Showing papers by "Danske Bank published in 2020"

A detailed look at crude oil price volatility prediction using macroeconomic variables

Abstract: We investigate whether crude oil price volatility is predictable by conditioning on macroeconomic variables. We consider a large number of predictors, take into account the possibility that relative predictive performance varies over the out‐of‐sample period, and shed light on the economic drivers of crude oil price volatility. Results using monthly data from 1983:M1 to 2018:M12 document that variables related to crude oil production, economic uncertainty and variables that either describe the current stance or provide information about the future state of the economy forecast crude oil price volatility at the population level 1 month ahead. On the other hand, evidence of finite‐sample predictability is very weak. A detailed examination of our out‐of‐sample results using the fluctuation test suggests that this is because relative predictive performance changes drastically over the out‐of‐sample period. The predictive power associated with the more successful macroeconomic variables concentrates around the Great Recession until 2015. They also generate the strongest signal of a decrease in the price of crude oil towards the end of 2008.

Differential Machine Learning

Abstract: Differential machine learning combines automatic adjoint differentiation (AAD) with modern machine learning (ML) in the context of risk management of financial Derivatives. We introduce novel algorithms for training fast, accurate pricing and risk approximations, online, in real-time, with convergence guarantees. Our machinery is applicable to arbitrary Derivatives instruments or trading books, under arbitrary stochastic models of the underlying market variables. It effectively resolves computational bottlenecks of Derivatives risk reports and capital calculations. Differential ML is a general extension of supervised learning, where ML models are trained on examples of not only inputs and labels but also differentials of labels wrt inputs. It is also applicable in many situations outside finance, where high-quality first-order derivatives wrt training inputs are available. Applications in Physics, for example, may leverage differentials known from first principles to learn function approximations more effectively. In finance, AAD computes pathwise differentials with remarkable efficacy so differential ML algorithms provide extremely effective pricing and risk approximations. We can produce fast analytics in models too complex for closed-form solutions, extract the risk factors of complex transactions and trading books, and effectively compute risk management metrics like reports across a large number of scenarios, backtesting and simulation of hedge strategies, or regulations like XVA, CCR, FRTB or SIMM-MVA. TensorFlow implementation is available on https://github.com/differential-machine-learning

History of Crowdfunding in the Context of Ever-Changing Modern Financial Markets

Abstract: The history of financial markets and finance are united by continuous fluctuations between economic cycles usually caused by structures that enable opportunism and moral hazards. Every crisis contains the seeds of change and innovation, but also risks for regulative overreactions. Crowdfunding as a form of financing is part of this series of innovations in the history of the financial markets. Understanding of the historical changes of both the financial market and the financial system as a whole helps to put new financial innovations, such as crowdfunding and, more broadly, fintech into perspective. The evolution of financial markets or corporate finance naturally will not end in crowdfunding. This chapter gives an overview of history of crowdfunding as part of the ever-changing modern financial markets and contextualizes it as a new, innovative, and modern form of financing in the financial markets.

Crude oil price changes and the United Kingdom real gross domestic product growth rate: An out-of-sample investigation

Abstract: We evaluate the impact of changes in the price of crude oil on the United Kingdom (U.K.) real gross domestic product (GDP) growth rate by way of an out-of-sample forecasting analysis. We compare the performance of several nonlinear models and determine, which aspects of nonlinearities are most useful for obtaining forecast improvements. Likewise, our approach takes into account the possibility that relative predictive performance can vary over the out-of-sample period. Results based on quarterly data from 1974 q 1 through 2018 q 4 illustrate that our conclusions depend on the definition of forecast improvement and whether we rely on pairwise or multiple forecast comparison. For instance, it is very difficult to find evidence that point forecasts exploiting crude oil price variables are statistically significant more accurate than point forecasts produced under the benchmark. On the other hand, the null hypothesis of no population-level predictability is borderline rejected for certain nonlinear crude oil price variables. We also observe notable differences between using real-time and ex-post revised GDP data with regards to local out-of-sample performance. The predictive power associated with the more successful crude oil price measures appears to concentrate in the early 1990s and around the onset of the Great Recession.

Should crude oil price volatility receive more attention than the price of crude oil? An empirical investigation via a large-scale out-of-sample forecast evaluation of US macroeconomic data

Abstract: Apart from the percentage change in the price of crude oil, there is a growing tradition of using various nonlinear transformations of the price of crude oil to forecast real gross domestic product growth rates, equity returns, inflation and other macroeconomic variables. This study attempts to quantify the additional potential predictive power afforded by crude oil price volatility relative to widely used crude oil price‐based variables for more than 300 US macroeconomic time series at the monthly and the quarterly sampling frequency. We observe that regressions employing crude oil price realized volatility and crude oil price realized semivolatilities tend to afford a more consistent pattern of out‐of‐sample prediction gains relative to competitors using well‐known crude oil price measures and the autoregressive benchmark at the quarterly and monthly sampling frequency. While it is somewhat harder to find evidence of finite‐sample predictive gains relative to the benchmark, the evidence is stronger with respect to population‐level predictability 1 quarter (1 month) ahead for the model with crude oil price realized semivolatilities across the considered data and models. Furthermore, point (density) forecasts employing crude oil price realized volatility tend to be more accurate than corresponding forecasts produced under the crude oil price‐based predictive regressions in a horse race.

Neural Networks with Asymptotics Control

Abstract: Artificial Neural Networks (ANNs) have recently been proposed as accurate and fast approximators in various derivatives pricing applications. ANNs typically excel in fitting functions they approximate at the input parameters they are trained on, and often are quite good in interpolating between them. However, for standard ANNs, their extrapolation behavior – an important aspect for financial applications – cannot be controlled due to complex functional forms typically involved. We overcome this significant limitation and develop a new type of neural networks that incorporate large-value asymptotics, when known, allowing explicit control over extrapolation. This new type of asymptotics-controlled ANNs is based on two novel technical constructs, a multi-dimensional spline interpolator with prescribed asymptotic behavior, and a custom ANN layer that guarantees zero asymptotics in chosen directions. Asymptotics control brings a number of important benefits to ANN applications in finance such as well-controlled behavior under stress scenarios, graceful handling of regime switching, and improved interpretability.

Rational Models for Inflation-Linked Derivatives

Abstract: We construct models for the pricing and risk management of inflation-linked derivatives. The models are rational in the sense that linear payoffs written on the consumer price index have prices that are rational functions of the state variables. The nominal pricing kernel is constructed in a multiplicative manner that allows for closed-form pricing of vanilla inflation products suchlike zero-coupon swaps, year-on-year swaps, caps and floors, and the exotic limited-price-index swap. We study the conditions necessary for the multiplicative nominal pricing kernel to give rise to short rate models for the nominal interest rate process. The proposed class of pricing kernel models retains the attractive features of a nominal multi-curve interest rate model, such as closed-form pricing of nominal swaptions, and it isolates the so-called inflation convexity-adjustment term arising from the covariance between the underlying stochastic drivers. We conclude with examples of how the model can be calibrated to EUR data.

Black Basket Analytics for Mid-Curves and Spread-Options

Abstract: To price mid-curve or spread options we need flexible joint distributions of two underlying rates with fixed marginals. A Copula approach is a standard method to produce such joint distributions.It has, however, several drawbacks, especially, a low number of free parameters. For example, the most popular Gaussian copula has one parameter -- correlation. Another complication with the Copulas is its numerical realization: a two dimensional numerical integration underlying the price can be slow and potentially noisy, eps. for sensitivities. In this paper we propose a new way to unify two marginal distributions such that it has a large number of parameters permitting to calibrate to mid-curve or spread options with multiple strikes. The method is based on a basket of log-normal processes (called Black Basket) having a fast analytical formulation and attractive simplicity.

Second-order stochastic volatility asymptotics and the pricing of foreign exchange derivatives

Abstract: We consider models for the pricing of foreign exchange derivatives, where the underlying asset volatility as well as the one for the foreign exchange rate are stochastic. Under this framework, sing...