Dr Otto Konstandatos

Konstandatos, O. 2008, Pricing Path Dependent Exotic Options, VDM Verlag, Germany.

Buchen, P.W. & Konstandatos, O. 2009, 'A New Approach to Pricing Double-Barrier Options with Arbitrary Payoffs and Exponential Boundaries', Applied Mathematical Finance, vol. 16, no. 6, pp. 497-515.
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We consider in this article the arbitrage free pricing of double knock-out barrier options with payoffs that are arbitrary functions of the underlying asset, where we allow exponentially time-varying barrier levels in an otherwise standard Black-Scholes model. Our approach, reminiscent of the method of images of electromagnetics, considerably simplifies the derivation of analytical formulae for this class of exotics by reducing the pricing of any double-barrier problem to that of pricing a related European option. We illustrate the method by reproducing the well-known formulae of Kunitomo and Ikeda (1992) for the standard knock-out double-barrier call and put options. We give an explanation for the rapid rate of convergence of the doubly infinite sums for affine payoffs in the stock price, as encountered in the pricing of double-barrier call and put options first observed by Kunitomo and Ikeda (1992).

Bermin, H., Buchen, P.W. & Konstandatos, O. 2008, 'Two exotic lookback options', Applied Mathematical Finance, vol. 15, no. 4, pp. 387-402.
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This paper formally analyses two exotic options with lookback features, referred to as extreme spread lookback options and look-barrier options, first introduced by Bermin. The holder of such options receives partial protection from large price movements in the underlying, but at roughly the cost of a plain vanilla contract. This is achieved by increasing the leverage through either floating the strike price (for the case of extreme spread options) or introducing a partial barrier window (for the case of look-barrier options). We show how to statically replicate the prices of these hybrid exotic derivatives with more elementary European binary options and their images, using new methods first introduced by Buchen and Konstandatos. These methods allow considerable simplification in the analysis, leading to closed-form representations in the Black?Scholes framework.

Buchen, P.W. & Konstandatos, O. 2005, 'A new method of pricing lookback options', Mathematical Finance, vol. 15, no. 2, pp. 245-259.
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A new method for pricing lookback options (a.k.a.hindsightoptions) is presented, which simplifies the derivation of analytical formulas for this class of exotics in the Black-Scholes framework. Underlying the method is the observation that a lookback option can be considered as an integrated form of a related barrier option. The integrations with respect to the barrier price are evaluated at the expiry date to derive the payoff of an equivalent portfolio of European-type binary options. The arbitrage-free price of the lookback option can then be evaluated by static replication as the present value of this portfolio. We illustrate the method by deriving expressions for generic, standard floating-, fixed-, and reverse-strike lookbacks, and then show how the method can be used to price the more complex partial-price and partial-time lookback options. The method is in principle applicable to frameworks with alternative asset-price dynamics to the Black-Scholes world.

Alexander, D.M., Bourke, P.D., Sheridan, P., Konstandatos, O. & Wright, J.J. 2004, 'Intrinsic connections in tree shrew V1 imply a global to local mapping', Vision Research, vol. 44, no. 9, pp. 857-876.
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The local-global map hypothesis states that locally organized response properties??such as orientation preference??result from visuotopically organized local maps of non-retinotopic response properties. In the tree shrew, the lateral extent of horizontal patchy connections is as much as 80?100% of V1 and is consistent with the length summation property. We argue that neural signals can be transmitted across the entire extent of V1 and this allows the formation of maps at the local scale that are visuotopically organized. We describe mechanisms relevant to the formation of local maps and report modeling results showing the same patterns of horizontal connectivity, and relationships to orientation preference, seen in vivo. The structure of the connectivity that emerges in the simulations reveals a `hub and spoke? organization. Singularities form the centers of local maps, and linear zones and saddle-points arise as smooth border transitions between maps. These findings are used to present the case for the local-global map hypothesis for tree shrew V1.

Alexander, D., Sheridan, P., Konstandatos, O., bourke, P. & Wright, J.J. 1999, 'Emergent symmetry of local and global maps in the primary visual cortex: self-organisation of orientation preference.', Complexity International, vol. 6.

Buchen, P.W., Konstandatos, O. & Kyng, T. 2009, 'Images and barriers on the road to real options valuation', The 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, Cairns, Australia, July 2009 in Proceedings of the 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, ed Anderssen, R.S., R.D. Braddock and L.T.H. Newham, Modelling & Simulation Society of Australia & New Zealand & International Association for Mathematic, Cairns, Australia, pp. 1486-1492.

Alexander, D., Sheridan, P., Bourke, P.D., Konstandatos, O. & Wright, J.J. 1998, 'Global and local symmetry of the primary visual cortex: Derivation of orientation preference', Sydney, Australia, January 1998 in Proceedings of the Ninth Australian Conference on Neural Networks, ed ?, ?, Sydney, Australia.

Alexander, D., Sheridan, P., Bourke, P.D., Konstandatos, O. & Wright, J.J. 1997, 'Global and local similarity of the primary visual cortex: Mechanisms of orientation preference', Montreux, Switzerland, January 1997 in Proceedings of the HELNET International Workshop on Neural Networks, ed M.J. van der Heyden and J. Mrsicogel and K. Weigel, VU University Press, Amsterdam, The Netherlands.

Konstandatos, O. 1997, 'Toowoomba foundry: Corrosion and wear in Mmoulding poxes', Melbourne, Australia, January 1997 in Proceedings of the Mathematics in Industry Study Group, ed Kerry Landman, Mathematics in Industry Study Group, Melbourne, Australia.

Buchen, P.W. & Konstandatos, O. 2006, 'Barriers, lookbacks and other exotica', SFMW (Q-Group Australia) Workshop, Sydney, Australia, October 2006.

Buchen, P.W. & Konstandatos, O. 2006, 'Pricing exotic options', Financial Integrity Research Network Two-Day Workshop on Exotic Options, Sydney, Australia, April 2006.

Konstandatos, O. 2004, 'A new method for pricing double barriers', National Symposium on Financial Mathematics, Melbourne, Australia, June 2004.

Konstandatos, O. 2004, 'Maximising your payoff', Quantitative Methods in Finance 2004 Conference, Sydney, Australia, December 2004.

Konstandatos, O. 2004, 'Pricing double barriers', Seminar Presentation, School of Finance and Economics, University of Technology, Sydney, Sydney, Australia, November 2004.

Konstandatos, O. 2003, 'A new framework for pricing lookbacks', Q Group Australia PhD Prize Presentation, Sydney, Australia, May 2003.

Konstandatos, O. 2002, 'Pricing partial lookbacks', ANZIAM Mini-Conference, Mollymook, Australia, February 2002.

Alexander, D., Sheridan, P., Bourke, P.D., Konstandatos, O. & Wright, J.J. 1998, Emergence under Hebbian learning of local maps in the primary visual cortex: Orientation preference in the tree shrew, Mental Health Research Institute, Melbourne, Australia.

Alexander, D., Sheridan, P., Bourke, P.D., Konstandatos, O., Wright, J.J. 1997, Global and local symmetry of the primary visual cortex: Derivation of orientation preference, Mental Health Research Institute, Melbourne, Australia.