Vai ai contenuti. | Spostati sulla navigazione | Spostati sulla ricerca | Vai al menu | Contatti | Accessibilità

| Crea un account

Pagliarani, Stefano (2014) Portfolio optimization and option pricing under defaultable Lévy driven models. [Tesi di dottorato]

Full text disponibile come:

[img]
Anteprima
Documento PDF
2799Kb

Abstract (inglese)

In this thesis we study some portfolio optimization and option pricing problems in market models where the dynamics of one or more risky assets are driven by Lévy processes, and it is divided in four independent parts.
In the first part we study the portfolio optimization problem, for the logarithmic terminal utility and the logarithmic consumption utility, in a multi-defaultable Lévy driven model.
In the second part we introduce a novel technique to price European defaultable claims when the pre-defaultable dynamics of the underlying asset follows an exponential Lévy process.
In the third part we develop a novel methodology to obtain analytical expansions for the prices of European derivatives, under stochastic and/or local volatility models driven by Lévy processes, by analytically expanding the integro-differential operator associated to the pricing problem.
In the fourth part we present an extension of the latter technique which allows for obtaining analytical expansion in option pricing when dealing with path-dependent Asian-style derivatives.

Abstract (italiano)

In questa tesi studiamo alcuni problemi di portfolio optimization e di option pricing in modelli di mercato dove le dinamiche di uno o più titoli rischiosi sono guidate da processi di Lévy. La tesi é divisa in quattro parti indipendenti.
Nella prima parte studiamo il problema di ottimizzare un portafoglio, inteso come massimizzazione di un’utilità logaritmica della ricchezza finale e di un’utilità logaritmica del consumo, in un modello guidato da processi di Lévy e in presenza di fallimenti simultanei.
Nella seconda parte introduciamo una nuova tecnica per il prezzaggio di opzioni europee soggette a fallimento, i cui titoli sottostanti seguono dinamiche che prima del fallimento sono rappresentate da processi di Lévy esponenziali.
Nella terza parte sviluppiamo un nuovo metodo per ottenere espansioni analitiche per i prezzi di derivati europei, sotto modelli a volatilità stocastica e locale guidati da processi di Lévy, espandendo analiticamente l’operatore integro-differenziale associato al problema di prezzaggio.
Nella quarta, e ultima parte, presentiamo un estensione della tecnica precedente che consente di ottenere espansioni analitiche per i prezzi di opzioni asiatiche, ovvero particolari tipi di opzioni il cui payoff dipende da tutta la traiettoria del titolo sottostante.

Statistiche Download - Aggiungi a RefWorks
Tipo di EPrint:Tesi di dottorato
Relatore:Vargiolu, Tiziano
Correlatore:Pascucci, Andrea - Cappoini, Agostino
Dottorato (corsi e scuole):Ciclo 26 > Scuole 26 > SCIENZE MATEMATICHE > MATEMATICA COMPUTAZIONALE
Data di deposito della tesi:23 Gennaio 2014
Anno di Pubblicazione:23 Gennaio 2014
Parole chiave (italiano / inglese):portfolio optimization, stochastic control, dynamic programming, HJB equation, jump-diffusion, multi-default, direct contagion, information-induced contagion, Lévy, exponential, default, equity-credit, default intensity, change of measure, Girsanov theorem, Esscher transform, characteristic function, abstract Cauchy problem, eigenvectors expansion, Fourier inversion, local volatility, analytical approximation, partial integro- differential equation, Fourier methods, local-stochastic volatility, asymptotic expansion, pseudo-differential calculus, implied volatility, CEV, Heston, SABR, Asian options, arith- metic average process, hypoelliptic operators, ultra-parabolic operators, Black and Scholes, option pricing, Greeks.
Settori scientifico-disciplinari MIUR:Area 01 - Scienze matematiche e informatiche > MAT/06 Probabilità e statistica matematica
Area 13 - Scienze economiche e statistiche > SECS-S/06 Metodi matematici dell'economia e delle scienze attuariali e finanziarie
Struttura di riferimento:Dipartimenti > Dipartimento di Matematica
Codice ID:6335
Depositato il:19 Mag 2015 14:38
Simple Metadata
Full Metadata
EndNote Format

Bibliografia

I riferimenti della bibliografia possono essere cercati con Cerca la citazione di AIRE, copiando il titolo dell'articolo (o del libro) e la rivista (se presente) nei campi appositi di "Cerca la Citazione di AIRE".
Le url contenute in alcuni riferimenti sono raggiungibili cliccando sul link alla fine della citazione (Vai!) e tramite Google (Ricerca con Google). Il risultato dipende dalla formattazione della citazione.

[1] A. A. Agrachev and Y. L. Sachkov, Control theory from the geometric viewpoint, vol. 87 of Encyclopaedia of Mathematical Sciences, Springer-Verlag, Berlin, 2004. Control Theory and Optimization, II. Cerca con Google

[2] C. Alexander and L. Nogueira, Stochastic local volatility, Proceedings of the Second IASTED Int. Conf. on Financial Engineering and Applications, Cambridge MA, USA, (2004), pp. 136–141. Cerca con Google

[3] L. Andersen, Option pricing with quadratic volatility: a revisit, Finance and Stochastics, 15 (2011), pp. 191–219. Cerca con Google

[4] L. Andersen and J. Andreasen, Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing, Review of Derivatives Research, 4 (2000), pp. 231–262. Cerca con Google

[5] L. Andersen and D. Buffum, Calibration and implementation of convertible bond models, J. Comput. Finance, 7 (2004), pp. 1–34. Cerca con Google

[6] J. Anderson and E. Dash, For lehman, more cuts and anxiety, The New York Times. Available online at http://www.nytimes.com/2008/08/29/business/29wall.html?dbk, (2008). Vai! Cerca con Google

[7] J. E. Angus, A note on pricing Asian derivatives with continuous geometric aver- aging, Journal of Futures Markets, 19 (1999), pp. 845–858. Cerca con Google

[8] F. Antonelli, A. Ramponi, and S. Scarlatti, Option-based risk management of a bond portfolio under regime switching interest rates, Decisions in Economics and Finance, 36 (2013), pp. 47–70. Cerca con Google

[9] F. Antonelli and S. Scarlatti, Pricing options under stochastic volatility: a power series approach, Finance Stoch., 13 (2009), pp. 269–303. Cerca con Google

[10] A. Antonov and M. Spector, Advanced analytics for the sabr model, SSRN, (2012). Cerca con Google

[11] M. Avellaneda, D. Boyer-Olson, J. Busca, and P. Friz, Reconstructing volatility, Risk, October (2004), pp. 91–95. Cerca con Google

[12] E. Ayache, P. Forsyth, and K. Vetzal, The valuation of convertible bonds with credit risk, J. Derivatives, 11 (2003), pp. 9–29. Cerca con Google

263 Cerca con Google

[13] L. Bachelier, Th ́eorie de la sp ́eculation, Ann. Sci. E ́cole Norm. Sup. (3), 17 (1900), pp. 21–86. Cerca con Google

[14] J. Backhaus and R. Frey, Pricing and hedging of portfolio credit derivatives with interacting default intensities, Int. J. Theor. Appl. Finance, 11 (2008), pp. 611–634. Cerca con Google

[15] G. Bakshi, C. Cao, and Z. Chen, Empirical performance of alternative option pricing models, Journal of Finance, 52 (1997), pp. 2003–49. Cerca con Google

[16] J. Baldeaux and A. Badran, Consistent modeling of vix and equity derivatives using a 3/2 plus jumps model, arXiv preprint arXiv:1203.5903, (2012). Cerca con Google

[17] V. Bally and A. Kohatsu-Higa, Lower bounds for densities of Asian type stochas- tic differential equations, J. Funct. Anal., 258 (2010), pp. 3134–3164. Cerca con Google

[18] O. Barndorff-Nielsen, Processes of normal inverse Gaussian type, Finance and Stochastics, 2 (1998), pp. 41–68. Cerca con Google

[19] E. Barucci, S. Polidoro, and V. Vespri, Some results on partial differential equations and Asian options, Math. Models Methods Appl. Sci., 11 (2001), pp. 475– 497. Cerca con Google

[20] D. S. Bates, Jumps and stochastic volatility: exchange rate processes implicit in Deutsche mark options, Review of Financial Studies, 9 (1996), pp. 69–107. Cerca con Google

[21] E. Bayraktar and H. Xing, Pricing Asian options for jump diffusion, Math. Finance, 21 (2011), pp. 117–143. Cerca con Google

[22] D. Becherer, The numeraire portfolio for unbounded semimartingales, Finance Stoch., 5 (2001), pp. 327–341. Cerca con Google

[23] A. B ́elanger, S. E. Shreve, and D. Wong, A general framework for pricing credit risk, Math. Finance, 14 (2004), pp. 317–350. Cerca con Google

[24] N. Bellamy, Wealth optimization in an incomplete market driven by a jump- diffusion process, J. Math. Econom., 35 (2001), pp. 259–287. Arbitrage and control problems in finance. Cerca con Google

[25] E. Benhamou, E. Gobet, and M. Miri, Smart expansion and fast calibration for jump diffusions, Finance Stoch., 13 (2009), pp. 563–589. Cerca con Google

[26] , Expansion formulas for European options in a local volatility model, Int. J. Theor. Appl. Finance, 13 (2010), pp. 603–634. Cerca con Google

[27] F. Benth and M. Schmeck, Stability of Merton’s portfolio optimization problem for L ́evy models, doi: 10.1080/17442508.2012.665056, Stochastics, (2012). Cerca con Google

[28] F. E. Benth, K. H. Karlsen, and K. Reikvam, Optimal portfolio management rules in a non-Gaussian market with durability and intertemporal substitution, Fi- nance Stoch., 5 (2001), pp. 447–467. Cerca con Google

[29] H. Berestycki, J. Busca, and I. Florent, Computing the implied volatility in stochastic volatility models, Comm. Pure Appl. Math., 57 (2004), pp. 1352–1373. Cerca con Google

264 Cerca con Google

[30] B. Bibby and M. Sorensen, A hyperbolic diffusion model for stock prices, Finance Stoch., 1 (1997), pp. 25–41. Cerca con Google

[31] T. Bielecki and I. Jang, Portfolio optimization with a defaultable security, Asia- Pacific Financial Markets, 13 (2006), pp. 113–127. Cerca con Google

[32] T. Bielecki and M. Rutkowski, Credit Risk: Modelling, Valuation and Hedging, Springer, 2001. Cerca con Google

[33] F. Black and M. Scholes, The pricing of options and corporate liabilities, The journal of political economy, 81 (1973), pp. 637–654. Cerca con Google

[34] L. Bo, Y. Wang, and X. Yang, An optimal portfolio problem in a defaultable market, Adv. in Appl. Probab., 42 (2010), pp. 689–705. Cerca con Google

[35] A. Borodin and P. Salminen, Handbook of Brownian motion: facts and formulae, Birkhauser, 2002. Cerca con Google

[36] S. I. Boyarchenko and S. Z. Levendorskii, Option pricing for truncated L ́evy processes, International Journal of Theoretical and Applied Finance, 03 (2000), pp. 549–552. Cerca con Google

[37] P. Boyle, M. Broadie, and P. Glasserman, Monte Carlo methods for secu- rity pricing, J. Econom. Dynam. Control, 21 (1997), pp. 1267–1321. Computational financial modelling. Cerca con Google

[38] H. Bu ̈hlmann and E. Platen, A discrete time benchmark approach for insurance and finance, Astin Bull., 33 (2003), pp. 153–172. Cerca con Google

[39] N. Cai and S. G. Kou, Pricing Asian options under a Hyper-Exponential jump diffusion model, to appear in Operations Research, (2011). Cerca con Google

[40] N. C. Caister, J. G. O’Hara, and K. S. Govinder, Solving the Asian option PDE using Lie symmetry methods, Int. J. Theor. Appl. Finance, 13 (2010), pp. 1265– 1277. Cerca con Google

[41] G. Callegaro, Credit risk models under partial information, Ph.D. Thesis, Scuola Normale Superiore di Pisa and University of Evry, 2010. Cerca con Google

[42] G. Callegaro, M. Jeanblanc, and W. J. Runggaldier, Portfolio optimiza- tion in a defaultable market under incomplete information, Decis. Econ. Finance, 35 (2012), pp. 91–111. Cerca con Google

[43] G. Callegaro and T. Vargiolu, Optimal portfolio for HARA utility functions in a pure jump multidimensional incomplete market, International Journal of Risk Assessment and Management - Special Issue on Measuring and Managing Financial Risk, 11 (2009), pp. 180–200. Cerca con Google

[44] A. Capponi and J. Figueroa-Lo ́pez, Dynamic portfolio optimization with a de- faultable security and regime-switching markets, To appear in Mathematical Finance, (2013). Cerca con Google

265 Cerca con Google

[45] A. Capponi, J. Figueroa-Lo ́pez, and J. Nisen, Pricing and semimartingale rep- resentations of vulnerable contingent claims in regime-switching markets, To appear in Mathematical Finance, (2013). Cerca con Google

[46] A. Capponi, S. Pagliarani, and T. Vargiolu, Pricing vulnerable claims in a L ́evy driven model, preprint SSRN, (2013). Cerca con Google

[47] P. Carr, H. Geman, D. B. Madan, and M. Yor, The fine structure of asset returns: an empirical investigations, Journal of Business, 75 (2002), pp. 305–332. Cerca con Google

[48] , From local volatility to local L ́evy models, Quant. Finance, 4 (2004), pp. 581– 588. Cerca con Google

[49] P. Carr and V. Linetsky, A jump to default extended CEV model: An application of Bessel processes, Finance and Stochastics, 10 (2006), pp. 303–330. Cerca con Google

[50] P. Carr and D. Madan, Option valuation using the fast Fourier transform, J. Comput. Finance, 2(4) (1999), pp. 61–73. Cerca con Google

[51] P. Carr and D. B. Madan, Local volatility enhanced by a jump to default, SIAM J. Financial Math., 1 (2010), pp. 2–15. Cerca con Google

[52] P. Carr and L. Wu, Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation, Journal of Financial Econometrics (Advance Access published July 21, 2009), (2009), pp. 1–41. Cerca con Google

[53] P. Carr and L. Wu, A simple robust link between american puts and credit protec- tion, Review of Financial Studies, 24 (2011), pp. 473–505. Cerca con Google

[54] W. Cheng, N. Costanzino, J. Liechty, A. Mazzucato, and V. Nistor, Closed-form asymptotics and numerical approximations of 1D parabolic equations with applications to option pricing, to appear in SIAM J. Fin. Math., (2011). Cerca con Google

[55] S.-Y. Choi, J.-P. Fouque, and J.-H. Kim, Option pricing under hybrid stochastic and local volatility, to appear in Quantitative Finance, (2013). Cerca con Google

[56] M. M. Christensen and K. Larsen, No arbitrage and the growth optimal portfolio, Stoch. Anal. Appl., 25 (2007), pp. 255–280. Cerca con Google

[57] P. Christoffersen, K. Jacobs, and Ornthanalai, Exploring Time-Varying Jump Intensities: Evidence from S&P500 Returns and Options, CIRANO, 2009. Cerca con Google

[58] I. Clark, Foreign Exchange Option Pricing: A Practitioner’s Guide, Wiley, Chich- ester, 2010. Cerca con Google

[59] A. Comtet, C. Monthus, and M. Yor, Exponential functionals of Brownian motion and disordered systems, J. Appl. Probab., 35 (1998), pp. 255–271. Cerca con Google

[60] R. Cont, N. Lantos, and O. Pironneau, A reduced basis for option pricing, SIAM J. Financial Math., 2 (2011), pp. 287–316. Cerca con Google

266 Cerca con Google

[61] R. Cont and P. Tankov, Financial modelling with jump processes, Chapman & Hall/CRC Financial Mathematics Series, Chapman & Hall/CRC, Boca Raton, FL, 2004. Cerca con Google

[62] F. Corielli, P. Foschi, and A. Pascucci, Parametrix approximation of diffusion transition densities, SIAM J. Financial Math., 1 (2010), pp. 833–867. Cerca con Google

[63] J.-M. Coron, Control and nonlinearity, vol. 136 of Mathematical Surveys and Mono- graphs, American Mathematical Society, Providence, RI, 2007. Cerca con Google

[64] A. Cousin, M. Jeanblanc, and J.-P. Laurent, Hedging CDO tranches in a Markovian environment, in Paris-Princeton Lectures on Mathematical Finance 2010, vol. 2003 of Lecture Notes in Math., Springer, Berlin, 2011, pp. 1–61. Cerca con Google

[65] J. Cox, Notes on option pricing I: Constant elasticity of diffusions, Unpublished draft, Stanford University, (1975). A revised version of the paper was published by the Journal of Portfolio Management in 1996. Cerca con Google

[66] J. Cvitanic ́ and I. Karatzas, Convex duality in constrained portfolio optimization, Ann. Appl. Probab., 2 (1992), pp. 767–818. Cerca con Google

[67] A. Dassios and J. Nagaradjasarma, The square-root process and Asian options, Quant. Finance, 6 (2006), pp. 337–347. Cerca con Google

[68] M. Davis and F. R. Lischka, Convertible bonds with market risk and credit risk, in Applied probability (Hong Kong, 1999), vol. 26 of AMS/IP Stud. Adv. Math., Amer. Math. Soc., Providence, RI, 2002, pp. 45–58. Cerca con Google

[69] J. N. Dewynne and W. T. Shaw, Differential equations and asymptotic solutions for arithmetic Asian options: ‘Black-Scholes formulae’ for Asian rate calls, European J. Appl. Math., 19 (2008), pp. 353–391. Cerca con Google

[70] J. N. Dewynne and P. Wilmott, A note on average rate options with discrete sampling, SIAM J. Appl. Math., 55 (1995), pp. 267–276. Cerca con Google

[71] M. Di Francesco and A. Pascucci, On a class of degenerate parabolic equations of Kolmogorov type, AMRX Appl. Math. Res. Express, 3 (2005), pp. 77–116. Cerca con Google

[72] M. Di Francesco, A. Pascucci, and S. Polidoro, The obstacle problem for a class of hypoelliptic ultraparabolic equations, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 464 (2008), pp. 155–176. Cerca con Google

[73] C. Donati-Martin, R. Ghomrasni, and M. Yor, On certain Markov processes attached to exponential functionals of Brownian motion; application to Asian options, Rev. Mat. Iberoamericana, 17 (2001), pp. 179–193. Cerca con Google

[74] G. G. Drimus, Options on realized variance by transform methods: a non-affine stochastic volatility model, Quant. Finance, 12 (2012), pp. 1679–1694. Cerca con Google

[75] D. Duffie, J. Pan, and K. Singleton, Transform analysis and asset pricing for affine jump-diffusions, Econometrica, 68 (2000), pp. 1343–1376. Cerca con Google

267 Cerca con Google

[76] D. Duffie and K. Singleton, Credit Risk, Princeton University Press, Princeton, NJ, 2003. Cerca con Google

[77] D. Dufresne, Weak convergence of random growth processes with applications to insurance, Insurance Math. Econom., 8 (1989), pp. 187–201. Cerca con Google

[78] , The distribution of a perpetuity, with applications to risk theory and pension funding, Scand. Actuar. J., (1990), pp. 39–79. Cerca con Google

[79] , Laguerre series for Asian and other options, Math. Finance, 10 (2000), pp. 407– 428. Cerca con Google

[80] , The integrated square-root process, (2001). Cerca con Google

[81] , Asian and Basket asymptotics, Research paper n.100, University of Montreal, Cerca con Google

(2002). Cerca con Google

[82] B. Dupire, Pricing with a smile, Risk, 7 (1994), pp. 18–20. Cerca con Google

[83] E. Ekstro ̈m and J. Tysk, Boundary behaviour of densities for non-negative diffu- sions, preprint, (2011). Cerca con Google

[84] B. Engelmann, F. Koster, and D. Oeltz, Calibration of the Heston stochastic local volatility model: A finite volume scheme, SSRN eLibrary, (2011). Cerca con Google

[85] B. Eraker, Do stock prices and volatility jump? Reconciling evidence from spot and option prices, The Journal of Finance, 59 (2004), pp. 1367–1404. Cerca con Google

[86] R. H. Estes and E. R. Lancaster, Some generalized power series inversions, SIAM J. Numer. Anal., 9 (1972), pp. 241–247. Cerca con Google

[87] C.-O. Ewald, Local volatility in the Heston model: a Malliavin calculus approach, J. Appl. Math. Stoch. Anal., (2005), pp. 307–322. Cerca con Google

[88] F. Fang and C. W. Oosterlee, A novel pricing method for European options based on Fourier-cosine series expansions, SIAM J. Sci. Comput., 31 (2008/09), pp. 826– 848. Cerca con Google

[89] W. Feller, Two singular diffusion problems, Ann. of Math. (2), 54 (1951), pp. 173– 182. Cerca con Google

[90] W. H. Fleming and H. M. Soner, Controlled Markov processes and viscosity solutions, vol. 25 of Stochastic Modelling and Applied Probability, Springer, New York, second ed., 2006. Cerca con Google

[91] C. Fontana and W. Runggaldier, Diffusion-based models for financial mar- kets without martingale measures, Risk Measures and Attitudes, EAA Series, (2013), pp. 45–81. Cerca con Google

[92] M. Forde and A. Jacquier, Small-time asymptotics for implied volatility under the heston model, International Journal of Theoretical and Applied Finance, 12 (2009), pp. 861–876. Cerca con Google

268 Cerca con Google

[93] , Small-time asymptotics for an uncorrelated local-stochastic volatility model, Applied Mathematical Finance, 18 (2011), pp. 517–535. Cerca con Google

[94] M. Forde, A. Jacquier, and R. Lee, The small-time smile and term structure of implied volatility under the heston model, SIAM Journal on Financial Mathematics, 3 (2012), pp. 690–708. Cerca con Google

[95] P. Foschi, S. Pagliarani, and A. Pascucci, Approximations for asian options in local volatility models, Journal of Computational and Applied Mathematics, 237 (2013), pp. 442–459. Cerca con Google

[96] P. Foschi and A. Pascucci, Path dependent volatility, Decis. Econ. Finance, 31 (2008), pp. 13–32. Cerca con Google

[97] J.-P. Fouque and C.-H. Han, Pricing Asian options with stochastic volatility, Quant. Finance, 3 (2003), pp. 353–362. Cerca con Google

[98] J.-P. Fouque, M. Lorig, and R. Sircar, Second order multiscale stochastic volatility asymptotics: Stochastic terminal layer analysis and calibration, ArXiv preprint arXiv:1209.0697, (2012). Cerca con Google

[99] J.-P. Fouque, G. Papanicolaou, R. Sircar, and K. Solna, Multiscale Stochas- tic Volatility for Equity, Interest-Rate and Credit Derivatives, Cambridge University Press, 2011. Cerca con Google

[100] N. C. Framstad, B. Oksendal, and A. Sulem, Optimal consumption and portfo- lio in a jump diffusion market with proportional transaction costs, J. Math. Econom., 35 (2001), pp. 233–257. Arbitrage and control problems in finance. Cerca con Google

[101] A. Friedman, Partial differential equations of parabolic type, Prentice-Hall Inc., Englewood Cliffs, N.J., 1964. Cerca con Google

[102] M. Fu, D. Madan, and T. Wang, Pricing continuous time Asian options: a comparison of Monte Carlo and Laplace transform inversion methods, J. Comput. Finance, 2 (1998), pp. 49–74. Cerca con Google

[103] K. Gao and R. Lee, Asymptotics of implied volatility to arbitrary order, (2011). Cerca con Google

[104] M. G. Garroni and J.-L. Menaldi, Green functions for second order parabolic integro-differential problems, vol. 275 of Pitman Research Notes in Mathematics Se- ries, Longman Scientific & Technical, Harlow, 1992. Cerca con Google

[105] J. Gatheral, The volatility surface, a practitioner’s guide, Wiley Finance, 2006. Cerca con Google

[106] J. Gatheral, E. P. Hsu, P. Laurence, C. Ouyang, and T.-H. Wang, Asymp- totics of implied volatility in local volatility models, Math. Finance, 22 (2012), pp. 591– 620. Cerca con Google

[107] H. Geman and A. Eydeland, Domino effect, RISK, 8 (1995), pp. 65–67. Cerca con Google

[108] H. Geman and M. Yor, Quelques relations entre processus de Bessel, options asia- tiques et fonctions confluentes hyperg ́eom ́etriques, C. R. Acad. Sci. Paris S ́er. I Math., 314 (1992), pp. 471–474. Cerca con Google

269 Cerca con Google

[109] S. Glasgow and S. Taylor, A novel reduction of the simple Asian option and Lie- group invariant solutions, Int. J. Theor. Appl. Finance, 12 (2009), pp. 1197–1212. Cerca con Google

[110] P. Glasserman, Monte Carlo methods in financial engineering, vol. 53 of Appli- cations of Mathematics (New York), Springer-Verlag, New York, 2004. Stochastic Modelling and Applied Probability. Cerca con Google

[111] E. Gobet and M. Miri, Weak approximation of averaged diffusion processes, Stochastic Processes and their Applications, 124 (2014), pp. 475–504. Cerca con Google

[112] P. Guasoni and S. Robertson, Optimal importance sampling with explicit formu- las in continuous time, Finance Stoch., 12 (2008), pp. 1–19. Cerca con Google

[113] I. Gyo ̈ngy, Mimicking the one-dimensional marginal distributions of processes hav- ing an Itˆo differential, Probab. Theory Relat. Fields, 71 (1986), pp. 501–516. Cerca con Google

[114] P. Hagan, D. Kumar, A. Lesniewski, and D. Woodward, Managing smile risk, Wilmott Magazine, 1000 (2002), pp. 84–108. Cerca con Google

[115] P. Hagan and D. Woodward, Equivalent Black volatilities, Appl. Math. Finance, 6 (1999), pp. 147–159. Cerca con Google

[116] V. Henderson and R. Wojakowski, On the equivalence of floating- and fixed- strike Asian options, J. Appl. Probab., 39 (2002), pp. 391–394. Cerca con Google

[117] P. Henry-Labord`ere, A general asymptotic implied volatility for stochastic volatil- ity models, eprint arXiv:cond-mat/0504317, (2005). Cerca con Google

[118] P. Henry-Labord`ere, Analysis, geometry, and modeling in finance, Chapman & Hall/CRC Financial Mathematics Series, CRC Press, Boca Raton, FL, 2009. Ad- vanced methods in option pricing. Cerca con Google

[119] , Analysis, geometry, and modeling in finance: Advanced methods in option pric- ing, vol. 13, Chapman & Hall, 2009. Cerca con Google

[120] P. Henry-Labordere, Calibration of local stochastic volatility models to market smiles: A Monte-Carlo approach, RISK, (2009), pp. 112–117. Cerca con Google

[121] S. Heston, A closed-form solution for options with stochastic volatility with appli- cations to bond and currency options, Rev. Financ. Stud., 6 (1993), pp. 327–343. Cerca con Google

[122] D. G. Hobson and L. C. G. Rogers, Complete models with stochastic volatility, Math. Finance, 8 (1998), pp. 27–48. Cerca con Google

[123] W. Hoh, Pseudo differential operators generating Markov processes, Habilitations- schrift, Universita ̈t Bielefeld, (1998). Cerca con Google

[124] L. Ho ̈rmander, Hypoelliptic second order differential equations, Acta Math., 119 (1967), pp. 147–171. Cerca con Google

[125] S. Howison, Matched asymptotic expansions in financial engineering, J. Engrg. Math., 53 (2005), pp. 385–406. Cerca con Google

270 Cerca con Google

[126] F. Hubalek and C. Sgarra, On the explicit evaluation of the geometric Asian op- tions in stochastic volatility models with jumps, J. Comput. Appl. Math., 235 (2011), pp. 3355–3365. Cerca con Google

[127] N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion pro- cesses, vol. 24 of North-Holland Mathematical Library, North-Holland Publishing Co., Amsterdam, second ed., 1989. Cerca con Google

[128] J. E. Ingersoll, Theory of Financial Decision Making, Blackwell, Oxford, 1987. Cerca con Google

[129] K. Itoˆ and H. P. McKean, Jr., Diffusion processes and their sample paths, Springer-Verlag, Berlin, 1974. Second printing, corrected, Die Grundlehren der math- ematischen Wissenschaften, Band 125. Cerca con Google

[130] A. Jacquier and M. Lorig, The smile of certain l ́evy-type models, ArXiv preprint arXiv:1207.1630, (2013). Cerca con Google

[131] M. Jeanblanc, M. Yor, and M. Chesney, Mathematical methods for financial markets, Springer Verlag, 2009. Cerca con Google

[132] M. Jeanblanc-Picqu ́e and M. Pontier, Optimal portfolio for a small investor in a market model with discontinuous prices, Appl. Math. Optim., 22 (1990), pp. 287– 310. Cerca con Google

[133] M. Jex, R. Henderson, and D. Wang, Pricing exotics under the smile, RISK, (1999), pp. 72–75. Cerca con Google

[134] W. P. Johnson, The curious history of Fa`a di Bruno’s formula, Amer. Math. Monthly, 109 (2002), pp. 217–234. Cerca con Google

[135] R. Jordan and C. Tier, Asymptotic approximations to deterministic and stochastic volatility models, SIAM J. Financial Math., 2 (2011), pp. 935–964. Cerca con Google

[136] B. Jourdain and M. Sbai, Exact retrospective Monte Carlo computation of arith- metic average Asian options, Monte Carlo Methods Appl., 13 (2007), pp. 135–171. Cerca con Google

[137] N. Ju, Pricing Asian and basket options, Journal of Computational Finance, 5 (1998), pp. 79–104. Cerca con Google

[138] J. Kallsen, Optimal portfolios for exponential L ́evy processes, Math. Methods Oper. Res., 51 (2000), pp. 357–374. Cerca con Google

[139] R. E. Kalman, Y. C. Ho, and K. S. Narendra, Controllability of linear dynam- ical systems, Contributions to Differential Equations, 1 (1963), pp. 189–213. Cerca con Google

[140] I. Karatzas and S. Shreve, Brownian motion and stochastic calculus, vol. 113, Springer Verlag, 1991. Cerca con Google

[141] A. G. Z. Kemna and A. C. F. Vorst, A pricing method for options based on average asset values, Journal of Banking and Finance, 14 (1990), pp. 113–129. Cerca con Google

271 Cerca con Google

[142] F. Kilin, Accelerating calibration of the stochastic volatility models, Available at SSRN: http://ssrn.com/abstract=965248, Frankfurt School of Finance & Manage- ment, (CPQF Working Paper Series No. 6) (2007), pp. 1–19. Vai! Cerca con Google

[143] B. Kim and I.-S. Wee, Pricing of geometric Asian options under Heston’s stochastic volatility model, Quantitative Finance, 11 (2011), pp. 1–15. Cerca con Google

[144] T. Kobayashi, N. Nakagawa, and A. Takahashi, Pricing convertible bonds with default risk, J. Fixed Income, 11 (2001), pp. 20–29. Cerca con Google

[145] R. Korn, F. Oertel, and M. Scha ̈l, The numeraire portfolio in financial mar- kets modeled by a multi-dimensional jump diffusion process, Decis. Econ. Finance, 26 (2003), pp. 153–166. Cerca con Google

[146] D. Kramkov and W. Schachermayer, The asymptotic elasticity of utility func- tions and optimal investment in incomplete markets, Ann. Appl. Probab., 9 (1999), pp. 904–950. Cerca con Google

[147] N. Kunitomo and A. Takahashi, Pricing average options, Japan Financial Re- view, 14 (1992), pp. 1–20 (in Japanese). Cerca con Google

[148] D. Lando, Credit Risk Modeling. Theory and Applications, Princeton University Press, 2004. Cerca con Google

[149] J. P. LaSalle, The time optimal control problem, in Contributions to the theory of nonlinear oscillations, Vol. V, Princeton Univ. Press, Princeton, N.J., 1960, pp. 1–24. Cerca con Google

[150] R. W. Lee, The moment formula for implied volatility at extreme strikes, Mathe- matical Finance, 14 (2004), pp. 469–480. Cerca con Google

[151] E. E. Levi, Sulle equazioni lineari totalmente ellittiche alle derivate parziali, Rend. Circ. Mat. Palermo, 24 (1907), pp. 275–317. Cerca con Google

[152] A. Lewis, Option Valuation under Stochastic Volatility, Finance Press, 2000. Cerca con Google

[153] A. Lewis, A simple option formula for general jump-diffusion and other exponential Cerca con Google

L ́evy processes, tech. rep., Finance Press, Aug. 2001. Cerca con Google

[154] A. Lewis, Geometries and smile asymptotics for a class of stochastic volatility models, Cerca con Google

(2007). Cerca con Google

[155] V. Linetsky, Spectral expansions for asian (average price) options, Operations Re- search, 52 (2004), pp. 856–867. Cerca con Google

[156] V. Linetsky, Pricing equity derivatives subject to bankruptcy, Mathematical Fi- nance, 16 (2006), pp. 255–282. Cerca con Google

[157] V. Linetsky, Chapter 6 Spectral methods in derivatives pricing, in Financial En- gineering, J. R. Birge and V. Linetsky, eds., vol. 15 of Handbooks in Operations Research and Management Science, Elsevier, 2007, pp. 223 – 299. Cerca con Google

[158] A. Lipton, Mathematical methods for foreign exchange, World Scientific Publishing Co. Inc., River Edge, NJ, 2001. A financial engineer’s approach. Cerca con Google

272 Cerca con Google

[159] [160] [161] Cerca con Google

[162] Cerca con Google

[163] Cerca con Google

[164] Cerca con Google

[165] Cerca con Google

[166] Cerca con Google

A. Lipton, The vol smile problem, Risk Magazine, 15 (2002), pp. 61–65. Cerca con Google

A. Lipton and W. McGhee, Universal barriers, RISK, (2002), pp. 81–85. Cerca con Google

J. Liu, F. Longstaff, and J. Pan, Dynamic asset allocation with event risk, The Journal of Finance, 58 (2003), pp. 231–259. Cerca con Google

J. L. Lopez and N. M. Temme, Two-point Taylor expansions of analytic functions, Studies in Applied Mathematics, 109 (2002), pp. 297–311. Cerca con Google

R. Lord and C. Kahl, Complex logarithms in Heston-like models, Math. Finance, 20 (2010), pp. 671–694. Cerca con Google

M. Lorig, Derivatives on multiscale diffusions: an eigenfunction expansion approach, To appear in Mathematical Finance, (2012). Cerca con Google

, Local L ́evy Models and their Volatility Smile, ArXiv preprint arXiv:1207.1630, (2012). Cerca con Google

, The Exact Smile of some Local Volatility Models, ArXiv preprint arXiv:1207.0750, (2012). Cerca con Google

[167] M. Lorig, S. Pagliarani, and A. Pascucci, Cerca con Google

[168] [169] [170] [171] [172] [173] [174] [175] Cerca con Google

[176] Cerca con Google

http://explicitsolutions.wordpress.com. Vai! Cerca con Google

M. Lorig, S. Pagliarani, and A. Pascucci, Analytical expansions for parabolic Cerca con Google

equations, ArXiv preprint arXiv:1312.3314, (2013). Cerca con Google

, Implied vol for any local-stochastic vol model, SSRN eLibrary – Cerca con Google

http://ssrn.com/abstract=2283874, (2013). Vai! Cerca con Google

, Pricing approximations and error estimates for local L ́evy-type models with Cerca con Google

default, SSRN preprint, (2013). Cerca con Google

, A family of density expansions for L ́evy-type processes with default, To appear Cerca con Google

on The Annals of Applied Probability, (2014). Cerca con Google

D. Madan, P. Carr, and E. Chang, The variance gamma process and option Cerca con Google

pricing, European Finance Review, 2 (1998), pp. 79–105. Cerca con Google

D. Madan and E. Seneta, The variance gamma (VG) model for share market Cerca con Google

returns, Journal of Business, 63 (1990), pp. 511–524. Cerca con Google

A. Mazzon and A. Pascucci, Fundamental solutions and density of the square root Cerca con Google

process, working paper, (2012). Cerca con Google

R. Mendoza-Arriaga, P. Carr, and V. Linetsky, Time-changed markov pro- cesses in unified credit-equity modeling, Mathematical Finance, 20 (2010), pp. 527– 569. Cerca con Google

R. Merton, On the pricing of corporate debt: the risk structure of interest rates, Journal of Finance, 29 (1974), pp. 449–470. Cerca con Google

273 Cerca con Google

[177] R. C. Merton, Option pricing when underlying stock returns are discontinuous., J. Financ. Econ., 3 (1976), pp. 125–144. Cerca con Google

[178] N. Moodley, The Heston model: A practical approach with Matlab code, University of the Witwatersrand, Johannesburg, South Africa, (2005). Cerca con Google

[179] Y. Muromachi, The growing recognition of credit risk in corporate and financial bond markets, NLI Research Institute, Working Paper, (1999). Cerca con Google

[180] J. Obloj, Fine-tune your smile: Correction to Hagan et al, Wilmott Magazine, (2008). Cerca con Google

[181] B. Oksendal and A. Sulem, Applied stochastic control of jump diffusions, Springer Verlag, 2005. Cerca con Google

[182] S.-M. Ould Aly, Mod ́elisation de la courbe de variance et mod`eles a` volatilit ́e stochastique, Ph.D. Thesis, Universit ́e de Paris-Est, 2011. Cerca con Google

[183] S. Pagliarani and A. Pascucci, Analytical approximation of the transition density in a local volatility model, Cent. Eur. J. Math., 10(1) (2012), pp. 250–270. Cerca con Google

[184] S. Pagliarani and A. Pascucci, Local stochastic volatility with jumps: analytical approximations, I. J. of Theor. Appl. Finance, 16 (2013). Cerca con Google

[185] S. Pagliarani, A. Pascucci, and C. Riga, Adjoint expansions in local L ́evy mod- els, SIAM J. Finan. Math., 4(1) (2013), pp. 265–296. Cerca con Google

[186] S. Pagliarani and T. Vargiolu, Portfolio optimization in a defaultable L ́evy- driven market model, Preprint SSRN, (2013). Cerca con Google

[187] A. Pascucci, Free boundary and optimal stopping problems for American Asian options, Finance Stoch., 12 (2008), pp. 21–41. Cerca con Google

[188] , PDE and martingale methods in option pricing, vol. 2 of Bocconi & Springer Series, Springer, Milan, 2011. Cerca con Google

[189] L. Pasin and T. Vargiolu, Optimal portfolio for HARA utility functions where risky assets are exponential additive processes, Economic Notes, 39 (2010), pp. 65–90. Cerca con Google

[190] V. Piterbarg, Markovian projection method for volatility calibration, Risk, 4 (2007), pp. 84–89. Cerca con Google

[191] E. Platen, A benchmark approach to finance, Math. Finance, 16 (2006), pp. 131–151. Cerca con Google

[192] P. E. Protter, Stochastic integration and differential equations, vol. 21 of Ap- plications of Mathematics (New York), Springer-Verlag, Berlin, second ed., 2004. Stochastic Modelling and Applied Probability. Cerca con Google

[193] S. Raible, L ́evy processes in finance: Theory, numerics, and empirical facts, tech. rep., PhD thesis, Universita ̈t Freiburg, 2000. Cerca con Google

[194] Y. Ren, D. Madan, and M. Q. Qian, Calibrating and pricing with embedded local volatility models, RISK, (2007), pp. 138–143. Cerca con Google

274 Cerca con Google

[195] J. Riordan, Derivatives of composite functions, Bull. Amer. Math. Soc., 52 (1946), pp. 664–667. Cerca con Google

[196] L. Rogers and Z. Shi, The value of an Asian option., J. Appl. Probab., 32 (1995), pp. 1077–1088. Cerca con Google

[197] K.-i. Sato, L ́evy processes and infinitely divisible distributions, vol. 68 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1999. Translated from the 1990 Japanese original, Revised by the author. Cerca con Google

[198] M. Schro ̈der, On constructive complex analysis in finance: explicit formulas for Asian options, Quart. Appl. Math., 66 (2008), pp. 633–658. Cerca con Google

[199] A. Sepp, Stochastic local volatility models: Theory and implementation, University of Leicester, (2010). Cerca con Google

[200] W. T. Shaw, Modelling financial derivatives with Mathematica, Cambridge Univer- sity Press, Cambridge, 1998. Mathematical models and benchmark algorithms, With 1 CD-ROM (Windows, Macintosh and UNIX). Cerca con Google

[201] , Pricing Asian options by contour integration, including asymptotic methods for low volatility, Working paper, Cerca con Google

http://www.mth.kcl.ac.uk/∼shaww/web page/papers/Mathematicafin.htm, (2003). Vai! Cerca con Google

[202] K. Shiraya and A. Takahashi, Pricing average options on commodities, forthcom- ing in Journal of Futures Markets, (2010). Cerca con Google

[203] K. Shiraya, A. Takahashi, and M. Toda, Pricing Barrier and Average Options Under Stochastic Volatility Environment, SSRN eLibrary, (2009). Cerca con Google

[204] A. Takahashi and N. Yoshida, Monte Carlo simulation with asymptotic method, J. Japan Statist. Soc., 35 (2005), pp. 171–203. Cerca con Google

[205] S. Taylor, Perturbation and symmetry techniques applied to finance, Ph. D. thesis, Frankfurt School of Finance & Management. Bankakademie HfB, (2011). Cerca con Google

[206] A. Valdez and T. Vargiolu, Optimal portfolio in a regime-switching model, in Seminar on Stochastic Analysis, Random Fields and Applications VI - Centro Stefano Franscini - Ascona, vol. 67 of Progress in Probability, Springer, 2013, pp. 435–449. Cerca con Google

[207] J. Vecer, A new pde approach for pricing arithmetic average Asian options, J. Comput. Finance, (2001), pp. 105–113. Cerca con Google

[208] J. Vecer and M. Xu, Unified Asian pricing, Risk, 15 (2002), pp. 113–116. Cerca con Google

[209] M. Widdicks, P. W. Duck, A. D. Andricopoulos, and D. P. Newton, The Black-Scholes equation revisited: asymptotic expansions and singular perturbations, Math. Finance, 15 (2005), pp. 373–391. Cerca con Google

[210] E. Wong, The construction of a class of stationary Markoff processes, in Proc. Sym- pos. Appl. Math., Vol. XVI, Amer. Math. Soc., Providence, R.I., 1964, pp. 264–276. Cerca con Google

275 Cerca con Google

[211] U. Wystup, Validation of the Tremor stochastic-local-volatility model, MathFinance AG, (2011). Cerca con Google

[212] G. Xu and H. Zheng, Basket options valuation for a local volatility jump-diffusion model with the asymptotic expansion method, Insurance Math. Econom., 47 (2010), pp. 415–422. Cerca con Google

[213] M. Yor, On some exponential functionals of Brownian motion, Adv. in Appl. Probab., 24 (1992), pp. 509–531. Cerca con Google

[214] , Sur certaines fonctionnelles exponentielles du mouvement brownien r ́eel, J. Appl. Probab., 29 (1992), pp. 202–208. Cerca con Google

[215] J. E. Zhang, A semi-analytical method for pricing and hedging continuously sampled arithmetic average rate options, J. Comput. Finance, 5 (2001), pp. 1–20. Cerca con Google

Download statistics

Solo per lo Staff dell Archivio: Modifica questo record