# Recent Publications

**A multiple-curve Lévy forward rate model in a two-price economy.**

Preprint (2016) (with Ch. Gerhart) (pdf)**A Lévy-driven asset price model with bankruptcy and liquidity risk.**Preprint (2016) (with P. Bäurer) (pdf)**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