Fields and Applications IV, Progress in Probability 58, R.C. Dalang, M. Dozzi, F. Russo (eds.), Birkhäuser Verlag (2004) 221–264 (with E.A. von Hammerstein)**Both sides of the fence: a statistical and regulatory view of electricity risk.**Energy & Power Risk Management 8, no. 6 (2003), 34–38 (with G. Stahl) © 2003 Incisive Media Plc.**Time consistency of Lévy models.**Quantitative Finance 3 (1) (2003) 40–50 (with F. Özkan) (pdf)

This is an electronic version of an article published in Quantitative Finance 3 (1) (2003) 40–50. Quantitative Finance is available online at: Taylor & Francis Online doi:10.1088/1469-7688/3/1/304**Risk management based on stochastic volatility.**Journal of Risk 5, no. 2 (2003) 19–44 (with J. Kallsen, J. Kristen)**The defaultable Lévy term structure: ratings and restructuring.**Mathematical Finance 13 (2003) 277–300 (with F. Özkan)

**The generalized hyperbolic model: financial derivatives and risk measures.**In Mathematical Finance-Bachelier Congress 2000, H. Geman, D. Madan, S. Pliska, T. Vorst (eds.), Springer Verlag (2002) 245–267 (with K. Prause)**Some analytic facts on the generalized hyperbolic model.**In Proceedings of the 3rd European Meeting of Mathematics, Progress in Mathematics 202, C. Casacuberta, et al. (eds.), Birkhäuser Verlag (2001) 367–378 (with S. Raible)**Recent advances in more realistic risk management: the hyperbolic model.**In Mastering Risk 2, C. Alexander (ed.), Prentice Hall-Financial Times (2001), 56–72**Application of generalized hyperbolic Lévy motions to finance.**In Lévy Processes: Theory and Applications, O.E. Barndorff-Nielsen, T. Mikosch, and S. Resnick (eds.), Birkhäuser Verlag (2001) 319–337**A new framework for the evaluation of market and credit risk.**In Datamining und Computational Finance, G. Bol, G. Nakhaeizadeh, K.-H. Vollmer (eds.), Physica Verlag, Wirtschaftswissenschaftliche Beiträge Bd. 174 (2000) 51–67 (with J. Breckling, P. Kokic)**A tailored suit for risk management: the hyperbolic model.**In Measuring risk in complex stochastic systems, J.Franke, W. Härdle, and G. Stahl (eds.), Lecture Notes in Statistics 147, Springer (2000) 189–202 (with J. Breckling, P. Kokic)**Term structure models driven by general Lévy processes.**Mathematical Finance 9 (1999) 31–54 (with S. Raible)**Grundideen moderner Finanzmathematik.**Mitteilungen der DMV 3/98 (1998) 10–20**The true nature of market risk.**Submitted to Net Exposure (1998) (with U. Keller)**New insights into smile, mispricing and value at risk: the hyperbolic model.**Journal of Business 71 (1998) 371–405 (with U. Keller, K. Prause)**On the range of options prices.**Finance and Stochastics 1 (1997) 131–140 (with J. Jacod)**Hyperbolic distributions in finance.**Bernoulli 1 (1995) 281–299 (with U. Keller)**On modelling questions in security valuation.**Mathematical Finance 2 (1992) 17–32