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Discussion Paper
The Low Volatility Puzzle: Is This Time Different?
As stock market volatility hovers near all-time lows, some analysts are questioning whether investors are complacent, drawing an analogy to the lead-up to the financial crisis. But, is this time different? We follow up on our previous post by investigating the persistence of low volatility periods. Historically, realized stock market volatility is persistent and mean-reverting: low volatility today predicts slightly higher, but still low, volatility one month and one year from now. Moreover, as of mid-September, the market is pricing implied volatility of 19 percent in one to two years? time. ...
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Equity Volatility Term Premia
This paper estimates the term-structure of volatility risk premia for the stock market. Realized variance term premia are increasing in systematic risk and predict variance swap returns. Implied volatility term premia are decreasing in risk initially, but then increase at a lag, predicting VIX futures returns. By modeling the logarithm of realized variance, the paper derives a closed-form relationship between the prices of variance swaps and VIX futures. The model provides accurate pricing and highlights periods of dislocation between the index options and VIX futures markets. Term premia ...
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Risk-Free Rates and Convenience Yields Around the World
We infer risk-free rates from index option prices to estimate safe asset convenience yields in ten G-11 currencies. Countries' convenience yields increase linearly with the level of their interest rates, with U.S. convenience yields being the fifth largest. During financial crises, convenience yields grow, but the difference between U.S. and foreign convenience yields generally does not. Covered interest parity (CIP) deviations using our option-implied rates are roughly the same size between the U.S. and each other country. A model where convenience yields depend on domestic financial ...
Discussion Paper
The Law of One Price in Equity Volatility Markets
Can option traders take a square root? Surprisingly, maybe not. This post shows that VIX futures prices exhibit significant deviations from their option-implied upper bounds—the square root of variance swap forward rates—thus violating the law of one price, a fundamental concept in economics and finance. The deviations widen during periods of market stress and predict the returns of VIX futures. Just as the stock market struggles with multiplication, the equity volatility market appears unable to take a square root at times.
Discussion Paper
The 2022 Spike in Corporate Security Settlement Fails
Settlement fails in corporate securities increased sharply in 2022, reaching levels not seen since the 2007-09 financial crisis. As a fraction of trading volume, fails that involve primary dealers reached an all-time high in the week of March 23, 2022. In this post, we investigate the 2022 spike in settlement fails for corporate securities and discuss potential drivers for this increase, including trading volume, corporate issuance, fails in bond ETFs, and operational problems.
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Merger options and risk arbitrage
Option prices embed predictive content for the outcomes of pending mergers and acquisitions. This is particularly important in merger arbitrage, where deal failure is a key risk. In this paper, I propose a dynamic asset pricing model that exploits the joint information in target stock and option prices to forecast deal outcomes. By analyzing how deal announcements affect the level and higher moments of target stock prices, the model yields better forecasts than existing methods. In addition, the model accurately predicts that merger arbitrage exhibits low volatility and a large Sharpe ratio ...
Discussion Paper
The Low Volatility Puzzle: Are Investors Complacent?
In recent months, some analysts and policymakers have raised concerns about the unusually low level of stock market volatility. For example, in the June Federal Open Market Committee (FOMC) minutes ?a few participants expressed concern that subdued market volatility, coupled with a low equity premium, could lead to a buildup of risks to financial stability.? In this post, we review this concern and find the evidence on investor complacency is mixed. On one hand, we present a view suggesting that historical volatility may have been abnormally high, rather than current volatility being ...
Discussion Paper
A Look at Convenience Yields around the World
This post estimates “convenience yields” for government debt in ten of the G11 currencies based on analysis from a recent paper. As in our companion post, we measure convenience yields with option-implied box rate data that is estimated from options traded on the main stock market index in each country. We find that a country’s average convenience yield is closely related to its level of interest rates. In addition, we find that average covered interest parity (CIP) deviations are roughly the same across countries when they are measured with box rates. We rationalize these findings with ...
Discussion Paper
Short-Dated Term Premia and the Level of Inflation
Since the advent of derivatives trading on short-term interest rates in the 1980s, financial commentators have often interpreted market prices as directly reflecting the expected path of future interest rates. However, market prices generally embed risk premia (or “term premia” in reference to measures of risk premia over different horizons) reflecting the compensation required to bear the risk of the asset. When term premia are large in magnitude, derivatives prices may differ substantially from investor expectations of future rates. In this post, we assess whether term premia have ...
Discussion Paper
Options for Calculating Risk-Free Rate
One of the most fundamental concepts in finance is the notion of a risk-free rate. This interest rate tells us how much money investors are guaranteed to receive in the future by saving one dollar today. As a result, risk-free rates reflect investors’ preferences for payoffs in the future relative to the present. Yields on U.S. Treasury securities are generally viewed as a standard benchmark for the risk-free rate, but they may also feature a “convenience yield,” reflecting Treasuries’ special, money-like properties. In this post, we estimate a risk-free rate implicit in the prices of ...