Abstract: Hawkes (1971a, 1971b, 1972) introduced a family of models for stochastic point processes called ‘self-exciting and mutually exciting point processes’ the essential property of which was that the oc...

Abstract: In this paper, we show how we can deploy machine learning techniques in the context of traditional quant problems. We illustrate that for many classical problems, we can arrive at speed-ups of seve...

Abstract: The rough Bergomi model introduced by Bayer et al. [Quant. Finance, 2015, 1–18] has been outperforming conventional Markovian stochastic volatility models by reproducing implied volatility smiles in a very realistic manner, in particular for short maturities. We investigate here the dynamics of the VIX and the forward variance curve generated by this model, and develop efficient pricing algorithms for VIX futures and options. We further analyse the validity of the rough Bergomi model to jointly describe the VIX and the SPX, and present a joint calibration algorithm based on the hybrid scheme by Bennedsen et al. [Finance Stoch., forthcoming].

Abstract: To improve existing online portfolio selection strategies in the case of non-zero transaction costs, we propose a novel framework named Transaction Cost Optimization (TCO). The TCO framework incorporates the L1 norm of the difference between two consecutive allocations together with the principles of maximizing expected log return. We further solve the formulation via convex optimization, and obtain two closed-form portfolio update formulas, which follow the same principle as Proportional Portfolio Rebalancing (PPR) in industry. We empirically evaluate the proposed framework using four commonly used data-sets. Although these data-sets do not consider delisted firms and are thus subject to survival bias, empirical evaluations show that the proposed TCO framework may effectively handle reasonable transaction costs and improve existing strategies in the case of non-zero transaction costs.

Abstract: Partial cointegration is a weakening of cointegration that allows for the ‘cointegrating’ residual to contain a random walk and a mean-reverting component. We derive its representation in state space, provide a maximum likelihood-based estimation routine, and a suitable likelihood ratio test. Then, we explore the use of partial cointegration as a means for identifying promising pairs and for generating buy and sell signals. Specifically, we benchmark partial cointegration against several classical pairs trading variants from 1990 until 2015, on a survivor bias free data-set of the S&P 500 constituents. We find annualized returns of more than 12% after transaction costs. These results can only partially be explained by common sources of systematic risk and are well superior to classical distance-based or cointegration-based pairs trading variants on our data-set.

Abstract: The rough Bergomi model, introduced by Bayer et al. [Quant. Finance, 2016, 16(6), 887–904], is one of the recent rough volatility models that are consistent with the stylised fact of implied volati...

Abstract: This study aims to shed light on the debate concerning the choice between discrete-time and continuous-time hazard models in making bankruptcy or any binary prediction using interval censored data. Building on the theoretical suggestions from various disciplines, we empirically compare widely used discrete-time hazard models (with logit and clog-log links) and the continuous-time Cox Proportional Hazards (CPH) model in predicting bankruptcy and financial distress of the United States Small and Medium-sized Enterprises (SMEs). Consistent with the theoretical arguments, we report that discrete-time hazard models are superior to the continuous-time CPH model in making binary predictions using interval censored data. Moreover, hazard models developed using a failure definition based jointly on bankruptcy laws and firms’ financial health exhibit superior goodness of fit and classification measures, in comparison to models that employ a failure definition based either on bankruptcy laws or firms’ financial heal...

Abstract: High-dimensional Hawkes processes with exponential kernels are used to describe limit order books in order-driven financial markets. The dependencies between orders of various types are carefully s...

Abstract: The growing interdependence between financial markets has attracted special attention from academic researchers and finance practitioners for the purpose of optimal portfolio design and contagion analysis. This article develops a tractable regime-switching version of the copula functions to model the intermarkets linkages during turmoil and normal periods, while taking into account structural changes. More precisely, Markov regime-switching C-vine and D-vine decompositions of the Student’s t copula are proposed and applied to returns on diversified portfolios of stocks, represented by the G7 stock market indices. The empirical results show evidence of regime shifts in the dependence structure with high contagion risk during crisis periods. Moreover, both the C- and D-vines highly outperform the multivariate Student’s t copula, which suggests that the shock transmission path is as important as the dependence itself, and is better detected with a vine copula decomposition.

Abstract: Regime-based asset allocation has been shown to add value over rebalancing to static weights and, in particular, reduce potential drawdowns by reacting to changes in market conditions. The predomin...

Abstract: This paper develops a pairs trading framework based on a mean-reverting jump–diffusion model and applies it to minute-by-minute data of the S&P 500 oil companies from 1998 to 2015. The established ...

Abstract: This study uses an endogenous Markov-switching framework to examine the interrelatedness of the volatility dynamics of the US and Korean markets. Previous literature assumes that the US market impl...

Abstract: We develop a multivariate statistical arbitrage strategy based on vine copulas—a highly flexible instrument for linear and nonlinear multivariate dependence modeling. In an empirical application on...

Abstract: We consider the problem of pricing basket options in a multivariate Black–Scholes or Variance-Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high-dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse-grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster than Monte Carlo or Quasi Monte Carlo methods in dimensions up to 35.

Abstract: A parsimonious generalization of the Heston model is proposed where the volatility-of-volatility is assumed to be stochastic. We follow the perturbation technique of Fouque et al [Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives, 2011, Cambridge University Press] to derive a first-order approximation of the price of options on a stock and its volatility index. This approximation is given by Heston’s quasi-closed formula and some of its Greeks. It can be efficiently calculated since it requires to compute only Fourier integrals and the solution of simple ODE systems. We exemplify the calibration of the model with S&P 500 and VIX data.

Abstract: We extend the regime-switching model to the rich class of time-changed Levy processes and use the Fourier cosine expansion (COS) method to price several options under the resulting models. The exte...

Abstract: Undergraduate textbooks in economics are usually rather dull affairs. Apart from minor variations in micro-/macro-emphasis, one can almost imagine, cover unopened, the content, the lay-out (lots an...

Abstract: This paper extends the Fourier-cosine (COS) method to the pricing and hedging of variable annuities embedded with guaranteed minimum withdrawal benefit (GMWB) riders. The COS method facilitates efficient computation of prices and hedge ratios of the GMWB riders when the underlying fund dynamics evolve under the influence of the general class of Levy processes. Formulae are derived to value the contract at each withdrawal date using a backward recursive dynamic programming algorithm. Numerical comparisons are performed with results presented in Bacinello et al. [Scand. Actuar. J., 2014, 1–20], and Luo and Shevchenko [Int. J. Financ. Eng., 2014, 2, 1–24], to confirm the accuracy of the method. The efficiency of the proposed method is assessed by making comparisons with the approach presented in Bacinello et al. [op. cit.]. We find that the COS method presents highly accurate results with notably fast computational times. The valuation framework forms the basis for GMWB hedging. A local risk minimisation app...

Abstract: In this paper, we investigate the role of eight commodity futures in asset allocation in China during the period January 2004–December 2015. The Chinese commodities and stocks are moderately correl...

Abstract: Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering ...

Abstract: Hawkes processes are a class of simple point processes that are self-exciting and have a clustering effect, with wide applications in finance, social networks and many other fields. This paper cons...

Abstract: Portfolios in which all assets contribute equally to the conditional value-at-risk (CVaR) represent an interesting variation of the popular risk parity investment strategy. This paper considers the...

Abstract: This paper investigates Barroso and Santa-Clara’s [J. Financ. Econ., 2008, 116, 111–120] risk-managed momentum strategy in an industry momentum setting. We investigate several traditional momentum ...

Abstract: We present an approach for modelling dependencies in exponential Levy market models with arbitrary margins originated from time changed Brownian motions. Using weak subordination of Buchmann et al. [Bernoulli, 2017], we face a new layer of dependencies, superior to traditional approaches based on pathwise subordination, since weakly subordinated processes are not required to have independent components considering multivariate stochastic time changes. We apply a subordinator being able to incorporate any joint or idiosyncratic information arrivals. We emphasize multivariate variance gamma and normal inverse Gaussian processes and state explicit formulae for the Levy characteristics. Using maximum likelihood, we estimate multivariate variance gamma models on various market data and show that these models are highly preferable to traditional approaches. Consistent values of basket-options under given marginal pricing models are achieved using the Esscher transform, generating a non-flat implied correlation ...

Abstract: We consider the estimation of binary election outcomes as martingales and propose an arbitrage pricing when one continuously updates estimates. We argue that the estimator needs to be priced as a binary option as the arbitrage valuation minimizes the conventionally used Brier score for tracking the accuracy of probability assessors. We create a dual martingale process $Y$, in $[L,H]$ from the standard arithmetic Brownian motion, $X$ in $(-\infty, \infty)$ and price elections accordingly. The dual process $Y$ can represent the numerical votes needed for success. We show the relationship between the volatility of the estimator in relation to that of the underlying variable. When there is a high uncertainty about the final outcome, 1) the arbitrage value of the binary gets closer to 50\%, 2) the estimate should not undergo large changes even if polls or other bases show significant variations. There are arbitrage relationships between 1) the binary value, 2) the estimation of $Y$, 3) the volatility of the estimation of $Y$ over the remaining time to expiration. We note that these arbitrage relationships were often violated by the various forecasting groups in the U.S. presidential elections of 2016, as well as the notion that all intermediate assessments of the success of a candidate need to be considered, not just the final one.

Abstract: Model predictive control with proportional transactions costs provides a good approximation to the optimal trading strategy

Abstract: This paper provides the optimal multivariate ntertemporal portfolio for an ambiguity averse investor, who has access to stocks and derivative markets, in closed form. The stock prices follow stochastic co-variance processes and the investor can have different levels of uncertainty about the diffusion parts of the stocks and the covariance structure. We find strong evidence that the optimal exposures to stock and covariance risks are significantly affected by ambiguity aversion. Welfare analyses show that investors who ignore model uncertainty incur large losses, larger than those suffered under the embedded one-dimensional cases. We further confirm large welfare losses from not trading in derivatives as well as ignoring intertemporal hedging, we study the impact of ambiguity in that regard and justify the importance of including these factors in the scope of portfolio optimization. Conditions for a well-behaved solution in general and verification theorems for the incomplete market case are provided.

Abstract: Instantaneous risk is described by the arrival rate of jumps in log price relatives. As a consequence there is then no concept of a mean return compensating risk exposures, as zero is the only inst...

Abstract: This paper attempts to investigate if adopting accurate forecasts from Neural Network (NN) models can lead to statistical and economically significant benefits in portfolio management decisions. In order to achieve that, three NNs, namely the Multi-Layer Perceptron, Recurrent Neural Network and the Psi Sigma Network (PSN), are applied to the task of forecasting the daily returns of three Exchange Traded Funds (ETFs). The statistical and trading performance of the NNs is benchmarked with the traditional Autoregressive Moving Average models. Next, a novel dynamic asymmetric copula model (NNC) is introduced in order to capture the dependence structure across ETF returns. Based on the above, weekly re-balanced portfolios are obtained and compared using the traditional mean–variance and the mean–CVaR portfolio optimization approach. In terms of the results, PSN outperforms all models in statistical and trading terms. Additionally, the asymmetric skewed t copula statistically outperforms symmetric copulas when ...