Calibration in Option Pricing with Forward and Backward Reduced Models
Jose Silva*, University of Wuppertal; E. Jan ter Maten, University of Wuppertal; Michael Guenther, University of Wuppertal
This work presents the calibration of a stochastic volatility model, the Heston Model using Model Order Reduction. The calibration within the context of financial markets usually goes along the following lines. After defining which model or models suit the behaviour of each market the best, e.g. FX Markets, Stock Markets, etc., the information regarding currently priced instruments in the market is gathered. Using simple, quick models one obtains an estimate of at which value of the parameters is the market currently trading. These estimates are posteriorly used to priced more complexed or exotic products.
A very common calibration process involves a least-squares minimization problem in which each cost function evaluation involves solving one partial differential equation (PDE) per each set of parameters available on the market. This can quickly become prohibitively expensive to solve numerically. For that reason two parallel strategies are presented in this work, which should improve considerably the cost of such calibrations.
Obtaining a Dupire-type equation for both models, we proceed to calibrate option prices to market data by a least-squares minimization. We present the results showing the computational efficiency and comparing it with the ones resulting from a parametric reduced order model. We use Alternating-Direction Implicit schemes to numerically solve the partial differential equations in both approaches.
Prediction of Federal Funds Target Rate: A Dynamic Logistic Bayesian Model Average Approach
Hernán Alzate*, Bancolombia S.A.; Andrés Ramírez-Hassan, EAFIT University
In this paper we examine which macroeconomic and financial variables have most predictive power for the target repo rate decisions made by the Federal Reserve. We conduct the analysis for the FOMC decisions during the period June 1998-April 2015 using dynamic logistic models with dynamic Bayesian Model Averaging that allows to perform predictions in real-time with great flexibility. The computational burden of the algorithm is reduced by adapting a Markov Chain Monte Carlo Model Composition: MC3. We found that the outcome of the FOMC meetings during the sample period are predicted well: Logistic DMA-Up and Dynamic Logit-Up models present hit ratios of 87,2 and 88,7; meanwhile, hit ratios for the Logistic DMA-Down and Dynamic Logit-Down models are 79,8 and 68,0, respectively.
Stochastic Portfolio Theory: A Machine Learning Perspective
Alexander Vervuurt*, University of Oxford; Yves-Laurent Kom Samo, University of Oxford
We propose a novel application of Gaussian processes to financial asset allocation. Our approach is deeply rooted in Stochastic Portfolio Theory (SPT), a stochastic analysis framework recently introduced by Robert E. Fernholz that aims at flexibly analyzing the performance of certain investment strategies in stock markets relative to benchmark indices. In particular, SPT has exhibited some investment strategies based on company sizes that, under realistic assumptions, outperform benchmark indices with probability 1 over certain time horizons. Galvanized by this result, we consider the inverse problem that consists of learning (from historical data) an optimal investment strategy based on any given set of trading characteristics, and using a user-specified optimality criterion that may go beyond the outperformance of a benchmark index. Although the inverse problem is of the utmost interest to investment management practitioners, it can hardly be tackled using the SPT framework. We show that our machine learning approach learns investment strategies that considerably outperform existing SPT strategies in the US stock market.