Consistent variance curve models

Finance and Stochastics

Volumn 10, Issue 2, 2006, Pages 178-203

  Buehler, Hans ^a,b  

^a DEUTSCHE BANK AG   (Germany)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Arbitrage free term structure dynamics; Consistent paramcthzations; Heath Jarrow Morton theory; Market models; Options on variance; Variance swaps

Indexed keywords

EID: 33646676773     PISSN: 09492984     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00780-006-0008-2     Document Type: Article

References (26)

1. Björk, T., Christensen, B.J.: Interest rate dynamics and consistent forward curves. Math Finance 9, 323-348 (1999)
2. Björk, T., Svensson, L.: On the existence of finite dimensional realizations for nonlinear forward rate models, Math Finance 11, 205-243 (2001)
3. Brace, A., Goldys, B., Klebaner, F., Womersley, R.: A market model of stochastic implied volatility with application to the BGM model. WP 2001, http://www.maths.unsw.edu.au/~rsw./Finance/svol.pdf
4. Buehler, H.: Expensive martingales. Quant Finance (2006. in press)
5. Cont, R., da Fonseca, J., Durrleman, V.: Stochastic models of implied volatility surfaces. Econ Notes 31, 361-377 (2002)
6. Demeterfi, K., Derraan, E., Kamal, M., Zou, J.: More than you ever wanted to know about volatility swaps. Quantitative Strategies Research Notes, Goldman Sachs (1999)
7. Duffie, D., Pan, J., Singleton, K.: Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68, 1343-1376 (2000)
8. Dupire, B.: Arbitrage pricing with stochastic volatility. In: Peter Carr (ed.) Derivatives pricing, Risk Books, pp. 197-215 (2004)
9. Fengler, M., Härdle, W., Mammen, E.: Implied volatility string dynamics. CASE Discussion Paper Series No. 2003-54 (2003)
10. Filipović, D.: Consistency problems for Heath-Jarrow-Morton interest rate models. Lecture Notes in Mathematics, vol. 1760. Berlin Heidelberg New York: Springer 2001
11. Filipović, D., Teichmann, J.: On the geometry of the term structure of interest rates. Proc R Soc Lond A 460, 129-167 (2004)
12. Föllmer, H., Schied, A.: Stochastic finance. 2nd edn. de Gruyter (2004)
13. Fouque, J-P., Papanicolaou, G., Sircar, K.: Derivatives in financial markets with stochastic volatility. Cambridge: Cambridge University Press 2000
14. Gatheral, J.: Case studies in financial modelling. Course notes, Courant Institute of Mathematical Sciences. Fall (2004), http://www.math.nyu.edu/ fellows_fin_math/gatheral/case_studies.html
15. Haffner, R.: Stochastic implied volatility. Berlin Heidelberg New York: Springer 2004
16. Heath, D., Jarrow, R., Morton, A.: Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation. Econometrica 60, 77-106 (1992)
17. Heston, S.: A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev Financ Stud 6, 327-343 (1993)
18. Musiela, M.: Stochastic PDEs and term structure models. Journées Internationales de France, IGR-AFFI, La Baule (1993)
19. Neuberger, A.: Volatility trading. London: London Business School WP 1990
20. Overhaus, M., Bermudez, A., Buehler, H., Ferraris, A., Jordinson, C., Lamnouar, A.: Equity hybrid derivatives. New York Wiley: 2006, in press
21. da Prato, G., Zabczyk, J.: Stochastic equations in infinite dimensions. Cambridge University Press Cambridge 1992
22. Protter, P.: Stochastic integration and differential equations. 2nd edn. Berlin Heidelberg New York: Springer 2004
23. Revuz, D., Yor, M.: Continuous martingales and Brownian motion. 3rd edn. Berlin Heidelberg New York: Springer 1999
24. Schönbucher, P.J.: A market model for stochastic implied volatility. Phil Trans R Soc A 357, 2071-2092 (1999)
25. Schweizer, M., Wissel, J.: On the term structure of implied volatilities. NCCR FINRISK working paper No. 271,ETH Zurich, http://www.nccr-finrisk.unizh. ch/wp/index.php?action=query&id=271
26. Teichmann, J.: Stochastic evolution equations in infinite dimension with applications to term structure problems. Lecture notes. (2005) http://www.fam.tuwien.ac.at/-jteichma/