Capturing parameter risk with convex risk measures

Karl Friedrich Bannör1, Matthias Scherer1
1Parkring 11, 85748, Garching bei München, Germany

Tóm tắt

Từ khóa


Tài liệu tham khảo

Acerbi C (2002) Spectral measures of risk: a coherent representation of subjective risk aversion. J Bank Finance 26(7):1505–1518

Acerbi C, Tasche D (2002) On the coherence of expected shortfall. J Bank Finance 26(7):1487–1503

Albrecher H, Mayer P, Schoutens W, Tistaert J (2007) The little Heston trap. Wilmott Mag 1:83–92

Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math Finance 9(3):203–228

Avellaneda M, Levy A, Paras A (1995) Pricing and hedging derivative securities in markets with uncertain volatilities. Appl Math Finance 2:73–88

Barndorff-Nielsen OE, Shephard N (2001) Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics. J R Stat Soc Ser B (Stat Methodol) 63:167–241

Bartoszynski R (1961) A characterization of the weak convergence of measures. Ann Math Stat 32(2):561–576

Bion-Nadal J (2009) Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk. J Math Econ 45(11):738–750

Carr P, Madan D (1999) Option valuation using the fast Fourier transform. J Comput Finance 2:61–73

Carr P, Geman H, Madan D (2001) Pricing and hedging in incomplete markets. J Financ Econ 62:131–167

Černy A (2009) Mathematical techniques in finance: tools for incomplete markets, 2nd edn. Princeton University Press, Princeton

Cherny A, Madan D (2010) Markets as a counterparty: an introduction to conic finance. Int J Theoret Appl Finance 13(8):1149–1177

Clark P (1973) A subordinated stochastic process model with finite variance for speculative prices. Econometrica 41(1):135–155

Cont R (2006) Model uncertainty and its impact on the pricing of derivative instruments. Math Finance 16(3):519–547

Cont R, Tankov P (2004) Financial modelling with jump processes. Chapman and Hall/CRC Financial Mathematics Series, Boca Raton

Detlefsen K, Härdle W (2007) Calibration risk for exotic options. J Deriv 14(4):47–63

Fisher R (1915) Frequency distribution of the values of the correlation coefficient in samples of an indefinitely large population. Biometrika 10(4):507–521

Föllmer H, Leukert P (1999) Quantile hedging. Finance Stochast 3(3):251–273

Föllmer H, Leukert P (2000) Efficient hedging. Finance Stochast 4(2):117–146

Föllmer H, Schied A (2002) Convex measures of risk and trading constraints. Finance Stochast 6(4):429–447

Föllmer H, Schied A (2011) Stochastic Finance, 3rd edn. De Gruyter, Boston

Föllmer H, Schweizer M (1990) Hedging of contingent claims under incomplete information. In: Applied stochastic analysis, pp 389–414

Frittelli M, Scandolo G (2006) Risk measures and capital requirements for processes. Math Finance 16(4):589–612

Guillaume F., Schoutens W. (2011) Calibration risk: illustrating the impact of calibration risk under the Heston model. Rev Deriv Res

Gupta A., Reisinger C. (2012) Robust calibration of financial models using Bayesian estimators. J Comput Finance (to appear)

Gupta A, Reisinger C, Whitley A (2010) Model uncertainty and its impact on derivative pricing. In: Bocker K (ed) Rethinking risk measurement and reporting, pp 137–175

Heston S (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev Financ Stud 6(2):327–343

Hörmander L (1990) The analysis of linear partial differential operators I: distribution theory and Fourier analysis. Springer, Berlin

Jessen C, Poulsen R (2010) Empirical performance of model for barrier option valuation. Working Paper

Jouini E, Schachermayer W, Touzi N (2006) Law invariant risk measures have the Fatou property. Adv Math Econ 9(1):49–71

Knight F (1921) Risk, uncertainty, and profit. Hart, Schaffner & Marx, Boston

Krätschmer V (2006) On σ-additive robust representation of convex risk measures for unbounded financial positions in the presence of uncertainty about the market model. SFB 649, Deutsche Forschungsgemeinschaft

Krätschmer V, Schied A, Zähle H (2012) Comparative and qualitative robustness for law-invariant risk measures. Working Paper

Kusuoka S (2001) On law invariant coherent risk measures. Adv Math Econ 3

Lindström E (2010) Implication of parameter uncertainty on option prices. Adv Decis Sci

Madan D, Senata E (1990) The variance gamma model for share market returns. J Bus 63(4):511–524

Madan D, Carr P, Chang E (1998) The variance gamma process and option pricing. Rev Finance 2(1):79–105

Margrabe W (1975) The value of an option to exchange one asset for another. J Finance 23(1):177–186

McNeil A., Frey R., Embrechts P. (2005) Quantitative risk management. Princeton University Press, Princeton

Olkin I, Pratt R (1958) Unbiased estimation of certain correlation coefficients. Ann Math Stat 29(1):201–211

Schoutens W, Simons E, Tistaert J (2004) A perfect calibration! Now what? Wilmott Mag 3

Schweizer M (1991) Option hedging for semimartingales. Stoch Process Appl 37(2):339–363

van der Vaart A (2000) Asymptotic statistics. Cambridge Series in Statistical and Probabilistic Mathematics

Weber S (2006) Distribution invariant measures, information, and dynamic consistency. Math Finance 16(2):419–442

Werner D. (2007) Funktionalanalysis. Springer, Berlin

Xu M (2006) Risk measure pricing and hedging in incomplete markets. Ann Finance 2:51–71