Variance swaps and intertemporal asset pricing (original) (raw)
Related papers
2018
This paper proposes a tractable self-exciting double-jump model for stock return and its variance processes, extending existing two-factor term structure models of variance swap rates in the literature to a new three-factor model. Various goodness-of-fit tests show that our three-factor model outperforms the two-factor model in fitting the S&P 500 return and its variance swap rates. Importantly, our three factors can significantly predict aggregate equity returns as opposed to the ones proposed in the traditional two-factor models in the literature. In stark contrast to the existing literature, our empirical results indicate that variance swap rates have more powerful predictive ability than variance risk premiums (VRPs) for the market returns as suggested by the stock price models investigated in the present paper. Unlike the popular double-jump model in the literature, our new model allows us to solve the optimal variance swap investment in a semi-closed form which greatly facilit...
The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments
Journal of Financial and Quantitative Analysis, 2010
This paper performs specification analysis on the term structure of variance swap rates on the S&P 500 index and studies the optimal investment decision on the variance swaps and the stock index. The analysis identifies 2 stochastic variance risk factors, which govern the short and long end of the variance swap term structure variation, respectively. The highly negative estimate for the market price of variance risk makes it optimal for an investor to take short positions in a short-term variance swap contract, long positions in a long-term variance swap contract, and short positions in the stock index. * Egloff, daniel.egloff@quantcatalyst.com, QuantCatalyst,
Variance Risk Premium Demystified
SSRN Electronic Journal, 2008
We study the dynamics and cross-sectional properties of the variance risk premia embedded in options on stocks and indices, approximated by the synthetic variance swap returns. Several important stylized facts and contributions arise. First, variance risk premia for indices are systematically larger (more negative) than for individual securities. Second, there are systematic cross-sectional differences in the price of variance in individual stocks. Linking variance swaps to firm size/bookto-market, and stock turnover characteristics, an investor gains access to several lucrative long-short strategies with Sharpe Ratios around 2.85. Third, principal component analysis reveals at most one important factor driving both stock and variance swap returns, which corresponds to the traditional market factor. For the remainder of the dynamics, the stock and its variance processes are nearly linearly independent. Fourth, we find the leverage effect through analysis of the relationship between the variance risk premium and stock to variance correlation. The systematic (market factor) part of the leverage effect provides additional evidence of the existence of one factor common to both variance swaps and stocks, but the contribution of the market risk premium to the total variance premium is very small. These findings stress the importance of using variance-based instruments in the portfolio of an investor.
Ariance Swaps , Non-Normality and Macroeconomic and Financial Isks
2014
This paper studies the determinants of the variance risk premium and discusses the hedging possibilities offered by variance swaps. We start by showing that the variance risk premium responds to changes in higher order moments of the distribution of market returns. But the uncertainty that determines the variance risk premium – the fear by investors to deviations from normality in returns – is also strongly related to a variety of macroeconomic and financial risks associated with default, employment growth, convailable online 19 December 2013 eywords: ariance risk premium on-normality conomic risks sumption growth, stock market and market illiquidity risks. We conclude that the variance risk premium reflects the market willingness to pay for hedging against these financial and macroeconomic sources of risk. An out-of-sample asset allocation exercise shows that the inclusion of the variance swap reduces the modified value-at-risk with respect to a portfolio holding exclusively the eq...
Hedging (Co)Variance Risk with Variance Swaps
International Journal of Theoretical and Applied Finance, 2011
In this paper, we quantify the impact on the representative agent's welfare of the presence of derivative products spanning covariance risk. In an asset allocation framework with stochastic (co)variances, we allow the agent to invest not only in the stocks but also in the associated variance swaps. We solve this optimal portfolio allocation program using the Wishart Affine Stochastic Correlation framework, as introduced in Da Fonseca, Grasselli and Tebaldi (2007): it shares the analytical tractability of the single-asset counterpart represented by the [36] model and it seems to be the natural framework for studying multivariate problems when volatilities as well as correlations are stochastic. What is more, this framework shows how variance swaps can implicitly span the covariance risk. We provide the explicit solution to the portfolio optimization problem and we discuss the structure of the portfolio loadings with respect to model parameters. Using real data on major indexes, w...
We propose a direct and robust method for quantifying the variance risk premium on financial assets. We show that the risk-neutral expected value of return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. We propose to use the difference between the realized variance and this synthetic variance swap rate to quantify the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premiums on five stock indexes and 35 individual stocks. (JEL G10, G12, G13)
Variance trading and market price of variance risk
Journal of Econometrics, 2014
This paper develops a new approach for variance trading. We show that the discretely-sampled realized variance can be robustly replicated under very general conditions, including when the price can jump. The replication strategy specifies the exact timing for rebalancing in the underlying. The deviations from the optimal schedule can lead to surprisingly large hedging errors. In the empirical application, we synthesize the prices of the variance contract on S&P 500 index over the period from 01/1990 to 12/2009. We find that the market variance risk is priced, its risk premium is negative and economically very large. The variance risk premium cannot be explained by the known risk factors and option returns.
Variance swaps on defaultable assets and market implied time-changes. Unpublished manuscript
2013
We compute the value of a variance swap when the underlying is modeled as a Markov process time changed by a Lévy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent Lévy measure, local stochastic volatility and have a local stochastic default intensity. Moreover, the Lévy subordinator that drives the underlying can be obtained directly by observing European call/put prices. To illustrate our general framework, we provide an explicit formula for the value of a variance swap when the diffusion is modeled as (i) a Lévy subordinated geometric Brownian motion with default and (ii) a Lévy subordinated Jump-to-default CEV process (see Carr and Linetsky (2006)). Our results extend the results of Mendoza-Arriaga et al. (2010), by allowing for joint valuation of credit and equity derivatives as well as variance swaps.
Variance Swaps on Defaultable Assets and Market Implied Time-Changes
SIAM Journal on Financial Mathematics, 2016
We compute the value of a variance swap when the underlying is modeled as a Markov process time changed by a Lévy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent Lévy measure, local stochastic volatility and have a local stochastic default intensity. Moreover, the Lévy subordinator that drives the underlying can be obtained directly by observing European call/put prices. To illustrate our general framework, we provide an explicit formula for the value of a variance swap when the diffusion is modeled as (i) a Lévy subordinated geometric Brownian motion with default and (ii) a Lévy subordinated Jump-to-default CEV process (see Carr and Linetsky (2006)). Our results extend the results of Mendoza-Arriaga et al. (2010), by allowing for joint valuation of credit and equity derivatives as well as variance swaps.