## First-passage and risk evaluation under stochastic volatility

Masoliver, Jaume
Perello, Josep
##### Description
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.
Comment: 36 pages, 11 figures
##### Keywords
Quantitative Finance - Statistical Finance, Quantitative Finance - Risk Management