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The exogenous exclusion of these "doubling" strategies is somewhat arbitrary, however. Types of constraints that exclude continuous-trading arbitrage opportunities were studied by Kreps , Harrison and Kreps , and Dybvig . These papers provide constraints that are unsatisfactory from an institutional point of view since they have no market analogue. Margin requirements, on the other hand, have a market analogue. One purpose of this paper is to show that margin requirements also exclude continuous-trading arbitrage opportunities.
And S. Ross, 1976, The valuation of options for alternative stochastic processes, Journal of Financial Economics 3, 145-166. Cox, J. and M. Rubinstein, 1978, Option markets (Prentice-Hall, Englewood Cliffs, NJ) forthcoming. , 1946, Mathematical methods of statistics (Princeton University Press, Princeton, NJ). , 1976, A general theory for asset valuation under diffusion processes, Institute of Business and Economic Research working paper no. , 1975, The stock options manual (McGraw-Hili, New York).
We will return to this issue in section 5. 3. Approximate option valuation formula This section employs the generalized Edgeworth series expansion (4) discussed in section 2 to obtain an approximate option valuation formula. The logic of the approach is simple. Usingf(s) as the true distribution of the stock price at maturity, the expected value at maturity of a payout protected option on that stock can be obtained. 2 The generalized Edgeworth series expansion then gives us an approximate expected valve for the option at maturity in terms of the approximating distribution a(s).