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Empirical evidence of the hedging pressure risk premium exists only in the futures contracts with delivery-related options. Since hedging pressure is supposed to exist for all futures contracts, the empirical evidence raises an interesting empirical question: whether the hedging pressure risk premium is in fact the risk premium associated with the delivery-related options. This chapter contains an empirical test of the non-redundancy between the two related but alternative sources of non-market risks. For the test, we employs a futures risk premia model in which the expected futures returns contain the market risk premium (proxied by the equity market risk premium) and two non-market risk premia (proxied by the hedging pressure effect and by the delivery risk premium reflected in the returns of futures options, respectively). Our main finding is that both the hedging pressure and the delivery risk premia are non-redundant and statistically significant for futures contracts with delivery-related options. This finding implies a substantial degree of segmentations between these futures markets and the underlying asset markets.

Volatility has become a traded commodity, and the value of extricating the implied volatility for a given underlying asset’s market value from observed option premia has long been recognized. This contribution offers a least-squared error approach based on Standardized Options that offers the potential to overcome the well-known problem of “smiles and frowns.”

The topic of volatility measurement and estimation is central to financial and more generally time-series econometrics. In this chapter, we begin by surveying models of volatility, both discrete and continuous, and then we summarize some selected empirical findings from the literature. In particular, in the first sections of this chapter, we discuss important developments in volatility models, with focus on time-varying and stochastic volatility as well as nonparametric volatility estimation. The models discussed share the common feature that volatilities are unobserved and belong to the class of missing variables. We then provide empirical evidence on “small” and “large” jumps from the perspective of their contribution to overall realized variation, using high-frequency price return data on 25 stocks in the DOW 30. Our “small” and “large” jump variations are constructed at three truncation levels, using extant methodology of Barndorff-Nielsen and Shephard (2006), Andersen, Bollerslev, and Diebold (2007), and Aït-Sahalia and Jacod (2009a, 2009b, 2009c). Evidence of jumps is found in around 22.8% of the days during the 1993–2000 period, much higher than the corresponding figure of 9.4% during the 2001–2008 period. Although the overall role of jumps is lessening, the role of large jumps has not decreased, and indeed, the relative role of large jumps, as a proportion of overall jumps, has actually increased in the 2000s.

How do stock prices evolve over time? The standard assumption of geometric Brownian motion, questionable as it has been right along, is even more doubtful in light of the recent stock market crash and the subsequent prices of U.S. index options. With the development of rich and deep markets in these options, it is now possible to use options prices to make inferences about the risk-neutral stochastic process governing the underlying index. We compare the ability of models including Black–Scholes, naïve volatility smile predictions of traders, constant elasticity of variance, displaced diffusion, jump diffusion, stochastic volatility, and implied binomial trees to explain otherwise identical observed option prices that differ by strike prices, times-to-expiration, or times. The latter amounts to examining predictions of future implied volatilities.

Certain naïve predictive models used by traders seem to perform best, although some academic models are not far behind. We find that the better-performing models all incorporate the negative correlation between index level and volatility. Further improvements to the models seem to require predicting the future at-the-money implied volatility. However, an “efficient markets result” makes these forecasts difficult, and improvements to the option-pricing models might then be limited.

The pricing kernel puzzle of Jackwerth (2000) concerns the fact that the empirical pricing kernel implied in S&P 500 index options and index returns is not monotonically decreasing in wealth as standard economic theory would suggest. Thus, those options are currently priced in a way such that any risk-averse investor would increase his/her utility by trading in them. We provide a representative agent model where volatility is a function of a second momentum state variable. This model is capable of generating the empirical patterns in the pricing kernel, albeit only for parameter constellations that are not typically observed in the real world.

Theory suggests that as long as a country runs a balanced budget regime, there is no linkage between fiscal variables and the interest rates. In the case of fiscal expansion that is not sufficiently covered by government revenues, however, the government has two options to finance its deficit: printing money or additional borrowing. Both options lead to an increase in the risk premia on government bonds. One strand of literature focuses on a currency crisis that emerges as a necessary outcome in light of contradictions between fixed exchange rate, and fiscal and financial fundamentals. If government bonds are denominated in domestic currency, the government can reduce their real value by higher inflation or by devaluation of the national currency. In order to bear this risk foreign investors require a currency risk premium. Governments can eliminate the risk of currency devaluation by issuing bonds denominated in foreign currencies, but the default risk remains and it depends on public finances. Another strand of the literature looks at the relation between fiscal variables and government bond yields in the framework of portfolio balance model.

The currency premium is one of the three components of the differential between local and foreign interest rates. Emerging economies such as South Africa typically face positive interest rate differentials, that is, a higher cost of capital than developed economies. In this chapter we aim at identifying the determinants of the South African rand–U.S. dollar currency premium using monthly data over the period 1997–2008. We carry out an empirical analysis using dynamic time series econometric techniques to estimate the determinants of the one-month and one-year currency premia. Our findings show that the currency premia at both horizons are driven by long-run movements in the expected inflation differential between South Africa and the United States, risk aversion as a proxy for the price of rand exchange risk, and the volatility of the rand exchange rate as an indicator of the quantity of that risk. Misalignments in the real effective or rand–U.S. dollar bilateral exchange rates display mixed results in terms of their impact and statistical significance on both currency premium. Our parameter estimators overall are stable and robust to sample variations. Monetary policy is an important determinant of currency premia at both one-month and one-year horizons, but risk aversion is equally important to determine its time fluctuations.

The purpose of this chapter is to outline new methodological developments in business valuation, with particular attention to how those developments are being used in litigation involving lost profits and the value of operating businesses. In addition to methodological developments, the chapter also includes a discussion of recent legal developments, particularly selected cases that affect the use and standards for business valuation techniques within litigation settings. Finally, the chapter includes a mathematical appendix.

Long-term interest rates of small open economies (SOE) correlate strongly with the USA long-term rate. Can central banks in those countries decouple from the United States? An estimated Dynamic Stochastic General Equilibrium (DSGE) model for the UK (vis-á-vis the USA) establishes three structural empirical results: (1) Comovement arises due to nominal fluctuations, not through real rates or term premia; (2) the cause of comovement is the central bank of the SOE accommodating foreign inflation trends, rather than systematically curbing them; and (3) SOE may find themselves much more affected by changes in USA inflation trends than the United States itself. All three results are shown to be intuitive and backed by off-model evidence.