Abstract
In this paper we discuss the use of mathematical programming techniques linear, dynamic, and goal programming to the problem of the risk management of derivative securities (also known as contingent claims or options). We focus on the problem of the risk management of complex or exotic options in the presence of real market imperfections such as transaction costs. The advantages and disadvantages of the various approaches which have appeared in the literature are discussed including a new approach which we are developing.
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References
Aparicio, S.D., and S.D. Hodges, (1996), “Estimating Implied Distributions and Issues in Static Hedging”, Financial Options Research Centre Ninth Annual Conference 5-6 September, University of Warwick, Coventry, UK.
Black, F. and M. Scholes, (1973), “ The Pricing of Options and Corporate Liabilities”, Journal of Political Economy Vol. 81, pp 637–654.
Boyle, P. and T. Vorst, (1992), “ Option Replication in Discrete Time with Transactions Costs”, Journal of Finance, Vol. 47, pp 271–293.
Clewlow, L. and S.D. Hodges, (1994), “ Gamma Hedging in Incomplete Markets under Transaction Costs”, Financial Options Research Centre Preprint 94/52, University of Warwick, Coventry, England.
Clewlow, L. and S.D. Hodges, (1996), “ Optimal Delta-Hedging Under Transaction Costs”, Financial Options Research Centre Preprint 96/68, University of Warwick, Coventry, England.
Clewlow, L. and A. M. Pascoa, (1996), “ Static Hedging of Barrier Options in Realistic Markets”, Financial Options Research Centre Working Paper, University of Warwick, Coventry, England.
Davis, M. H. A. and V. G. Panas, (1991), “ European Option Pricing with Transactions Costs”, Proc 30th I E E E Conference on Decision and Control, pp 1299–1304.
Davis, M. H. A., V. G. Panas and T. Zariphopoulou, (1993), “ European Option Pricing with Transactions Costs”, SIAM Journal of Control and Optimisation, Vol. 31, pp 470–493.
Dembo, R., (1991), “ Scenario Optimization”, Annals of Operations Research, Vol. 30, pp 63–80.
Dempster, M.A.H., and X.C. Poiré, (1995), “ Stochastic Programming: A New Approach to Asset/Liability Management”, Financial Options Research Centre Eighth Annual Conference 22-23 June, University of Warwick, Coventry, UK.
Edirisinghe, C, V. Naik and R. Uppal, (1993), “ Optimal Replication of Options with Transactions Costs and Trading Restrictions”, Journal of Financial and Quantitative Analysis, Vol. 28, pp 117–138.
Hodges, S. D. and A. Neuberger, (1989), “ Optimal Replication of Contingent claims Under Transactions Costs, The Review of Futures Markets, Vol. 8, pp 222–239.
Hoggard T., A. E. Whalley, and P. Wilmott, (1994), “ Hedging Option Portfolios in the Presence of Transaction Costs”, Advances in Futures and Options Research, Vol. 7, pp 21–35.
Howe M. A., B. Rustem, and M. J. P. Selby, (1996), “ Multi-Period Minimax Hedging Strategies”, European Journal of Operational Research, Vol. 93, pp 185–204.
Leland, H. E., (1985), “ Option Pricing and Replication with Transactions Costs”, Journal of Finance, Vol. 40, pp 1283–1301.
Merton, R. C, (1973), “ Theory of Rational Option Pricing”, Bell Journal of Economics and Management Science, Vol. 4, pp 141–183.
Whalley A. E., and P. Wilmott, (1993), “ Counting the Cost”, Risk, Vol. 6(10), pp 59–66.
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© 1998 Springer Science+Business Media New York
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Clewlow, L., Hodges, S., Pascoa, A. (1998). Mathematical Programming and Risk Management of Derivative Securities. In: Zopounidis, C. (eds) Operational Tools in the Management of Financial Risks. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5495-0_14
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DOI: https://doi.org/10.1007/978-1-4615-5495-0_14
Publisher Name: Springer, Boston, MA
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