Implied Filtering Densities on Volatility's Hidden State

We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using Bayesian filtering. However, derivative data can be considered as conditional expectations that are already observed in the market, and which can be used as input to an inverse problem whose solution is an implied conditional density on volatility. Our analysis relies on a specification of the martingale change of measure, which we refer to as \textit{separability}. This specification has a multiplicative component that behaves like a risk premium on volatility uncertainty in the market. When applied to SPX options data, the estimated model and implied densities produce variance-swap rates that are consistent with the VIX volatility index. The implied densities are relatively stable over time and pick up some of the monthly effects that occur due to the options' expiration, indicating that the volatility-uncertainty premium could experience cyclic effects due to the maturity date of the options

Cross-correlation of long-range correlated series

A method for estimating the cross-correlation $C_{xy}(\tau)$ of long-range correlated series $x(t)$ and $y(t)$, at varying lags $\tau$ and scales $n$, is proposed. For fractional Brownian motions with Hurst exponents $H_1$ and $H_2$, the asymptotic expression of $C_{xy}(\tau)$ depends only on the lag $\tau$ (wide-sense stationarity) and scales as a power of $n$ with exponent ${H_1+H_2}$ for $\tau\to 0$. The method is illustrated on (i) financial series, to show the leverage effect; (ii) genomic sequences, to estimate the correlations between structural parameters along the chromosomes.Comment: 14 pages, 8 figure

Futures trading, spot price volatility and market efficiency: evidence from European real estate securities futures

In 2007 futures contracts were introduced based upon the listed real estate market in Europe. Following their launch they have received increasing attention from property investors, however, few studies have considered the impact their introduction has had. This study considers two key elements. Firstly, a traditional Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, the approach of Bessembinder & Seguin (1992) and the Gray’s (1996) Markov-switching-GARCH model are used to examine the impact of futures trading on the European real estate securities market. The results show that futures trading did not destabilize the underlying listed market. Importantly, the results also reveal that the introduction of a futures market has improved the speed and quality of information flowing to the spot market. Secondly, we assess the hedging effectiveness of the contracts using two alternative strategies (naïve and Ordinary Least Squares models). The empirical results also show that the contracts are effective hedging instruments, leading to a reduction in risk of 64 %

Debt Maturity Choices, Multi-stage Investments and Financing Constraints

We develop a dynamic investment options framework with optimal capital structure and analyze the effect of debt maturity. We find that in the absence of financing constraints short-term debt maximizes firm value. In contrast with most literature results, in the absence of constraints, higher volatility may increase initial debt for firms with low initial revenues, issuing long term debt that expires after the investment option maturity. This effect, which is due to the option value of receiving the value of assets and remaining tax savings, does not hold for short term debt and firms with high profitability, where an increase in volatility reduces the firm value. The importance of short-term debt is reduced in the presence of non-negative equity net worth or debt financing constraints and firms behave more conservatively in the use of initial debt. With non-negative equity net worth, higher volatility has adverse effects on the firm value, while with debt financing constraints higher volatility may enhance firm value for firms with relatively low revenue that have out-of-the-money investment options