Journal of Applied Mathematics

Recovery of Time-Dependent Parameters of a Black-Scholes-Type Equation: An Inverse Stieltjes Moment Approach

Marianito R. Rodrigo and Rogemar S. Mamon

Full-text: Open access

Abstract

We show that the problem of recovering the time-dependent parameters of an equation of Black-Scholes type can be formulated as an inverse Stieltjes moment problem. An application to the problem of implied volatility calculation in the case when the model parameters are time varying is provided and results of numerical simulations are presented.

Article information

Source
J. Appl. Math., Volume 2007 (2007), Article ID 62098, 8 pages.

Dates
First available in Project Euclid: 27 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.jam/1204126688

Digital Object Identifier
doi:10.1155/2007/62098

Mathematical Reviews number (MathSciNet)
MR2353920

Zentralblatt MATH identifier
1141.91021

Citation

Rodrigo, Marianito R.; Mamon, Rogemar S. Recovery of Time-Dependent Parameters of a Black-Scholes-Type Equation: An Inverse Stieltjes Moment Approach. J. Appl. Math. 2007 (2007), Article ID 62098, 8 pages. doi:10.1155/2007/62098. https://projecteuclid.org/euclid.jam/1204126688


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References

  • L. Andersen and R. Brotherton-Ratcliffe, ``The equity option volatility smile: an implicit finite-difference approach,'' Journal of Computational Finance, vol. 1, no. 2, pp. 5--37, 1998.
  • P. P. Boyle and D. Thangaraj, ``Volatility estimation from observed option prices,'' Decisions in Economics and Finance, vol. 23, no. 1, pp. 31--52, 2000.
  • B. Dupire, ``Pricing with a smile,'' Risk, vol. 7, no. 1, pp. 18--20, 1994.
  • F. Black and M. Scholes, ``The pricing of options and corporate liabilities,'' Journal of Political Economy, vol. 81, no. 3, pp. 637--654, 1973.
  • N. Akhiezer, The Classical Moment Problem and Some Related Questions in Analysis, Hafner, New York, NY, USA, 1965.
  • E. Derman and I. Kani, ``Riding on a smile,'' Risk, vol. 7, no. 2, pp. 32--39, 1994.
  • D. Chance, ``Leap into the unknown,'' in Over the Rainbow: New Developments in Exotic Options and Complex Swaps, R. Jarrow, Ed., pp. 251--256, Risk, London, UK, 1995.
  • M. R. Rodrigo and R. S. Mamon, ``A new representation of the local volatility surface,'' CARISMA Technical Report, Brunel University, London, UK, 2007.
  • R. Hafner, Stochastic Implied Volatility, vol. 545 of Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, Germany, 2004.