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Non-uniqueness of option prices. (English) Zbl 0709.62504
Summary: This note shows that, for a stock whose prices follow a general stochastic process, there may be infinitely many option-pricing formulas which are compatible with the stock prices and an assumed risk-free rate of return.

62P05 Applications of statistics to actuarial sciences and financial mathematics
91G20 Derivative securities (option pricing, hedging, etc.)
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[1] Albrecht, P., A note on immunization under a general stochastic equilibrium model of the term structure, Insurance: mathematics and economics, 4, 239-244, (1985) · Zbl 0587.62190
[2] Beenstock, M.; Brasse, V., Using options to price maturity guarantees, Journal of the institute of actuaries, 113, 151-166, (1986)
[3] Black, F.; Scholes, M., The pricing of options and corporate liabilities, Journal of political economy, 81, 637-659, (1973) · Zbl 1092.91524
[4] (), 181-198, Reprinted in
[5] Boyle, P.P., Immunization under stochastic models of the term structure, Journal of the institute of actuaries, 105, 177-187, (1978)
[6] Boyle, P.P., Recent models of the term structure of interest rates with actuarial applications, Transactions of the 21st international congress of actuaries, 4, 95-104, (1980), Topic
[7] Boyle, P.P., Risk sharing, incentives and moral hazard, (), 31-75, NATO ASI series, Series C · Zbl 0537.90010
[8] Boyle, P.P., Perspectives on mortgage default insurance, (), 185-199
[9] Brennan, M.J.; Schwartz, E.S., Pricing and investment strategies for guaranteed equity-linked life insurance, (1979), Irwin Homewood, IL
[10] Clancy, R.P., Options on bonds and applications to product pricing, Transactions of the society of actuaries, 37, 97-130, (1985), Discussion 131-151
[11] Collins, T.P., An exploration of the immunization approach to provision for the unit-linked policies with guarantees, Journal of the institute of actuaries, 109, 241-284, (1982)
[12] Cox, J.C.; Ross, S.A., The valuation of options for alternative stochastic processes, Journal of financial economics, 3, 145-166, (1976)
[13] Cox, J.C.; Rubinstein, M., A survey of alternative option-pricing, (), 3-33
[14] Cox, J.C.; Rubinstein, M., Options markets, (1985), Prentice-Hall Englewood Cliffs, NJ
[15] Cox, J.C.; Ingersoll, J.E.; Ross, S.A., Duration and the measure of basis risk, Journal of business, 52, 51-61, (1979)
[16] Cox, J.C.; Ross, S.A.; Rubinstein, M., Option pricing: A simplified approach, Journal of financial economics, 7, 229-263, (1979) · Zbl 1131.91333
[17] Ho, T.S.Y.; Lee, S.-B., Term structure movements and pricing interest rate contingent claims, Journal of finance, 41, 1011-1029, (1986)
[18] Ingersoll, J.E., Theory of financial decision making, (1987), Rowan and Littlefield Totowa, NJ
[19] Jarrow, R.A.; Rudd, A., Option pricing, (1983), Irwin Homewood, IL
[20] Malliaris, A.G.; Brock, A.W., Stochastic methods in economics and finance, (1981), North-Holland Amsterdam · Zbl 0479.90003
[21] Merton, R.C., An analytic derivation of the cost of deposit insurance and loan guarantees: an application of modern option pricing theory, Journal of banking and finance, 1, 3-11, (1977)
[22] Omberg, E., A note on the convergence of binomial-pricing and compound-option models, Journal of finance, 42, 463-469, (1987)
[23] Page, F.H.; Sanders, A.B., A general derivation of the jump process option pricing formula, Journal of financial and quantitative analysis, 21, 437-446, (1986)
[24] Parkinson, M., Option pricing: the American put, Journal of business, 50, 21-36, (1977)
[25] ()
[26] Rendleman, R.J.; Bartter, B.J., Two state option pricing, Journal of finance, 34, 1093-1110, (1979)
[27] Sharpe, W.F., Corporate pension funding policy, Journal of financial economics, 3, 183-193, (1976)
[28] Smith, C.W., Option pricing: A review, Journal of financial economics, 3, 3-51, (1976)
[29] Smith, C.W., Applications of option pricing analysis, (), 79-121
[30] (), Reprinted in
[31] Smith, C.W., On the convergence of insurance and finance research, Journal of risk and insurance, 53, 693-717, (1986)
[32] Weinberger, A., New solutions to investment management problems, (), 99-103
[33] Wilkie, A.D., An option pricing approach to bonus policy, Journal of the institute of actuaries, 114, 21-77, (1987), Discussion 78-90
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