Showing papers in "Quantitative Finance in 2017"
TL;DR: In this paper, the authors proposed an extreme risk spillover network for analysing the intimate value at risk (VaR) and the Granger causality risk test (GRLT) to quantify the risk of spillovers.
Abstract: Using the CAViaR tool to estimate the value-at-risk (VaR) and the Granger causality risk test to quantify extreme risk spillovers, we propose an extreme risk spillover network for analysing the int...
163 citations
TL;DR: In this paper, the authors construct a model of the underlying asset price process which is dynamically consistent to the power law and derive an asymptotic expansion of the implied volatility as the time to maturity tends to zero.
Abstract: The Black–Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time to maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian motion with Hurst parameter less than half. The fractional Brownian motion is correlated with a Brownian motion which drives the asset price process. We derive an asymptotic expansion of the implied volatility as the time to maturity tends to zero. For this purpose, we introduce a new approach to validate such an expansion, which enables us to treat more general models than in the literature. The local-stochastic volatility model is treated as well under an essentially minimal regularity condition in order to show such a standard model cannot be dynamically consistent to the power law.
97 citations
TL;DR: In this article, the authors propose a financial market model in which speculators follow a linear mix of technical and fundamental trading rules to determine their orders, and the model is able to explain a number of stylized facts of financial markets quite well.
Abstract: We propose a financial market model in which speculators follow a linear mix of technical and fundamental trading rules to determine their orders. Volatility clustering arises in our model due to speculators’ herding behaviour. In case of heightened uncertainty, speculators observe other speculators’ actions more closely. Since speculators’ trading behaviour then becomes less heterogeneous, the market maker faces a less balanced excess demand and consequently adjusts prices more strongly. Estimating our model using the method of simulated moments reveals that it is able to explain a number of stylized facts of financial markets quite well. Various robustness checks with respect to the model setup reveal that our results are quite stable.
76 citations
TL;DR: Using stochastic control techniques, the optimal dynamic pairs trading strategy model for a portfolio of cointegrated assets is proposed and an out-of-sample test is conducted with historical data from three exchanges, with two cointegrating relations.
Abstract: We propose an optimal dynamic pairs trading strategy model for a portfolio of cointegrated assets. Using stochastic control techniques, we compute analytically the optimal portfolio weights and rel...
64 citations
TL;DR: In this paper, the authors present a nonparametric estimation procedure for the multivariate Hawkes point process, where the timeline is cut into bins and, for each component process, the number of points in each bin is counted.
Abstract: In this paper, we present a nonparametric estimation procedure for the multivariate Hawkes point process. The timeline is cut into bins and—for each component process—the number of points in each bin is counted. As a consequence of earlier results in Kirchner [Stoch. Process. Appl., 2016, 162, 2494–2525], the distribution of the resulting ‘bin-count sequences’ can be approximated by an integer-valued autoregressive model known as the (multivariate) INAR(p) model. We represent the INAR(p) model as a standard vector-valued linear autoregressive time series with white-noise innovations (VAR(p)). We establish consistency and asymptotic normality for conditional least-squares estimation of the VAR(p), respectively, the INAR(p) model. After appropriate scaling, these time-series estimates yield estimates for the underlying multivariate Hawkes process as well as corresponding variance estimates. The estimates depend on a bin-size and a support s. We discuss the impact and the choice of these parameters. All resu...
64 citations
TL;DR: In this article, the multivariate Hawkes process coupled with the nonparametric estimation procedure first proposed in Bacry and Muzy [IEEE Trans. Inform. Theory, 2016, 62, 2184-2202] was successfully used to study complex interactions between the time of arrival of orders and their size observed in a limit order book market.
Abstract: We show that multivariate Hawkes processes coupled with the nonparametric estimation procedure first proposed in Bacry and Muzy [IEEE Trans. Inform. Theory, 2016, 62, 2184–2202] can be successfully used to study complex interactions between the time of arrival of orders and their size observed in a limit order book market. We apply this methodology to high-frequency order book data of futures traded at EUREX. Specifically, we demonstrate how this approach is amenable not only to analyse interplay between different order types (market orders, limit orders, cancellations) but also to include other relevant quantities, such as the order size, into the analysis, showing also that simple models assuming the independence between volume and time are not suitable to describe the data.
61 citations
TL;DR: A new time-varying optimal copula (TVOC) model to identify and capture the optimal dependence structure of bivariate time series at every time point is proposed and the half-rotated copulas can accurately describe the asymmetric negative extreme dependence across different markets.
Abstract: This paper proposes a new time-varying optimal copula (TVOC) model to identify and capture the optimal dependence structure of bivariate time series at every time point. In the TVOC model, half-rotated copulas are constructed to measure the nonlinear and asymmetric negative dependence, and the distribution-free test for independence is introduced to verify the dependent relationship and reduce the computational time. The TVOC model is then employed to research the dependence structure between security and commodity markets. We find evidence that the dependence structures across different markets vary over time and that emergencies are usually the major cause of sudden changes in the dependence structure. We also show that the TVOC model captures the dynamic characteristics of the direction and intensity of the dependence as well as the dynamic characteristics of the types of dependence structure. In particular, the half-rotated copulas can accurately describe the asymmetric negative extreme dependence acr...
60 citations
TL;DR: The authors showed that risk premium is strongly correlated with tail-risk skewness but very little with volatility, and proposed an objective criterion to assess the quality of a risk-premium portfolio.
Abstract: We present extensive evidence that “risk premium” is strongly correlated with tail-risk skewness but very little with volatility. We introduce a new, intuitive definition of skewness and elicit a linear relation between the Sharpe ratio of various risk premium strategies (Equity, Fama-French, FX Carry, Short Vol, Bonds, Credit) and their negative skewness. We find a clear exception to this rule: trend following (and perhaps the FamaFrench “High minus Low”), that has positive skewness and positive excess returns, suggesting that some strategies are not risk premia but genuine market anomalies. Based on our results, we propose an objective criterion to assess the quality of a risk-premium portfolio.
55 citations
TL;DR: In this paper, the authors introduce and establish the main properties of the quadratic Hawkes price model and show that the model is time-reversal asymmetric, similar to financial markets whose time evolution has a preferred direction.
Abstract: We introduce and establish the main properties of QHawkes (‘Quadratic’ Hawkes) models. QHawkes models generalize the Hawkes price models introduced in Bacry and Muzy [Quant. Finance, 2014, 14(7), 1147–1166], by allowing feedback effects in the jump intensity that are linear and quadratic in past returns. Our model exhibits two main properties that we believe are crucial in the modelling and the understanding of the volatility process: first, the model is time-reversal asymmetric, similar to financial markets whose time evolution has a preferred direction. Second, it generates a multiplicative, fat-tailed volatility process, that we characterize in detail in the case of exponentially decaying kernels, and which is linked to Pearson diffusions in the continuous limit. Several other interesting properties of QHawkes processes are discussed, in particular the fact that they can generate long memory without necessarily being at the critical point. A non-parametric fit of the QHawkes model on NYSE stock data sh...
55 citations
TL;DR: It is shown that the machine-learning approach discussed in this study can be developed as a very useful pricing tool, and potentially a market condition change detector.
Abstract: Support vector regression (SVR) has long been proven to be a successful tool to predict financial time series. The core idea of this study is to outline an automated framework for achieving a faster and easier parameter selection process, and at the same time, generating useful prediction uncertainty estimates in order to effectively tackle flexible real-world financial time series prediction problems. A Bayesian approach to SVR is discussed, and implemented. It is found that the direct implementation of the probabilistic framework of Gao et al. returns unsatisfactory results in our experiments. A novel enhancement is proposed by adding a new kernel scaling parameter to overcome the difficulties encountered. In addition, the multi-armed bandit Bayesian optimization technique is applied to automate the parameter selection process. Our framework is then tested on financial time series of various asset classes (i.e. equity index, credit default swaps spread, bond yields, and commodity futures) to ensure its ...
51 citations
TL;DR: The authors compare and contrast time series momentum (TSMOM) and moving average (MA) trading rules to understand the sources of their profitability and find that TSMOM signals occur at points that coincide with a MA direction change.
Abstract: We compare and contrast time series momentum (TSMOM) and moving average (MA) trading rules so as to better understand the sources of their profitability. These rules are closely related; however, there are important differences. TSMOM signals occur at points that coincide with a MA direction change, whereas MA buy (sell) signals only require price to move above (below) a MA. Our empirical results show MA rules frequently give earlier signals leading to meaningful return gains. Both rules perform best outside of large stock series which may explain the puzzle of their popularity with investors, yet lack of supportive evidence in academic studies.
TL;DR: In this article, the authors study the problem of the optimal execution of a large trade in the propagator model with non-linear transient impact and find that the optimal solution for a buy programme typically features a few short intense buying periods separated by long periods of weak selling.
Abstract: We study the problem of the optimal execution of a large trade in the propagator model with non-linear transient impact. From brute force numerical optimization of the cost functional, we find that the optimal solution for a buy programme typically features a few short intense buying periods separated by long periods of weak selling. Indeed, in some cases, we find negative expected cost. We show that this undesirable characteristic of the non-linear transient impact model may be mitigated either by introducing a bid–ask spread cost or by imposing convexity of the instantaneous market impact function for large trading rates; the objective in each case is to robustify the solution in a parsimonious and natural way.
TL;DR: In this article, the authors introduce indicators for profiling markets under directional change (DC) and analyse empirical high-frequency data on major equities traded on the UK stock market.
Abstract: Market prices are traditionally sampled in fixed time intervals to form time series. Directional change (DC) is an alternative approach to record price movements. Instead of sampling at fixed intervals, DC is data driven: price changes dictate when a price is recorded. DC provides us with a complementary way to extract information from data. It allows us to observe features that may not be recognized in time series. The argument is that time series and DC-based analysis complement each other. With data sampled at irregular time intervals in DC, however, some of the time series indicators cannot be used in DC-based analysis. For example, returns must be time adjusted and volatility must be amended accordingly. A major objective of this paper is to introduce indicators for profiling markets under DC. We analyse empirical high-frequency data on major equities traded on the UK stock market, and through DC profiling extract information complementary to features observed through time series profiling.
TL;DR: In this article, the authors proposed a probabilistic approach to the reconstruction of the empirical network, combining some important known quantities (like the size of the banks) with a realistic stochastic representation of the remaining structural elements to evaluate relevant measures for the contagion risk after default of one unit.
Abstract: One lesson of the financial crisis erupting in 2008 has been that domino effects constitute a serious threat to the stability of the financial sector, i.e. the failure of one node in the interbank network might entail the danger of contagion to large parts of the entire system. How important this effect is, depends on the exact topology of the network on which the supervisory authorities have typically very incomplete knowledge. In order to explore the extent of contagion effects and to analyse the effectiveness of macroprudential measures to contain such effects, a reconstruction of the quantitative features of the empirical network would be needed. We propose a probabilistic approach to such a reconstruction: we propose to combine some important known quantities (like the size of the banks) with a realistic stochastic representation of the remaining structural elements. Our approach allows us to evaluate relevant measures for the contagion risk after default of one unit (i.e. the number of expected subs...
TL;DR: In this paper, the authors introduce novel "doubly mean-reverting" processes based on conditional modelling of model spreads between pairs of stocks, which can capture local market inefficiencies that are elusive for traditional pairs trading strategies.
Abstract: This paper introduces novel ‘doubly mean-reverting’ processes based on conditional modelling of model spreads between pairs of stocks. Intraday trading strategies using high frequency data are proposed based on the model. This model framework and the strategies are designed to capture ‘local’ market inefficiencies that are elusive for traditional pairs trading strategies with daily data. Results from real data back-testing for two periods show remarkable returns, even accounting for transaction costs, with annualized Sharpe ratios of 3.9 and 7.2 over the periods June 2013–April 2015 and 2008, respectively. By choosing the particular sector of oil companies, we also confirm the observation that the commodity price is the main driver of the share prices of commodity-producing companies at times of spikes in the related commodity market.
TL;DR: This paper conducted a horse race of conventional statistical methods and more recent machine learning methods as early warning models and found that the conventional statistical approaches are outperformed by more advanced machine learning models, such as k-nearest neighbours and neural networks.
Abstract: This paper presents first steps towards robust models for crisis prediction. We conduct a horse race of conventional statistical methods and more recent machine learning methods as early-warning models. As individual models are in the literature most often built in isolation of other methods, the exercise is of high relevance for assessing the relative performance of a wide variety of methods. Further, we test various ensemble approaches to aggregating the information products of the built models, providing more robust basis for measuring country-level vulnerabilities. Finally, we provide approaches to estimating model uncertainty in early-warning exercises, particularly model performance uncertainty and model output uncertainty. The approaches put forward in this paper are shown with Europe as a playground. Generally, our results show that the conventional statistical approaches are outperformed by more advanced machine learning methods, such as k-nearest neighbours and neural networks, and particularly ...
TL;DR: In this article, the authors present the symmetric thermal optimal path (TOPS) method to determine the time-dependent lead-lag relationship between two stochastic time series.
Abstract: We present the symmetric thermal optimal path (TOPS) method to determine the time-dependent lead-lag relationship between two stochastic time series. This novel version of the previously introduced thermal optimal path (TOP) method alleviates some inconsistencies by imposing that the lead-lag relationship should be invariant with respect to a time reversal of the time series after a change of sign. This means that, if ‘X comes before Y’, this transforms into ‘Y comes before X’ under a time reversal. We show that a previously proposed bootstrap test lacks power and leads too often to a lack of rejection of the null that there is no lead-lag correlation when it is present. We introduce instead two novel tests. The first criterion, based on the free energy p-value , quantifies the probability that a given lead-lag structure could be obtained from random time series with similar characteristics except for the lead-lag information. The second self-consistent test embodies the idea that, for the lead-lag path t...
TL;DR: Based on daily and one-minute high-frequency returns, this paper examined the lead-lag dependence between the CSI 300 index spot and futures markets from 2010 to 2014 using a nonparametric and non-linear method based on the thermal optimal path method.
Abstract: Based on daily and one-minute high-frequency returns, this paper examines the lead–lag dependence between the CSI 300 index spot and futures markets from 2010 to 2014. A nonparametric and non-linear method based on the thermal optimal path method is adopted. Empirical results of the daily data indicate that the lead–lag relationship between the two markets is within one day but this relationship is volatile since neither of the two possible situations (the futures leads or lags behind the spot market) takes a dominant place. Our results using the high-frequency data demonstrate that there is a price discovery in the Chinese futures market: the intraday one-minute futures return leads the cash return by 0–5 min regardless of the price trend of the market.
TL;DR: In this article, the first recursive quantization-based approach for pricing options in the presence of stochastic volatility was proposed, which can be applied to any model for which an Euler scheme is available for the underlying price process and allows one to price vanillas, as well as exotics, thanks to the knowledge of the transition probabilities for the discretized stock process.
Abstract: We provide the first recursive quantization-based approach for pricing options in the presence of stochastic volatility. This method can be applied to any model for which an Euler scheme is available for the underlying price process and it allows one to price vanillas, as well as exotics, thanks to the knowledge of the transition probabilities for the discretized stock process. We apply the methodology to some celebrated stochastic volatility models, including the Stein and Stein [Rev. Financ. Stud. 1991, (4), 727–752] model and the SABR model introduced in Hagan et al. [Wilmott Mag., 2002, 84–108]. A numerical exercise shows that the pricing of vanillas turns out to be accurate; in addition, when applied to some exotics like equity-volatility options, the quantization-based method overperforms by far the Monte Carlo simulation.
TL;DR: The present multiple time step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho model is especially useful for long-term options and for exotic options.
Abstract: In this paper, we will present a multiple time step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho model. The proposed method is an extension of the one time step Monte Carlo method that we proposed in an accompanying paper Leitao et al. [Appl. Math. Comput. 2017, 293, 461–479], for pricing European options in the context of the model calibration. A highly efficient method results, with many very interesting and nontrivial components, like Fourier inversion for the sum of log-normals, stochastic collocation, Gumbel copula, correlation approximation, that are not yet seen in combination within a Monte Carlo simulation. The present multiple time step Monte Carlo method is especially useful for long-term options and for exotic options.
TL;DR: Markowitz optimal portfolio theory (Markowitz 1987), also known as the Mean-Variance theory, has had a tremendous impact and hundreds of papers are devoted to this topic as mentioned in this paper.
Abstract: Markowitz optimal portfolio theory (Markowitz 1987), also known as the Mean-Variance theory, has had a tremendous impact and hundreds of papers are devoted to this topic. This theory addresses the ...
TL;DR: In this paper, a detailed methodological study of the application of the modified profile likelihood method for the calibration of nonlinear financial models characterized by a large number of parameters is presented, which is particularly relevant because one of its parameters, the critical time signalling the burst of the bubble, is arguably the target of choice for dynamical risk management.
Abstract: We present a detailed methodological study of the application of the modified profile likelihood method for the calibration of nonlinear financial models characterized by a large number of parameters. We apply the general approach to the Log-Periodic Power Law Singularity (LPPLS) model of financial bubbles. This model is particularly relevant because one of its parameters, the critical time signalling the burst of the bubble, is arguably the target of choice for dynamical risk management. However, previous calibrations of the LPPLS model have shown that the estimation of is in general quite unstable. Here, we provide a rigorous likelihood inference approach to determine , which takes into account the impact of the other nonlinear (so-called ‘nuisance’) parameters for the correct adjustment of the uncertainty on . This provides a rigorous interval estimation for the critical time, rather than the point estimation in previous approaches. As a bonus, the interval estimates can also be obtained for the nuisan...
TL;DR: In this paper, a three-dimensional mixed vine copula is proposed to model the evolution of the Danish and German spot electricity prices and the Danish wind power production, and a realistic hedging portfolio is constructed by identifying various instruments available in the market, such as real options in the form of the right to transfer electri...
Abstract: When energy trading companies enter into long-term agreements with wind power producers, where a fixed price is paid for the fluctuating production, they are facing a joint price and volumetric risk. Since the pay-off of such agreements is non-linear, a hedging portfolio would ideally consist of not only forwards, but also a basket of e.g. call and put options. Illiquidity and an almost non-existent market for options challenge however the optimal hedging of joint price and volumetric risk in many market places. Here, we consider the case of the Danish power market, and exploit its strong positive correlation with the much more liquid German market to construct a proxy hedge. We propose a three-dimensional mixed vine copula to model the evolution of the Danish and German spot electricity prices and the Danish wind power production. We construct a realistic hedging portfolio by identifying various instruments available in the market, such as real options in the form of the right to transfer electri...
TL;DR: Pettifor has several targets in her short book: bankers of course, and a rival group of "heterodox" economists, but above all "orthodox" economists as mentioned in this paper. But this is a short book.
Abstract: Ann Pettifor has several targets in her sights in this short book: bankers of course, and a rival group of ‘heterodox’ economists, but above all ‘orthodox’ economists. A high profile campaigner and...
TL;DR: In this paper, a parametric model for the simulation of limit order books is proposed, where limit orders, market orders and cancellations are submitted according to point processes with state-dependent intensities.
Abstract: We propose a parametric model for the simulation of limit order books. We assume that limit orders, market orders and cancellations are submitted according to point processes with state-dependent intensities. We propose new functional forms for these intensities, as well as new models for the placement of limit orders and cancellations. For cancellations, we introduce the concept of " priority index " to describe the selection of orders to be cancelled in the order book. Parameters of the model are estimated using likelihood maximization. We illustrate the performance of the model by providing extensive simulation results, with a comparison to empirical data and a standard Poisson reference.
TL;DR: In this paper, a multi-period mean-variance (MV) portfolio allocation is proposed for a defined contribution pension plan and sustainable withdrawal rates for an endowment, where the investment portfolio can be allocated between a risk-free investment and a risky asset.
Abstract: In contrast to single-period mean-variance (MV) portfolio allocation, multi-period MV optimal portfolio allocation can be modified slightly to be effectively a down-side risk measure. With this in mind, we consider multi-period MV optimal portfolio allocation in the presence of periodic withdrawals. The investment portfolio can be allocated between a risk-free investment and a risky asset, the price of which is assumed to follow a jump diffusion process. We consider two wealth management applications: optimal de-accumulation rates for a defined contribution pension plan and sustainable withdrawal rates for an endowment. Several numerical illustrations are provided, with some interesting implications. In the pension de-accumulation context, Bengen (1994)’s [J. Financial Planning, 1994, 7, 171–180], historical analysis indicated that a retiree could safely withdraw 4% of her initial retirement savings annually (in real terms), provided that her portfolio maintained an even balance between diversified equiti...
TL;DR: In this paper, the authors proposed the construction of financial cycle measures for the US based on a large data set of macroeconomic and financial variables using a dynamic factor model and investigated whether these financial cycle components have significant predictive power for economic activity, inflation and short-term interest rates.
Abstract: The analysis of the financial cycle and its interaction with the macroeconomy has become a central issue for the design of macroprudential policy since the 2007–08 financial crisis. This paper proposes the construction of financial cycle measures for the US based on a large data set of macroeconomic and financial variables. More specifically, we estimate three synthetic financial cycle components that account for the majority of the variation in the data set using a dynamic factor model. We investigate whether these financial cycle components have significant predictive power for economic activity, inflation and short-term interest rates by means of Granger causality tests in a factor-augmented VAR set-up. Further, we analyze whether the synthetic financial cycle components have significant forecasting power for the prediction of economic recessions using dynamic probit models. Our main findings indicate that all financial cycle measures improve the quality of recession forecasts significantly. In particu...
TL;DR: In this article, a model for multivariate intertemporal portfolio choice in complete and incomplete markets with a multi-factor stochastic covariance matrix of asset returns is considered and optimal investment strategies are derived in closed form.
Abstract: We consider a model for multivariate intertemporal portfolio choice in complete and incomplete markets with a multi-factor stochastic covariance matrix of asset returns. The optimal investment strategies are derived in closed form. We estimate the model parameters and illustrate the optimal investment based on two stock indices: S&P500 and DAX. It is also shown that the model satisfies several stylized facts well known in the literature. We analyse the welfare losses due to suboptimal investment strategies and we find that investors who invest myopically, ignore derivative assets, model volatility by one factor and ignore stochastic covariance between asset returns can incur significant welfare losses.
TL;DR: In this paper, the second volume on stochastic volatility and option pricing, Alan Lewis extended his previous work with a particular focus on jump modelling. The Heston or Feller 3/2 models are frequently rewo...
Abstract: In his second volume on stochastic volatility and option pricing, Alan Lewis extends his previous work with a particular focus on jump modelling. The Heston or Feller 3/2 models are frequently rewo...
TL;DR: In this article, a duplex banking network is constructed by credit relationships and information interaction via the banks' balance sheet to model the structure of systemic risk and investigate the dynamic mechanism of contagion in terms of default and liquidity infection along with the factors that affect the extent of the contagion.
Abstract: This paper constructs a duplex banking network formed by credit relationships and information interaction via the banks’ balance sheet to model the structure of systemic risk and investigate the dynamic mechanism of contagion in terms of default and liquidity infection along with the factors that affect the extent of the contagion. We systematically explain the role that duplex banking networks play in different aspects of risk contagion. Through theoretical analysis and simulations, we conclude that asymmetric information interaction would increase the inflexibility of the system, which leads to liquidity shortage and possibly the collapse of the whole market. The weakness of systemic risk in the interior of the complex banking system can be characterized by the partial discount factor using illiquid assets in the information network. By improving the connectedness of the information network of the duplex networks, the spread of contagion can be partially slowed.