Handbook of Recent Advances in Commodity and Financial Modeling by Giorgio Consigli Silvana Stefani & Giovanni Zambruno

Author:Giorgio Consigli, Silvana Stefani & Giovanni Zambruno
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

7.2 General Setup

In this section we propose a class of stochastic volatility models, in discrete time, through which we are able to price options using the information extrapolated from the VIX index.

Given a filtered probability space , we consider a market with two assets: riskless with dynamics: B t = B t−1exp(r)

risky with price dynamics:

(7.1)

where r is the deterministic free rate observed in the market; λ 0 and λ 1 are real valued model parameters while σ must be non negative; X t is a discrete time stochastic process describing log returns; and is independent from V t .

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