Esscher transforms and consumption-based models

Insurance: Mathematics and Economics

Volumn 45, Issue 3, 2009, Pages 337-347

  Badescu, Alex ^a   Elliott, Robert J ^b,c   Siu, Tak Kuen ^d  

^a UNIVERSITY OF CALGARY   (Canada)

^b UNIVERSITY OF CALGARY   (Canada)

^c UNIVERSITY OF ADELAIDE   (Australia)

^d Faculty of Economics and Business   (Australia)

Author keywords

Consumption based model; Esscher transform; Esscher Girsanov transform; Euler equation; Exponential affine form; Radon Nikodym derivative; Stochastic discount factor; Utility function

Indexed keywords

EID: 71649101035     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2009.08.001     Document Type: Article

References (52)

1. Badescu A.M., and Kulperger R.J. GARCH option pricing: A semiparametric approach. Insurance: Mathematics and Economics 43 1 (2008) 69-84
2. Badescu A.M., Kulperger R.J., and Lazar E. Option valuation with normal mixture GARCH models. Studies in Nonlinear Dynamics & Econometrics 12 2 (2008) Article 5
3. Barndorff-Nielsen O.E. Normal inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of Statistics 24 (1997) 1-13
4. Bertholon H., Monfort A., and Pegoraro F. Econometric asset pricing modelling. Journal of Financial Econometrics 6 4 (2008) 407-458
5. Black F., and Scholes M. The pricing of options and corporate liabilities. Journal of Political Economy 81 (1973) 637-659
6. Breeden D.T. An intertemporal asset pricing model with stochastic consumption and investment opportunities. Journal of Financial Economics 7 3 (1979) 265-296
7. Brennan M.J. The pricing of contingent claims in discrete time models. Journal of Finance 24 1 (1979) 53-68
8. Brown D.P., and Gibbons M.R. A simple econometric approach for utility-based asset pricing models. Journal of Finance 40 2 (1985) 359-381
9. Bühlmann H. An economic premium principle. ASTIN Bulletin 11 1 (1980) 52-60
10. Bühlmann H. The general economic premium principle. ASTIN Bulletin 14 1 (1984) 13-21
11. Bühlmann H., Delbaen F., Embrechts P., and Shiryaev A.N. No-arbitrage, change of measures and conditional Esscher transforms. CWI Quarterly 9 4 (1996) 291-317
12. Bühlmann H., Delbaen F., Embrechts P., and Shiryaev A.N. On Esscher transforms in discrete finance models. ASTIN Bulletin 28 2 (1998) 171-186
13. Camara A. An extended set of risk neutral valuation relationships for the pricing of contingent claims. Review of Derivative Research 3 (1999) 67-83
14. Camara A. A generalization of the Brennan-Rubinstein approach for the pricing derivatives. Journal of Finance 2 (2003) 805-819
15. Campbell J.Y., Lo A.W., and MacKinlay A.C. The Econometrics of Financial Markets (1997), Princeton University Press, Princeton
16. Chan T. Pricing contingent claims on stocks driven by Lévy processes. Annals of Applied Probability 9 2 (1999) 504-528
17. Christoffersen, P., Redouane, E., Feunou, B., Jacobs, K., 2009. Option valuation with conditional heteroskedasticity and non-normality. Review of Financial Studies (forthcoming)
18. Cox J., Ingersoll J., and Ross S. A theory of the term structure of interest rates. Econometrica 53 2 (1985) 385-407
19. Duan J.-C. The GARCH option pricing model. Mathematical Finance 5 (1995) 13-32
20. Duan, J.-C., 1999. Conditionally fat-tailed distributions and the volatility smile in options, unpublished manuscript. University of Toronto
21. Duffie D., and Zame B. The consumption-based capital asset pricing model. Econometrica 57 (1989) 1279-1298
22. Elliott R.J., Chan L., and Siu T.K. Option pricing and Esscher transform under regime switching. Annals of Finance 1 4 (2005) 423-432
23. Elliott R.J., Hunter W.C., Kopp P.E., and Madan D.B. Pricing via multiplicative price decomposition. Journal of Financial Engineering 4 (1995) 247-262
24. Elliott R.J., and Madan D.B. A discrete time equivalent martingale measure. Mathematical Finance 9 6 (1998) 825-841
25. Embrechts P. Actuarial versus financial pricing of insurance. Risk Finance 1 (2000) 17-26
26. Elliott R.J., Siu T.K., and Chan L. Option pricing for GARCH models with Markov switching. International Journal of Theoretical and Applied Finance 9 6 (2006) 825-841
27. Epstein L., and Zin S. Substitution, risk aversion, and temporal behavior of consumption and asset returns: A theoretical framework. Econometrica 57 (1989) 937-969
28. Epstein L., and Zin S. Substitution, risk aversion, and temporal behavior of consumption and asset returns: An empirical analysis. Journal of Political Economy 99 (1991) 263-286
29. Esscher F. On the probability function in the collective theory of risk. Skandinavisk Aktuarietidskrift 15 (1932) 175-195
30. Garcia R., Renault E., and Semenov A. Disentangling risk aversion and intertemporal substitution through a reference level. Finance Research Letters 3 (2006) 181-193
31. Gerber H.U., and Shiu E.S.W. Option pricing by Esscher transforms (with discussions). Transactions of the Society of Actuaries 46 (1994) 99-191
32. Gerber H.U., and Goovaerts M.J. On the representation of additive principles of premium calculation. Scandinavian Actuarial Journal 4 (1981) 221-227
33. Goovaerts M.J., and Laeven R. Actuarial risk measures for financial derivative pricing. Insurance: Mathematics and Economics 42 2 (2008) 540-547
34. Goovaerts M.J., Kaas R., Laeven R.J.A., and Tang Q. A comonotonic image of independence for additive risk measures. Insurance: Mathematics and Economics 35 3 (2004) 581-594
35. Gourieroux C., and Monfort A. Econometric specifications of stochastic discount factor models. Journal of Econometrics 136 (2007) 509-530
36. Hansen L.P., and Richard S. The role of Conditioning information in deducing testable restrictions implied by dynamic asset pricing models. Econometrica 55 (1987) 587-613
37. Hansen L.P., and Jagannathan R. Assesing specification errors in stochastic discount factor models. Journal of Finance 52 2 (1992) 557-590
38. Harrison M.J., and Kreps D.M. Martingales and arbitrage in multiperiod security markets. Journal of Economic Theory 20 (1979) 381-408
39. Harrison J., and Pliska S. Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and Their Applications 11 3 (1981) 215-260
40. Harrison J., and Pliska S. A stochastic calculus model of continuous trading: Complete markets. Stochastic Processes and their Applications 15 3 (1983) 313-316
41. Iwaki H., Kijima M., and Morimoto Y. An economic premium principle in a multiperiod economy. Insurance: Mathematics and Economics 28 3 (2001) 325-339
42. Iwaki H. An economic premium principle in a continuous-time economy. Journal of the Operations Research Society of Japan 45 4 (2002) 346-361
43. Lucas R. Asset pricing in an exchange economy. Econometrica 46 (1978) 1429-1445
44. Merton R.C. An intertemporal capital asset pricing model. Econometrica 41 (1973) 867-887
45. Rubinstein M. The valuation of uncertain income streams and the pricing of options. Bell Journal of Economics 7 (1976) 407-425
46. Siu T.K., Tong H., and Yang H. On pricing derivatives under GARCH models: A dynamic Gerber-Shiu approach. North American Actuarial Journal 8 3 (2004) 17-32
47. Siu T.K. Fair valuation of participating policies with surrender options and regime switching. Insurance: Mathematics and Economics 37 3 (2005) 533-552
48. Siu, T.K., 2009. Esscher transform: From actuarial science to quantitative Finance. Encyclopedia of Quantitative Finance (forthcoming)
49. Schroder M. Risk-neutral parameter shifts and derivatives pricing in discrete time. Journal of Finance 59 5 (2004) 2375-2402
50. Taylor S.J. Modeling Financial Time Series (1986), John Wiley & Sons, New York
51. Wang S.S. A class of distortion operators for pricing financial and insurance risks. Journal of Risk and Insurance 67 1 (2000) 15-36
52. Wang S.S. Equilibrium pricing transforms: New results on Bühlmann's 1980 economic model. ASTIN Bulletin 32 (2003) 213-234