Numerix, the leading provider of cross-asset analytics for derivatives valuations and risk management, today announces new quantitative research published in SSRN titled “‘Hot-Start' Initialization of the Heston Model.” Authored by Dr. Serguei Mechkov, Senior VP of Quantitative Research at Numerix, the paper suggests a new way of setting up multifactor models with hidden variables. As a practical example, the Heston model is considered in this research.
A logical way of making a model more closely fit the observed behavior is to augment its dimension by adding a hidden process that somehow affects the evolution of the principal observable value. The complete model specification then acquires the parameters of the hidden process and its possible correlation with the principal process. This also requires describing how the hidden process starts.
“The very fact that the process is hidden makes it illogical to assume that its latent variable has some definite value today as part of the initial conditions of the model. A more logical initial condition is a distribution of the latent variable based on the previous history of the market. We refer to this as a “hot-start” initialization of the process,” said Dr. Serguei Mechkov, Senior VP of Quantitative Research at Numerix.
The research claims that the standard initial condition, which assigns some fixed value to the stochastic volatility subprocess, is illogical and greatly underestimates the effect of the hidden variable. For instance, a stochastic volatility model generates a significantly weaker implied volatility smile at short maturities. A good initial condition should specify the distribution of the hidden variable instead of a particular fixed value. The most straightforward way of initializing a hidden variable is by specifying its equilibrium distribution, which assumes that this component of the multifactor process has been started well before the observable part.
Mechkov adds: “In our opinion, the hot-start initialization opens a way to better fit the market at all maturities. It is also important for the future market scenarios generated by a multifactor model.”