IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Estimating Relative Risk Aversion, Risk-Neutral and Real-World Densities using Brazilian Real Currency Options

  • José Renato Haas Ornelas
  • José Santiago Fajardo Barbachan
  • Aquiles Rocha de Farias

Building Risk-Neutral Densities (RND) from options data can provide market-implied expectations about the future behavior of a financial variable. This paper uses the Liu et all (2007) approach to estimate the option-implied risk-neutral densities from the Brazilian Real/US Dollar exchange rate distribution. We then compare the RND with actual exchange rates, on a monthly basis, in order to estimate the relative risk-aversion of investors and also obtain a real-world density for the exchange rate. We are the first to calculate relative risk-aversion and the option-implied real world Density for an emerging market currency. Our empirical application uses a sample of exchange-traded Brazilian Real currency options from 1999 to 2011. The RND is estimated using a Mixture of Two Log-Normals distribution and then the real-world density is obtained by means of the Liu et al. (2007) parametric risk-transformations. Our estimated value of the relative risk aversion parameter is around 2.7, which is in line with other articles that have estimated this parameter for the Brazilian Economy. Our out-of-sample evaluation results showed that the RND has some ability to forecast the Brazilian Real exchange rate. However, when we incorporate the risk aversion into RND in order to obtain a Real-world density, the outof- sample performance improves substantially. Therefore, we would suggest not using the “pure” RND, but rather taking into account risk aversion in order to forecast the Brazilian Real exchange rate.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.bcb.gov.br/pec/wps/ingl/wps269.pdf
Download Restriction: no

Paper provided by Central Bank of Brazil, Research Department in its series Working Papers Series with number 269.

as
in new window

Length:
Date of creation: Mar 2012
Date of revision:
Handle: RePEc:bcb:wpaper:269
Contact details of provider: Web page: http://www.bcb.gov.br/?english

References listed on IDEAS
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.:

as in new window
  1. Marcos R. de Castro & Solange N. Gouvea & André Minella & Rafael C. dos Santos & Nelson F. Souza-Sobrinho, 2011. "SAMBA: Stochastic Analytical Model with a Bayesian Approach," Working Papers Series 239, Central Bank of Brazil, Research Department.
  2. Angelo M. Fasolo, 2011. "The Accuracy of Perturbation Methods to Solve Small Open Economy Models," Working Papers Series 262, Central Bank of Brazil, Research Department.
  3. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December.
  4. Jens Carsten Jackwerth, 1998. "Recovering Risk Aversion from Option Prices and Realized Returns," Finance 9803002, EconWPA.
  5. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
  6. Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 143-159, March.
  7. Benjamin M. Tabak & Dimas M. Fazio & Daniel O. Cajueiro, 2011. "Profit, Cost and Scale Efficiency for Latin American Banks: Concentration-Performance Relationship," Working Papers Series 244, Central Bank of Brazil, Research Department.
  8. Marian Micu, 2005. "Extracting expectations from currency option prices: a comparison of methods," Computing in Economics and Finance 2005 226, Society for Computational Economics.
  9. Leonardo S. Alencar, 2011. "Revisiting Bank Pricing Policies in Brazil: evidence from loan and deposit markets," Working Papers Series 235, Central Bank of Brazil, Research Department.
  10. Robert R. Bliss & Nikolaos Panigirtzoglou, 2004. "Option-Implied Risk Aversion Estimates," Journal of Finance, American Finance Association, vol. 59(1), pages 407-446, 02.
  11. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  12. Lycia M. G. Araujo & Guilherme M. R. Gomes & Solange M. Guerra & Benjamin M. Tabak, 2011. "Comparação da Eficiência de Custo para BRICs e América Latina," Working Papers Series 252, Central Bank of Brazil, Research Department.
  13. Marcos M. Abe & Eui J. Chang & Benjamin M. Tabak, 2007. "Forecasting Exchange Rate Density using Parametric Models: The Case of Brazil," Working Papers Series 138, Central Bank of Brazil, Research Department.
  14. Ricardo Schechtman & Wagner Piazza Gaglianone, 2011. "Macro Stress Testing of Credit Risk Focused on the Tails," Working Papers Series 241, Central Bank of Brazil, Research Department.
  15. Pierre-Richard Agénor & K. Alper & Luiz A. Pereira da Silva, 2011. "Capital Regulation, Monetary Policy and Financial Stability," Working Papers Series 237, Central Bank of Brazil, Research Department.
  16. Liu, Xiaoquan & Shackleton, Mark B. & Taylor, Stephen J. & Xu, Xinzhong, 2007. "Closed-form transformations from risk-neutral to real-world distributions," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1501-1520, May.
  17. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
  18. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-63, May.
  19. Yacine Aït-Sahalia & Andrew W. Lo, . "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," CRSP working papers 332, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
  20. Leonardo Soriano de Alencar & Márcio I. Nakane, 2003. "Real Balances in the Utility Function: Evidence for Brazil," Working Papers Series 68, Central Bank of Brazil, Research Department.
  21. Leonardo S. Alencar, 2011. "Um Exame sobre como os Bancos Ajustam seu Índice de Basileia no Brasil," Working Papers Series 251, Central Bank of Brazil, Research Department.
  22. Pierre-Richard Agénor & Luiz A. Pereira da Silva, 2013. "Macroprudential Regulation and the Monetary Transmission Mechanism," Centre for Growth and Business Cycle Research Discussion Paper Series 185, Economics, The Univeristy of Manchester.
  23. Tabak, Benjamin M. & Fazio, Dimas M. & Cajueiro, Daniel O., 2012. "The relationship between banking market competition and risk-taking: Do size and capitalization matter?," Journal of Banking & Finance, Elsevier, vol. 36(12), pages 3366-3381.
  24. Kabir K. Dutta & David F. Babbel, 2005. "Extracting Probabilistic Information from the Prices of Interest Rate Options: Tests of Distributional Assumptions," The Journal of Business, University of Chicago Press, vol. 78(3), pages 841-870, May.
  25. Arnildo da Silva Correa & Jaqueline Terra Moura Marins & Myrian Beatriz Eiras das Neves & Antonio Carlos Magalhães da Silva, 2011. "Credit Default and Business Cycles: an empirical investigation of Brazilian retail loans," Working Papers Series 260, Central Bank of Brazil, Research Department.
  26. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
  27. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
  28. Eduardo Luis Lundberg, 2011. "Bancos Oficiais e Crédito Direcionado – o que diferencia o mercado de crédito brasileiro?," Working Papers Series 258, Central Bank of Brazil, Research Department.
  29. Fabia A. de Carvalho & Marcos Valli, 2011. "Fiscal Policy in Brazil through the Lens of an Estimated DSGE Model," Working Papers Series 240, Central Bank of Brazil, Research Department.
  30. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  31. Leonardo Pio Perez, 2011. "Optimal costs of sovereign default," Working Papers Series 236, Central Bank of Brazil, Research Department.
  32. Pierre-Richard Agénor & K. Alper & L. Pereira da Silva, 2012. "Sudden Floods, Prudential Regulation and Stability in an Open Economy," Working Papers Series 267, Central Bank of Brazil, Research Department.
  33. Fabia A. de Carvalho, 2012. "Uma Breve Análise de Medidas Alternativas à Mediana na Pesquisa de Expectativas de Inflação do Banco Central do Brasil," Working Papers Series 264, Central Bank of Brazil, Research Department.
  34. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:bcb:wpaper:269. 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: (Francisco Marcos Rodrigues Figueiredo)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.