Narrow Results

A time series model for the FX dynamics is presented which takes into account structural peculiarities of the market, namely its heterogeneity and an information flow from long to short time horizons. The model emerges from an analogy between FX dynamics and hydrodynamic turbulence. The heterogeneity of the market is modeled in the form of a multiplicative cascade of time scales ranging from several minutes to a few months, analogous to the Kolmogorov cascade in turbulence.

The model reproduces well the important empirical characteristics of FX rates for major currencies, as the heavy-tailed distribution of returns, their change in shape with the increasing time interval, and the persistence of volatility.

We perform out-of-sample prediction on both fixed and black market Chinese renminbi/US dollar, and black market rial/US dollar exchange rates by using the time-delay embedding technique and the local linear prediction method. We also predict an artificially generated chaotic time series with and without noise for the purpose of validation of the methods used in this study. In all examples tested, our prediction results significantly outperform those by the benchmark mean value predictor based on a statistic defined by Harvey et al. [11]. Another interesting result found in this paper is that one may use the embedding dimension as a measure of volatility of a financial asset.

In this article we model the stock market volatility in the US, the UK, France, Germany and Japan by means of using fractionally integrated techniques. The results, based on the tests of Robinson [24] show that the volatility series can be well described in terms of I(d) statistical processes, with d higher than 0.5 but smaller than 1, implying thus nonstationary but mean-reverting behaviour.

In this paper, we test for causal relationship between China's stock markets by using returns and a measure of volatility for the Shanghai Composite index, the Shenzhen Composite Subindex, and the Hong Kong Hang Seng Index. We also show that the stock index series are nonstationary and that cointegrating vectors and error correction models do not exist for the series.

Based on these tests, for the return series, we conclude that Shenzhen Granger caused Shanghai before 1994. For the volatility data, we find that there exists a positive feedback relationship between Shanghai and Shenzhen stock markets, and that Hong Kong volatility Granger causes Shanghai volatility, but not vice versa.

This paper uses a new restriction imposed by the no-arbitrage condition on interest rate processes to estimate the parameters of the short-term rates for US, France, UK and Germany. A general process that nests almost all previous one-factor models is estimated. The results show that the volatility structure of US short-term rate is similar to the processes suggested by Duffie and Kahn [9] or Chan et al. [4] depending on the proxy used for the short-term rate and the time period covered by the study. The volatility structures of the short-term rates in France and Germany do not have constant elasticity with respect to the short-term rate, while the elasticity of UK's short-term rate is constant and equal to 1.5.

There are two common methods for pricing European call options on a stock with known dividends. The market practice is to use the Black–Scholes formula with the stock price reduced by the present value of the dividends. An alternative approach is to increase the strike price with the dividends compounded to expiry at the risk-free rate. These methods correspond to different stock price models and thus in general give different option prices. In the present paper we generalize these methods to time- and level-dependent volatilities and to arbitrary contract functions. We show, for convex contract functions and under very general conditions on the volatility, that the method which is market practice gives the lower option price. For call options and some other common contracts we find bounds for the difference between the two prices in the case of constant volatility.

In this paper, we investigate the price interdependence between seven international stock markets, namely Irish, UK, Portuguese, US, Brazilian, Japanese and Hong Kong, using a new testing method, based on the wavelet transform to reconstruct the data series, as suggested by Lee [11]. We find evidence of intra-European (Irish, UK and Portuguese) market co-movements with the US market also weakly influencing the Irish market. We also find co-movement between the US and Brazilian markets and similar intra-Asian co-movements (Japanese and Hong Kong). Finally, we conclude that the circle of impact is that of the European markets (Irish, UK and Portuguese) on both American markets (US and Brazilian), with these in turn impacting on the Asian markets (Japanese and Hong Kong) which in turn influence the European markets. In summary, we find evidence for intra-continental relationships and an increase in importance of international spillover effects since the mid 1990s, while the importance of historical transmissions has decreased since the beginning of this century.

The aim of this paper is to study the impact of stock returns volatility of reference entities on credit default swap rates using a new dataset from the Japanese market. The majority of empirical research suggests the inadequacy of multinormal distribution and then the failure of methods based on correlation for measuring the structure of dependency. Using a copula approach, we can model the different relationships that can exist in different ranges of behavior. We study the bivariate distributions of credit default swap rates and the measure of stock return volatility estimated with GARCH (1,1) and focus on one parameter Archimedean copula. Starting from the empirical rank correlation statistics (Kendall's tau and Spearman's rho), we estimate the parameter values of each copula function presented in our study. Then, we choose the appropriate Archimedean copula that better fit to our data. We emphasize the finding that pairs with higher rating present a weaker dependence coefficient and then, the impact of stock return volatility on credit default swap rates is higher for the lowest rating class.

We generalize earlier results on barrier options for puts and calls and log-normal stock processes to general local volatility models and convex contracts. We show that Γ ≥ 0, that Δ has a unique sign and that the option price is increasing with the volatility for convex contracts in the following cases:

• If the risk-free rate of return dominates the dividend rate, then it holds for up-and-out options if the contract function is zero at the barrier and for down-and-in options in general.

• If the risk-free rate of return is dominated by the dividend rate, then it holds for down-and-out options if the contract function is zero at the barrier and for up-and-in options in general.

We apply our results to show that a hedger who misspecifies the volatility using a time-and-level dependent volatility will super-replicate any claim satisfying the above conditions if the misspecified volatility dominates the true (possibly stochastic) volatility almost surely.

Results in He–Leland (1993) are extended and properties of the risk-premium process in an equilibrium are examined in a pure exchange economy with a representative agent: for example, (i) the risk-premium process is characterized by using a martingale representation of the reciprocal of a terminal marginal utility, (ii) it is expressed as a (conditional) expected value including the relative risk aversion coefficient of a terminal utility and the Jacobian matrix process of the state variables, and, (iii) a "mean-reverting" property relates to the monotonic decreasing property of the relative risk aversion coefficient.

This paper investigates the volatility process of the Brent crude oil futures markets using Markov-switching ARCH (SWARCH) model. The SWARCH model allows the conditional disturbances to change as time passes and even to switch in different regimes. The empirical evidence shows that the SWARCH (3,3) model performs the best goodness of fit and the best forecast performance among different fitting models. The estimation of smoothing probabilities of data under different regimes facilitates to capture the characteristics of the data, and the high-volatility regime is associated with some extraordinary events, such as the 1990's Persian Gulf War, the 1997's Asia Financial Crisis, and the 2001's 911 terrorist attack.

In this paper, fractional integrating dynamics in the return and the volatility series of stock market indices are investigated. The investigation is conducted using wavelet ordinary least squares, wavelet weighted least squares and the approximate Maximum Likelihood estimator. It is shown that the long memory property in stock returns is approximately associated with emerging markets rather than developed ones while strong evidence of long range dependence is found for all volatility series. The relevance of the wavelet-based estimators, especially, the approximate Maximum Likelihood and the weighted least squares techniques is proved in terms of stability and estimation accuracy.

We propose a Credit Value Adjustment (CVA) model capturing the Wrong Way Risk (WWR) that is not product-specific and is suitable for large-scale computations. The model is based on a doubly stochastic default process with the default intensities proxied by credit spreads. For different exposure structures, we show how credit–market correlation affects the CVA level, its sensitivities to credit and market factors, its volatility and the quality of hedging. The WWR is most significant for exposures highly sensitive to the market volatility in a situation when credit spreads are at moderate levels but both the market factors and credit spreads are volatile. In such conditions, ignoring credit–market correlations results in important CVA mispricing. While the benefits from hedging are always magnified in the situation of the WWR, the right way exposure case is more delicate: only a well-designed mix of credit and market hedges can bring volatility down. Our results raise doubts on the Basel III policy of recognizing credit but not market hedges for computing the CVA volatility capital charge.

This paper investigates the relationship between volatility and liquidity on the German electricity futures market based on high-frequency intraday prices. We estimate volatility by the time-weighted realized variance acknowledging that empirical intraday prices are not equally spaced in time. Empirical evidence suggests that volatility of electricity futures decreases as time approaches maturity, while coincidently liquidity increases. Established continuous-time stochastic models for electricity futures prices involve a growing volatility function in time and are thus not able to capture our empirical findings a priori. In Monte Carlo simulations, we demonstrate that incorporating increasing liquidity into the established models is key to model the decreasing volatility evolution.

In this paper, we introduce a dynamical model for the time evolution of probability density functions incorporating uncertainty in the parameters. The uncertainty follows stochastic processes, thereby defining a new class of stochastic processes with values in the space of probability densities. The purpose is to quantify uncertainty that can be used for probabilistic forecasting. Starting from a set of traded prices of equity indices, we do some empirical studies. We apply our dynamic probabilistic forecasting to option pricing, where our proposed notion of model uncertainty reduces to uncertainty on future volatility. A distribution of option prices follows, reflecting the uncertainty on the distribution of the underlying prices. We associate measures of model uncertainty of prices in the sense of Cont.

The Radial Basis Functions (RBF) interpolation is a popular approximation technique used to smooth scattered data in various dimensions. This study uses RBF interpolation to interpolate the volatility skew of the S&P500 index options. The interpolated skews are used to construct the risk-neutral densities of the index and its local volatility surface. The RBF interpolation is contrasted throughout the study with the cubic spline interpolation. An analysis of the densities and the local volatility shows that RBF are an effective and practical tool for interpolating the implied volatility surface.

We study a series of static and dynamic portfolios of Volatility Index (VIX) futures and their effectiveness to track the VIX. We derive each portfolio using optimization methods, and evaluate its tracking performance from both empirical and theoretical perspectives. Among our results, we show that static portfolios of different VIX futures fail to track VIX closely. VIX futures simply do not react quickly enough to movements in the spot VIX. In a discrete-time model, we design and implement a dynamic trading strategy that adjusts daily to optimally track VIX. The model is calibrated to historical data and a simulation study is performed to understand the properties exhibited by the strategy. In addition, compared to the volatility ETN, VXX, we find that our dynamic strategy has a superior tracking performance.

This primer provides a pairwise comparison of cryptocurrency characteristics with those of fiat currency and hard commodities to shed light on the nexus between cryptocurrencies, fiat currency, and hard commodities. Then, it synthesizes methods and results from empirical research that investigate the nexus. The findings reveal that the existing literature has not reached a consensus on the nature of cryptocurrencies, in particular whether they should be categorized as a currency or a commodity which indicates the research area is not yet saturated.

The following sections are included:

• Average Returns are the Main Focus
• Compound Return Facts: Tail Risks Dominate!
• Compound Returns a Function of Risk
• Big Problem: Tail Events More Frequent than Normal Distribution
• Think Tails of the Distribution: Concentrate on Normal Events
• Relative Performance Evaluation
• Investment Strategies — Asset Allocation Static Constraints are Costly
• Factors that Affect Terminal Wealth
• Measuring Tail Risk Using Market Prices
• Tail Gains/Losses from Opiton Prices
• Enhancing Compound Returns Through Dynamic Risk Management (1996—2015)
• Using Option Prices to Forecast Risk Changing Risk Proactively
• Using Option Prices to Measure Risk
• Uncertainty of the Distribution of Returns
• Adaptive Strategy — Pre and Post “2008” Crisis
• Issues

I consider the Black–Scholes–Merton option-pricing model from several angles, including personal, technical and, most importantly, from the perspective of a paradigm-shifting mathematical formula.