References
- Andersen, L. (2011). Option Pricing with quadratic volatility: a revisit. Finance and Stochastics, 15(2), 191–219. http://dx.doi.org/10.1007/s00780-010-0142-8 doi: 10.1007/s00780-010-0142-8
- Bahra, B. (1997). Implied Risk-Neutral Probability Density Functions from Options Prices: Theory and Application. Bank of England Working papers. London: Bank of England.
- Breeden, D. T., & Litzenberger, R. H. (1978). Prices of state-contingent claims implicit in option prices. The Journal of Business, 51(4), 621–651. http://dx.doi.org/10.1086/296025 doi: 10.1086/296025
- Brunner, B., & Hafner, R. (2003). Arbitrage-free estimation of the risk-neutral density from the implied volatility smile. Journal of Computational Finance, 7(1), 75–106.
- de Jong, C., & Huisman, R. (2000). From skews to a skewed-t: modelling option-implied returns by a skewed student-t. Computational Intelligence for Financial Engineering, Proceedings of the IEEE 2000 Conference, 132–142. http://dx.doi.org/10.1109/CIFER.2000.844611
- Dumas, B., Fleming, J., & Whaley, R. E. (1998). Implied volatility functions: empirical tests. The Journal of Finance, 53(6), 2059–2106. http://dx.doi.org/10.1111/0022-1082.00083 doi: 10.1111/0022-1082.00083
- Fabozzi, F., Tunaru, R., & Albota, G. (2009). Estimating risk-neutral density with parametric models in interest rate markets. Quantitative Finance, 9(1), 55–70. http://dx.doi.org/10.1080/14697680802272045 doi: 10.1080/14697680802272045
- Federal Reserve Bank of Minneapolis. (2013). Methodology for estimating risk-neutral probability density functions. Paper available from author.
- Figlewski, S. (2008). Estimating the Implied Risk-neutral Density for the US Market Portfolio. Volatility and Time-series Econometrics: Essays in Honor of Robert F. Engle. Oxford, UK: Oxford University Press.
- Hull, J. C. (2003). Options, Futures, and Other Derivatives (7th ed.). Upper Saddle River, New Jersey: Pearson Education, Inc.
- Jackwerth, J. C. (2000). Recovering risk aversion from option prices and realized returns. Review of Financial Studies, 13(2), 433–451. http://dx.doi.org/10.1093/rfs/13.2.433 doi: 10.1093/rfs/13.2.433
- Jones, E., Oliphant, E., & Peterson, P. (2001). SciPy: Open source scientific tools for Python. Retrieved from http://www.scipy.org
- Melick, W. R., & Thomas, C. P. (1997). Recovering an asset’s implied PDF from option prices: an application to crude oil during the Gulf crisis. Journal of Financial and Quantitative Analysis, 32(1), 91–115. http://dx.doi.org/10.2307/2331318
- Mizrach, B. (2007). Recovering probabilistic information from options prices and the underlying. Rutgers University. Retrieved from http://www.fdic.gov/bank/analytical/cfr/2007/apr/mizrach.pdf
- Poon, S. H., & Granger, C. (2005). Practical issues in forecasting volatility. Financial Analysts Journal, 61(1), 45–56. http://dx.doi.org/10.2469/faj.v61.n1.2683 doi: 10.2469/faj.v61.n1.2683
- Shimko, D. C. (1993). Bounds of probability. Risk (Concord, NH), 6(4), 33–37.
- Shimko, D.C. (1994). Optimal probability trading strategies. J.P. Morgan Securities Derivatives Research, 1–8. Paper available from author.
- Wilmott, P. (1998). Derivatives: The Theory and Practice of Financial Engineering (1st ed.). West Sussex: John Wiley and Sons.