We usually think of volatility as the standard deviation of a series, e.g. price returns however while this applies to historic volatility (ex-post) what do we do when it comes to addressing expected volatility (ex-ante)?
Three types of models:
-local volatility models,
-stochastic volatility models and
-deterministic volatility models
Local volatility models assume the volatility is constant (standard deviation) and hence a function of price and time. The local volatility model is therefore considered a generalisation of the Black-Scholes model.
Two factor stochastic volatility model (Stochastic Alpha Beta Rho – Sabr):
− Assumes volatility is stochastic, Sabr (ρ, υ).
Beta fixes the underlying volatility process and is fixed at 80% for equities, 0 for IR (volatilities are Gaussian) and 1 for currencies (volatilities are lognormal)
Three factor deterministic volatility model (Quadratic – Quad):
− Quad(ρ, υ, γ) – no assumption on the dynamics of the volatility process.
Four factor deterministic volatility model (Stochastic Volatility Inspired – SVI):
− SVI(ρ, υ, γ, ξ) – no assumption on the dynamics of the volatility process
Most South African banks seem to use deterministic models with up to 6 factors.
References:
A lot of research has been published by Dr Antonie Kotzé…
http://www.quantonline.co.za/publications_and_research.html http://www.quantonline.co.za/documents/Volatility%20Surface%2025%20Feb%202011.pdf
http://www.quantonline.co.za/documents/Generating%20South%20African%20Volatility%20Surface.pdf
