State Price Densities implied from weather derivatives
A State Price Density (SPD) is the density function of a risk neutral equivalent martingale measure for option pricing, and is indispensible for exotic option pricing and portfolio risk management. Many approaches have been proposed in the last two decades to calibrate a SPD using financial options from the bond and equity markets. Among these, non and semi parametric methods were preferred because they can avoid model mis-specification of the underlying and thus give insight into complex portfolio propelling. However, these methods usually require a large data set to achieve desired convergence properties. Despite recent innovations in finan- cial and insurance markets, many markets remain incomplete and there exists an illiquidity issue. One faces the problem in estimation by e.g. kernel techniques that there are not enough observations locally available. For this situation, we employ a Bayesian quadrature method because it allows us to incorporate prior assumptions on the model parameters and hence avoids problems with data sparsity. It is able to compute the SPD of both call and put options simultaneously, and is particularly robust when the market faces the illiquidity issue. By comparing our approach with other approaches, we show that the traditional way of estimating the SPD by differ- entiating an interpolation of option prices does not hold in practice. As illustration, we calibrate the SPD for weather derivatives, a classical example of incomplete mar- kets with financial contracts payoffs linked to non-tradable assets, namely, weather indices. Finally, we study the dynamics of the implied SPD's and related to weather data.
|Date of creation:||May 2013|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://sfb649.wiwi.hu-berlin.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ait-Sahalia, Yacine & Lo, Andrew W., 2000.
"Nonparametric risk management and implied risk aversion,"
Journal of Econometrics,
Elsevier, vol. 94(1-2), pages 9-51.
- Yacine Ait-Sahalia & Andrew W. Lo, 2000. "Nonparametric Risk Management and Implied Risk Aversion," NBER Working Papers 6130, National Bureau of Economic Research, Inc.
- Yatchew, Adonis & Hardle, Wolfgang, 2006. "Nonparametric state price density estimation using constrained least squares and the bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 579-599, August.
- Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826.
- Giacomini, Raffaella & Gottschling, Andreas & Haefke, Christian & White, Halbert, 2007.
"Mixtures of t-distributions for Finance and Forecasting,"
216, Institute for Advanced Studies.
- Giacomini, Raffaella & Gottschling, Andreas & Haefke, Christian & White, Halbert, 2008. "Mixtures of t-distributions for finance and forecasting," Journal of Econometrics, Elsevier, vol. 144(1), pages 175-192, May.
- Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819.
- Fan, Jianqing & Mancini, Loriano, 2009. "Option Pricing With Model-Guided Nonparametric Methods," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1351-1372.
- Ming Yuan, 2009. "State price density estimation via nonparametric mixtures," Papers 0910.1430, arXiv.org.
- Yacine Ait-Sahalia & Jefferson Duarte, 2002.
"Nonparametric Option Pricing under Shape Restrictions,"
NBER Working Papers
8944, National Bureau of Economic Research, Inc.
- Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
- Fred Benth & Wolfgang Karl HÃ¤rdle & Brenda LÃ³pez Cabrera, 2009. "Pricing of Asian temperature risk," SFB 649 Discussion Papers SFB649DP2009-046, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833.
- Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
- Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
- Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521580137.
- Haitao Li & Feng Zhao, 2009. "Nonparametric Estimation of State-Price Densities Implicit in Interest Rate Cap Prices," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4335-4376, November.
- Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
When requesting a correction, please mention this item's handle: RePEc:hum:wpaper:sfb649dp2013-026. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (RDC-Team)
If references are entirely missing, you can add them using this form.