A family of density expansions for Lévy-type processes

Annals of Applied Probability - Tập 25 Số 1 - 2015
Matthew Lorig1,2, Stefano Pagliarani1,2, Andrea Pascucci1,2
1CMAP ECOLE POLYTECHNIQUE ROUTE DE SACLAY, ROOM 5:30-04 91128 PALAISEAU CEDEX FRANCE
2Princeton University, Università di Padova and Università di Bologna

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Tài liệu tham khảo

Dupire, B. (1994). Pricing with a smile. <i>Risk</i> <b>7</b> 18–20.

Eraker, B. (2004). Do stock prices and volatility jump? Reconciling evidence from spot and option prices. <i>The Journal of Finance</i> <b>59</b> 1367–1404.

Madan, D., Carr, P. and Chang, E. (1998). The variance gamma process and option pricing. <i>European Finance Review</i> <b>2</b> 79–105.

Bielecki, T. R. and Rutkowski, M. (2002). <i>Credit Risk</i>: <i>Modelling</i>, <i>Valuation and Hedging</i>. Springer, Berlin.

Christoffersen, P., Jacobs, K. and Ornthanalai, C. (2009). <i>Exploring Time-Varying Jump Intensities</i>: <i>Evidence from S&amp;P</i>500 <i>Returns and Options</i>. CIRANO, Montreal.

Cox, J. (1975). Notes on option pricing I: Constant elasticity of diffusions. Unpublished draft, Stanford Univ. A revised version of the paper was published by the <i>Journal of Portfolio Management</i> in 1996.

Friedman, A. (1964). <i>Partial Differential Equations of Parabolic Type</i>. Prentice-Hall, Englewood Cliffs, NJ.

Hoh, W. (1998). Pseudo differential operators generating Markov processes. Habilitations-schrift, Universität Bielefeld, Bielefeld.

Jeanblanc, M., Yor, M. and Chesney, M. (2009). <i>Mathematical Methods for Financial Markets. Springer Finance</i>. Springer, London.

Levi, E. E. (1907). Sulle equazioni lineari totalmente ellittiche alle derivate parziali. <i>Rend. Circ. Mat. Palermo</i> (2) <b>24</b> 275–317.

Oksendal, B. and Sulem, A. (2005). <i>Applied Stochastic Control of Jump Diffusions</i>. Springer, Berlin.

Carr, P. and Linetsky, V. (2006). A jump to default extended CEV model: An application of Bessel processes. <i>Finance Stoch.</i> <b>10</b> 303–330.

Linetsky, V. (2006). Pricing equity derivatives subject to bankruptcy. <i>Math. Finance</i> <b>16</b> 255–282.

Mendoza-Arriaga, R., Carr, P. and Linetsky, V. (2010). Time-changed Markov processes in unified credit-equity modeling. <i>Math. Finance</i> <b>20</b> 527–569.

Andersen, L. and Andreasen, J. (2000). Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing. <i>Review of Derivatives Research</i> <b>4</b> 231–262.

Benhamou, E., Gobet, E. and Miri, M. (2009). Smart expansion and fast calibration for jump diffusions. <i>Finance Stoch.</i> <b>13</b> 563–589.

Boyarchenko, S. I. and Levendorskiĭ, S. Z. (2002). <i>Non-Gaussian Merton–Black–Scholes Theory. Advanced Series on Statistical Science &amp; Applied Probability</i> <b>9</b>. World Scientific, River Edge, NJ.

Capponi, A., Pagliarani, S. and Vargiolu, T. (2014). Pricing vulnerable claims in a Lévy driven model. <i>Finance Stoch.</i> <b>18</b> 755–789.

Carr, P. and Madan, D. B. (2010). Local volatility enhanced by a jump to default. <i>SIAM J. Financial Math.</i> <b>1</b> 2–15.

Carr, P., Geman, H., Madan, D. and Yor, M. (2002). The fine structure of asset returns: An empirical investigation. <i>The Journal of Business</i> <b>75</b> 305–333.

Di Francesco, M. and Pascucci, A. (2005). On a class of degenerate parabolic equations of Kolmogorov type. <i>Appl. Math. Res. Express AMRX</i> <b>3</b> 77–116.

Estes, R. H. and Lancaster, E. R. (1972). Some generalized power series inversions. <i>SIAM J. Numer. Anal.</i> <b>9</b> 241–247.

Garroni, M. G. and Menaldi, J.-L. (1992). <i>Green Functions for Second Order Parabolic Integro-Differential Problems. Pitman Research Notes in Mathematics Series</i> <b>275</b>. Longman Scientific &amp; Technical, Harlow; copublished in the United States with Wiley, New York.

Hagan, P. and Woodward, D. (1999). Equivalent Black volatilities. <i>Appl. Math. Finance</i> <b>6</b> 147–157.

Jacquier, A. and Lorig, M. (2013). The smile of certain Lévy-type models. <i>SIAM J. Financial Math.</i> <b>4</b> 804–830.

Linetsky, V. (2007). Spectral methods in derivatives pricing, Chapter 6. In <i>Financial Engineering</i> (J. R. Birge and V. Linetsky, eds.). <i>Handbooks in Operations Research and Management Science</i> <b>15</b> 223–299. Elsevier, Amsterdam.

López, J. L. and Temme, N. M. (2002). Two-point Taylor expansions of analytic functions. <i>Stud. Appl. Math.</i> <b>109</b> 297–311.

Lorig, M., Pagliarani, S. and Pascucci, A. (2013). Pricing approximations and error estimates for local Lévy-type models with default. Preprint. Available at <a href="arXiv:1304.1849">arXiv:1304.1849</a>.

Pagliarani, S. and Pascucci, A. (2012). Analytical approximation of the transition density in a local volatility model. <i>Cent. Eur. J. Math.</i> <b>10</b> 250–270.

Pagliarani, S., Pascucci, A. and Riga, C. (2013). Adjoint expansions in local Lévy models. <i>SIAM J. Financial Math.</i> <b>4</b> 265–296.

Pascucci, A. (2011). <i>PDE and Martingale Methods in Option Pricing. Bocconi &amp; Springer Series</i> <b>2</b>. Springer, Milan.