Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-02-06T06:53:16.521Z Has data issue: false hasContentIssue false
  • English
  • Français

Notes on Options, Hedging, Prudential Reserves and Fair Values

Published online by Cambridge University Press:  10 June 2011

A. D. Wilkie ,
M. P. Owen  and
H. R. Waters
A. D. Wilkie
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, U.K., Email: A.D.Wilkie@ma.hw.ac.uk and InQA Limited, Dennington, Ridgeway, Horsell, Woking GU21 4QR, U.K. E-mail: david.wilkie@inqa.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we present many investigations into the results of simulating the process of hedging a vanilla option at discrete times. We consider mainly a ‘maxi’ option (paying Max(A, B)), though calls, puts and ‘minis’ are also considered. We show the sensitivity of the variability of the hedging error to the actual investment strategy adopted, and to the many ways in which the simulated real world can diverge from the assumed option pricing model. We show how prudential reserves can be calculated, using conditional tail expectations, and how net premiums or fair values (which we present as the same) can be calculated, allowing for the necessary prudential reserves. We use two bond models, the very simple Black-Scholes one and a less unrealistic one. We also use the Wilkie model as an even more realistic real-world model, allowing for many complications in it to make it more realistic. We make observations on the important difference between real-world models and option pricing models, and emphasise the latter as the way of getting hedging quantities, and not just option prices.

Keywords

OptionsHedgingContingency ReservesQuantile ReservesConditional Tail ExpectationsPrudential ReservesShareholder ValueFair ValueInvestment StrategiesHedging ErrorsTransaction CostsPracticability of HedgingFat-tailed InnovationsStochastic HypermodelsStochastic BridgesBrownian BridgesOrnstein-Uhlenbeck Bridges
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 11 , Issue 2 , 01 June 2005 , pp. 199 - 293
Copyright
Copyright © Institute and Faculty of Actuaries 2005

References

Baxter, M. & Rennie, A. (1996). Financial calculus. Cambridge University Press.CrossRefGoogle Scholar
Boyle, P.P. & Emmanuel, D. (1980). Discretely adjusted option hedges. Journal of Financial Economics, 8, 259–282.CrossRefGoogle Scholar
Boyle, P.P. & Hardy, M.R. (1997). Reserving for maturity guarantees: two approaches. Insurance: Mathematics and Economics, 21, 113–127.Google Scholar
Dullaway, D. & Needleman, P.D. (2004). Realistic liabilities and risk capital margins for with-profits business. British Actuarial Journal, 10, 185–316.CrossRefGoogle Scholar
Faculty of Actuaries (2004). Asset models in life assurance; views from the Stochastic Accreditation Working Party, a discussion meeting. British Actuarial Journal, 10, 153–165.CrossRefGoogle Scholar
Ford, A., Benjamin, S., Gillespie, R.G., Hager, D.P., Loades, D.H., Rowe, B.N., Ryan, J.P., Smith, P. & Wilkie, A.D. (1980). Report of the Maturity Guarantees Working Party. Journal of the Institute of Actuaries, 107, 103–212.Google Scholar
Kendall, M.G. & Stuart, A. (1977). The advanced theory of statistics, volume 1, distribution theory. 4th edition. Charles Griffin & Company, London.Google Scholar
Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–188.CrossRefGoogle Scholar
Wilkie, A.D. (1995). More on a stochastic investment model for actuarial use. British Actuarial Journal, 1, 777–964.CrossRefGoogle Scholar
Wilkie, A.D., Waters, H.R. & Yang, S. (2003). Reserving, pricing and hedging for policies with guaranteed annuity options. British Actuarial Journal, 9, 263–425.CrossRefGoogle Scholar
Willmot, P. (1998). The theory and practice of financial engineering. Wiley.Google Scholar