First-passage and risk evaluation under stochastic volatility

Abstract

We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain approximate forms of these probabilities which prove, among other interesting properties, the non-existence of a mean first-passage time. One significant result is the evidence of extreme deviations --which implies a high risk of default-- when certain dimensionless parameter, related to the strength of the volatility fluctuations, increases. We believe that this may provide an effective tool for risk control which can be readily applicable to real markets.

36 pages, 11 figures

References in corpus (13)

• Economics need a scientific revolution
• Hitting Time Distributions in Financial Markets
• Mean Escape Time in a System with Stochastic Volatility
• Role of Noise in a Market Model with Stochastic Volatility
• Comparison between the probability distribution of returns in the Heston model and empirical data for stock indexes
• Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model
• The escape problem under stochastic volatility: the Heston model
• Scaling and data collapse for the mean exit time of asset prices
• The distribution of first-passage times and durations in FOREX and future markets
• Extreme times in financial markets
• Volatility: a hidden Markov process in financial time series
• Extreme times for volatility processes
• Mean Exit Time and Survival Probability within the CTRW Formalism

Cited by in corpus (10)

• The stabilizing effect of volatility in financial markets
• Scaling properties and universality of first-passage time probabilities in financial markets
• Non-stationary Feller process with time-varying coefficients
• Epstein-Zin Utility Maximization on a Random Horizon
• Extreme values and the level-crossing problem. An application to the Feller process
• Default Risk Modeling Beyond the First-Passage Approximation: Extended Black-Cox Model
• Dynamical stability of the weakly nonharmonic propeller-shaped planar Brownian rotator
• Maximum likelihood approach for several stochastic volatility models
• A study of first-passage time minimization via Q-learning in heated gridworlds
• Default risk modeling beyond the first-passage approximation: Position-dependent killing