A multivariate model for financial indices and an algorithm for detection of jumps in the volatility

Mario Bonino (1) , Matteo Camelia (1) , Paolo Pigato (2, 3)

1 Dipartimento di Matematica [Padova]
2 TOSCA - TO Simulate and CAlibrate stochastic models
3 IECL - Institut Élie Cartan de Lorraine

We consider a mean-reverting stochastic volatility model which satisfies some relevant stylized facts of financial markets. We introduce an algorithm for the detection of peaks in the volatility profile, that we apply to the time series of Dow Jones Industrial Average and Financial Times Stock Exchange 100 in the period 1984-2013. Based on empirical results, we propose a bivariate version of the model, for which we find an explicit expression for the decay over time of cross-asset correlations between absolute returns. We compare our theoretical predictions with empirical estimates on the same financial time series, finding an excellent agreement.

Mots clés: LongMemory; Financial Time Series; Stochastic Volatility; Cross-Correlations; Jump Detection

Domaines: Econométrie de la finance [q-fin.ST]; Probabilités [math.PR]

Mario Bonino, Matteo Camelia, Paolo Pigato. A multivariate model for financial indices and an algorithm for detection of jumps in the volatility. 2016. ⟨hal-01408495⟩