For Banks
Banking and Financial StudiesRisk-Neutral Probability Density Functions
- Commentary
- Feedback
- Archive of past exhibits
- About this report
- How to interpret the risk-neutral probability density functions
- Methodology
Updated with data through May 16, 2013
Latest Report
May 16, 2013 [PDF]
Commentary
Trading in options on bank stocks was near six month averages last week. Upside volume percentages were high the CCAR firms (note the last blue bar in the chart below). Spot returns in the group were up smartly again including double digit percentage increases for MS and STT over the past two weeks. The median CCAR bank stock rose 6.6%.
RNPD standard deviations generally rose modestly relative to our last report and RNPD skews became less negative. Risk neutral probabilities of large changes remain in their downward trends.
Additional notes:
- Trading in options on BK stock was almost entirely below the current spot price. These shares rose approximately 7% over the past two weeks.
- MS options volumes were quite strong again last week. The RNPD was largely unchanged.
Other Commodity Markets
We continue to measure high volumes in the options markets across the spectrum of commodities and indices we follow. Changes in RNPD standard deviations derived from options were mixed, rising for the precious metals and the S&P 500, but falling for the grains.
Additional notes:
- Risk neutral probabilities of large downside moves in the S&P 500 remain elevated relative to large upside moves. RNPD standard deviations and skews rose last week as well. (See S&P 500 reports)
- Risk neutral probabilities of large upside moves fell in the grain markets last week as did RNPD standard deviations. Volatility smiles shifted lower. (See grain market reports)
- Gold and Silver spot prices reversed their rallies from two weeks ago. The RNPD skew for gold became more negative again last week. Tail risks, as measured by both RNPD standard deviation and risk neutral probabilities of large moves, rose in both markets. (See Gold and Silver reports)
- Options on exchange rate futures continue to trade actively in all three currencies we follow. Statistics from RNPDs derived from options on exchange rate futures remained largely unchanged again last week. (See exchange rate reports)
- The DJ Real Estate Index rose 2.1% over the past two weeks. The RNPD skew derived from options on the ETF became more negative and the standard deviation rose. These changes occurred on light trading. (See real estate report)
Feedback
Please send comments and suggestions to: option-report-feedback@mpls.frb.org.
Archive of past exhibits
About this report
Large changes in asset values or commodities prices can be associated with significant changes in economic output and price and financial stability. For that reason, policymakers seek to monitor market concerns about extreme movements—so-called tail events—in key asset and commodities markets. The prices of options to buy (“call options”) or sell (“put options”) assets or commodities in the future at specified prices (“strike prices”) provide valuable information about potential tail events. The prices of call and put options with differing strike prices can be used to estimate a probability density function of the payoff of the underlying asset or commodity.
In this report, we use options prices to produce what are known as “risk-neutral probability density functions” (RNPDs) for future asset and commodity values. Interpreting RNPDs can be subtle, because they combine both investors’ expectations of the future price of the traded asset or commodity and the compensation they received for taking on related aggregate economic risks. The changes over time in RNPDs that we show reflect changes to both of these components, and decomposing the change into the constituent parts is not possible without making additional strong assumptions. Nonetheless, we regard the RNPDs shown here as valuable barometers of financial market sensitivity to possible extreme movements in the prices of key assets and commodities.
We welcome feedback on all aspects of the report and material on this web page, which we consider a “work in progress.” Please send comments and suggestions to: option-report-feedback@mpls.frb.org.
How to Interpret the Risk-Neutral Probability
Density Functions
The exhibits contained in this report show density functions at three different points in time, allowing viewers to see how risk-neutral expectations of market participants have evolved over time. Specifically, we think it isuseful to examine the following characteristics within each exhibit and note how they have changed over time:
- Central tendency—Has the center of the density function shifted toward higher or lower values?
- Dispersion—Is the majority of the density function more or less tightly concentrated around its midpoint? One possible reason for a density function that is becoming less concentrated (and is more widely spread out) would be that investors are more uncertain about the future value of the asset.
- Skewness—Is the density function largely symmetric around its midpoint, or is it skewed to the right or the left? The latter would suggest that investors are more concerned about changes in one direction than the other.
- Tail thickness—Do the density functions have roughly the same amount of mass in their tails? If the weight present in one or both tails suddenly increases, it could indicate that the probability of a large change has increased.
Methodology for Estimating Risk Neutral Probability Density Functions
How the Minneapolis Fed estimates Risk Neutral Probability Density Functions [PDF]
