Disentangling Volatility from Jumps

Abstract

Realistic models for financial asset prices used in portfolio choice, option pricing or risk management include both a continuous Brownian and a jump components. This paper studies our ability to distinguish one from the other. I find that, surprisingly, it is possible to perfectly disentangle Brownian noise from jumps. This is true even if, unlike the usual Poisson jumps, the jump process exhibits an infinite number of small jumps in any finite time interval, which ought to be harder to distinguish from Brownian noise, itself made up of many small moves.

Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics

“…has been suggested and shown to be a consistent estimator for the integrated volatility, even when there are jumps in return processes (see Barndorff-Nielsen and Shephard, 2004;and Aït-Sahalia, 2004). Despite the intuition that jumps in a process may impact its volatility estimation, it remains consistent no matter how large or small jumps are mixed with the diffusive part of pricing models.…”

“…We find the similar result from the comparison in Table 2: the probability of successful detection of a jump at some given time decreases under stochastic volatility. For another robustness check, we also study the case where the stochastic volatility is driven by a general model that accommodates stochastic elasticity of variance and a nonlinear drift (e.g., Aït-Sahalia, 1996;Aït-Sahalia, 2004;and Bakshi et al, 2005) as…”

Equivalent martingale measures and Lévy processes

“…Here the presence of jumps is more important since emerging markets are affected by many shocks that produce such a diversity of jumps. For a discussion about which type of jumps can be observed in asset returns see Aït-Sahalia (2004) and Huang and Wu (2004).…”

Optimal Portfolio Problem for Stochastic-Volatility, Jump-Diffusion Models with Jump-Bankruptcy Condition: Practical Theory

“…Although unlimited borrowing and short-selling play an important role in pure diffusion models, it is shown that borrowing and short selling are constrained for jump-diffusions. Finite range jump-amplitude models can allow constraints to be very large in contrast to infinite range models which severely restrict the optimal instantaneous stock-fraction to [0,1]. The reasonable constraints in the optimal stock-fraction due to jumps in the wealth argument for stochastic dynamic programming jump integrals remove a singularity in the stock-fraction due to vanishing volatility.…”