Calibration of Hestons Stochastic Volatility Model

Since the ground-breaking work of Black, Scholes [2] and Merton [4] the development of financial market models has gone a long way. Nowadays quite sophisticated models are employed in the financial market industry to price and hedge options. But before the models can be applied in practice, one has to implicitely identify the unknown model parameters from given market data. Usually, as an industry standard, a set of standard option prices serves as an appropriate set of market data. A good model must hence be able to provide a suitable fit of this so-called volatility surface.

In a joint research project, the University of Trier developed an algorithm for the identification of the underlying parameters of Hestons stochastic volatility model [3].

Publications:
Gerlich,F., Giese,A.M., Maruhn,J.H., Sachs,E.W., Parameter Identification in Stochastic Volatility Models with Time-Dependent Model Parameters
submitted, 2006

Literature:
[1] L. Andersen and R. Brotherton-Ratcliffe. The equity option volatility smile: an implicit finite-difference approach.
The Journal of Computational Finance, 1(2):5–38, 1997/1998.
[2] Black, F., Scholes, M. The pricing of options and corporate liabilities.
Journal of Political Economy, Vol. 81, pp. 637-659, 1973.
[3] Heston, S. L. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.
The Review of Financial Studies, Volume 6, number 2, pp. 327-343, 1993.
[4] Merton, R. C.: Theory of rational option pricing.
Bell J. Econom. Manag. Sci. 4, pp. 141-183.

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