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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 ...
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
How Has Post-Crisis Banking Regulation Affected Hedge Funds and Prime Brokers?
“Arbitrageurs” such as hedge funds play a key role in the efficiency of financial markets. They compare closely related assets, then buy the relatively cheap one and sell the relatively expensive one, thereby driving the prices of the assets closer together. For executing trades and other services, hedge funds rely on prime brokers and broker-dealers. In a previous Liberty Street Economics blog post, we argued that post-crisis changes to regulation and market structure have increased the costs of arbitrage activity, potentially contributing to the persistent deviations in the prices of ...
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 ...
Report
Dealer Capacity and U.S. Treasury Market Functionality
We show a significant loss in U.S. Treasury market functionality when intensive use of dealer balance sheets is needed to intermediate bond markets, as in March 2020. Although yield volatility explains most of the variation in Treasury market liquidity over time, when dealer balance sheet utilization reaches sufficiently high levels, liquidity is much worse than predicted by yield volatility alone. This is consistent with the existence of occasionally binding constraints on the intermediation capacity of bond markets.
Report
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
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
Treasury Market When-Issued Trading Activity
When the U.S. Treasury sells a new security, the security is announced to the public, auctioned a number of days later, and then issued sometime after that. When-issued (WI) trading refers to trading of the new security after the announcement but before issuance. Such trading promotes price discovery, which may reduce uncertainty at auction, potentially lowering government borrowing costs. Despite the importance of WI trading, and the advent of Treasury trading volume statistics from the Financial Industry Regulatory Authority (FINRA), little is known publicly about the level of WI activity. ...
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.
Report
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 ...