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Introduction to Implied, Local and Stochastic Volatility


[1] Bera, Anil K. and Higgins, Matthew L., (1998). "A Survey of Arch Models: Properties, Estimation and Testing". Risk Books, Volatility, June−98, 23-59.

[2] Björk, Thomas, (1998). "Arbitrage Theory in Continuous Time". Oxford University Press Inc., New York.

[3] Dupire, Bruno, (1994). "Pricing with a Smile". Risk Magazine, 7, 18-20.

[4] Elder, John, (2002). "Hedging for Financial Derivatives". University of Oxford, Ph.D. Thesis.

[5] Ghomrasni, Raouf, (2003). "On Distributions Associated with the Generalized Lévy’s Stochastic Area Formula". University of Aarhus, Centre for Mathematical Physics and Stochastics (MaPhySto) [MPS]; RR 2003/4.

[6] Heston, Steven L., (1993). "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options". The Review of Financial Studies, Volume 6, Issue 2, 327-343.

[7] Hull, John, (1993). "Options, Futures, and other Derivation Securities". Prentice Hall, Inc.

[8] Kloeden, Peter E. and Platen, Eckhard, (1999). "Numerical Solution of Stochastic Differential Equations". Springer.

[9] Kloeden, Peter E., (2002). "The Systematic Derivation of Higher Order Numerical Schemes for Stochastic Differential Equations". Milan Journal of Mathematics.

[10] Lévy, P., (1950). "Wiener’s Random Function, and other Laplacian Random Functions". Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 171-187.

[11] Lewis, Alan L., (2000). "Option Valuation under Stochastic Volatility: with Mathematica Code". Finance Press.

[12] Schmitz, Klaus, (2004). "Introduction to Implied, Local and Stochastic Volatility". http://www.maths.ox.ac.uk/~schmitz/project1.htm

[13] Schmitz, Klaus, (2004). "Strong Taylor Schemes for Stochastic Volatility". http://www.maths.ox.ac.uk/~schmitz/project2.htm

[14] Shaw, William, (2000). "Instability of Implied Volatility, Fictitious Skews and Smiles and Hazards of Exotics". AIP Conference Proceedings, Vol. 553, 309-314.

[15] Shaw, William, (1999). "Modelling Financial Derivatives with Mathematica". Cambridge University Press.

[16] Shaw, William, (2003). "Stochastic Volatility, Models of Heston Type". University of Oxford, Course Notes.

[17] Wilmott, Paul, Howison, Sam and Dewynne, Jeff, (1995). "The Mathematics of Financial Derivatives". Cambridge University Press.

[18] Wilmott, Paul, (1998). "Derivatives: The Theory and Practice of Financial Engineering". John Wiley and Sons.

Prof. Klaus Schmitz

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