Adjoint-based Monte Carlo calibration of financial market models

Finance and Stochastics

Volumn 13, Issue 3, 2009, Pages 351-379

  Kaebe, C ^a   Maruhn, J H ^b   Sachs, E W ^a,c  

^a UNIVERSITY OF TRIER   (Germany)

^b UniCredit Markets and Investment Banking   (Germany)

^c VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Adjoint equation; Monte Carlo calibration; Multi layer method

Indexed keywords

EID: 70350627562     PISSN: 09492984     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00780-009-0097-9     Document Type: Article

References (23)

1. Andersen, L., Brotherton-Ratcliffe, R.: The equity option volatility smile: an implicit finite-difference approach. J. Comput. Finance 1, 5-38 (1997) /1998.
2. Bastin, F.: Trust-region algorithms for nonlinear stochastic programming and mixed logit models. PhD Thesis, Facultés Universitaires Notre-Dame de la Paix, Namur, Belgium (2004). http://www.fundp.ac.be/~fbastin/Thesis/fbphd.pdf.
3. Bastin, F., Cirillo, C., Toint, P.L.: Convergence theory for nonconvex stochastic programming with an application to mixed logit. Math. Program. Ser. B 108, 207-234 (2006).
4. Boggs, P.T.: Sequential quadratic programming. In: Ariek, I. (ed.) ACTA Numerica, pp. 1-52. Cambridge University Press, Cambridge (1995).
5. Coleman, T.F., Li, Y., Verma, A.: Reconstructing the unknown local volatility function. J. Comput. Finance 2, 77-102 (1999).
6. Cox, J., Ross, S.: The valuation of options for alternative stochastic processes. J. Financ. Econ. 3, 145-166 (1976).
7. Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Rev. 44, 525-597 (2002).
8. Gerlich, F., Giese, A.M., Maruhn, J.H., Sachs, E.W.: Parameter identification in stochastic volatility models with time-dependent model parameters. Technical Report, University of Trier (2006).
9. Giles, M.: Multi-level Monte Carlo path simulation. Technical Report 06/03, Oxford University Computing Laboratory (2006). http://people.maths.ox.ac.uk/oucl/publications/natr/NA-06-03.html.
10. Giles, M., Glasserman, P.: Smoking adjoints: fast Monte Carlo Greeks. Risk Technical Papers, p. 88 (2006).
11. Giles, M.: Monte Carlo evaluation of sensitivities in computational finance. In: Lipitakis, E.A. (ed.) HERCMA-The 8th Hellenic European Research on Computer Mathematics & its Applications Conference, pp. 29-44. ACM Digital Library, New York (2007).
12. Glasserman, P.: Monte Carlo Methods in Financial Engineering. Springer, Berlin (2003).
13. Hagan, P.S., Kumar, D., Lesniewski, A.S., Woodward, D.E.: Managing smile risk. Wilmott Mag. 1, 84-108 (2002).
14. Heston, S.L.: A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud. 6, 327-343 (1993).
15. Hull, J., White, A.: The pricing of options on assets with stochastic volatilities. J. Finance 42, 281-300 (1987).
16. Kaebe, C., Maruhn, J.H., Sachs, E.W.: Efficient derivative calculation for Monte Carlo based calibration problems in finance. Technical Report, University of Trier (2007).
17. Kelley, C.T., Sachs, E.W.: Multilevel algorithms for constrained compact fixed point problems. SIAM J. Sci. Comput. 15, 645-667 (1994).
18. Kindermann, S., Mayer, P., Albrecher, H., Engl, H.: Identification of the local speed function in a Lévy model for option pricing. J. Integral Equ. Appl. 20, 161-200 (2008).
19. Kloeden, P.E., Platen, E.: Numerical Solution of Stochastic Differential Equations. Springer, Berlin (1999).
20. Lewis, A.L.: Option Valuation under Stochastic Volatility. Finance Press (2000).
21. Lord, R., Koekkoek, R., van Dijk, D.: A comparison of biased simulation schemes for stochastic volatility models. Tinbergen Institute Discussion Papers (2006). http://papers.ssrn.com/sol3/papers.cfm?abstract_id=903116.
22. Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999).
23. Shapiro, A.: Monte Carlo sampling methods. In: Ruszcynski, A., Shapiro, A. (eds.) Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10, p. 353. Elsevier Science B.V., Amsterdam (2003).