Robustness of delta hedging for path-dependent options in local volatility models

Journal of Applied Probability

Volumn 44, Issue 4, 2007, Pages 865-879

  Schied, Alexander ^a   Stadje, Mitja ^b,c  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b PRINCETON UNIVERSITY   (United States)

^c Princeton University   (United States)

Author keywords

Delta hedging; Directional convexity; Local volatility; Robustness

Indexed keywords

EID: 38949187486     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1197908810     Document Type: Article

References (24)

1. BERGENTHUM, J. AND RÜSCHENDORF, L. (2006). Comparison of option prices in semimartingale models. Finance Stoch. 10, 222-249.
2. BÜHLER, H. (2005). Volatility markets. Consistent modeling, hedging and practical implementation. Doctoral thesis, TU Berlin.
3. BÜHLER, H. (2006). Consistent variance swap models. Finance Stoch. 10, 178-203.
4. CHERIDITO, P. (2001). Mixed fractional Brownian motion. Bernoulli 7, 913-934.
5. DAVIS, M. (2004). Complete-market models of stochastic volatility. Proc. R. Soc. London A 460, 11-26.
6. DUPIRE, B. (1997). Pricing and hedging with smiles. In Mathematics of Derivative Securities (Cambridge, 1995; Publ. Newton Inst. 15), Cambridge University Press, pp. 103-111.
7. EKSTRÖM, E., JANSON, S. AND TYSK, J. (2005). Superreplication of options on several underlying assets. J. Appl. Prob. 42, 27-38.
8. EL KAROUI, N., JEANBLANC- PICQUÉ, M. AND SHREVE, S. (1998). Robustness of the Black and Scholes formula. Math. Finance 8, 93-126.
9. FÖLLMER, H. (1981). Calcul d'Itô sans probabilités. In Séminaire de probabilités XV (Lecture Notes Math. 850), Springer, Berlin, pp. 143-150.
10. FÖLLMER, H. (1991). Probabilistic aspects of options. Rolf Nevanlinna Institute Reports B6, Helsinki.
11. FÖLLMER, H. (2001). Probabilistic aspects of financial risk. In European Congress of Mathematics (Barcelona 2000; Progr. Math. 201), Vol. I, Birkhäuser, Basel, pp. 21-36.
12. FÖLLMER, H. AND SCHIED, A. (2004). Stochastic Finance. An Introduction in Discrete Time (de Gruyter Studies Math. 27), 2nd edn. De Gruyter, Berlin.
13. GUSHCHIN, A. AND MORDECKI, È. (2002). Bounds on option prices for semimartingale market models. Proc. Steklov Inst. Math. 2002, 73-113.
14. GYÖNGY, I. (1986). Mimicking the one-dimensional marginal distributions of processes having an Itô differential. Prob. Theory Relat. Fields 71, 501-516.
15. HAJEK, B. (1985). Mean stochastic comparison of diffusions. Z. Wahrscheinlichkeitstk 68, 315-329.
16. HARDY, G. H., LITTLEWOOD, J. E. AND PÓLYA, G. (1952). Inequalities, 2nd edn. Cambridge University Press.
17. HOBSON, D. (1998). Volatility misspecification, option pricing and superreplication via coupling. Ann. Appl. Prob. 8, 193-205.
18. JANSON, S. AND TYSK, J. (2003). Volatility time and properties of option prices. Ann. Appl. Prob. 13, 890-913.
19. JANSON, S. AND TYSK, J. (2004). Preservation of convexity to solutions of parabolic equations. J. Differential Equat. 206, 182-226.
20. KARATZAS, I. AND SHREVE, S. E. (1991). Brownian Motion and Stochastic Calculus (Graduate Texts Math. 113), 2nd edn. Springer, Berlin.
21. LYONS, T. (1995). Uncertain volatility and the risk-free synthesis of derivatives. Appl. Math. Finance 2, 117-133.
22. SCHIED, A. (2005). Optimal investments for robust utility functionals in complete market models. Math. Operat. Res. 30, 750-764.
23. STADJE, M. (2005). Convexity of option prices in a local volatility model. Diploma thesis, TU Berlin.
24. WRIGHT, E. M. (1954). An inequality for convex functions. Amer. Math. Monthly 61, 620-622.