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A. Paul (1965)
SAMUELSON, . Proof that properly anticipated prices fluctuate randomly, Industrial Management Review, ., 6
A. Paul (1973)
SAMUELSON, . Proof That Properly Discounted Present Values of Assets Vibrate Journal of Economics and Management Science, , ., 4
Merton Miller (1958)
The Cost of Capital, Corporation Finance and the Theory of InvestmentThe American Economic Review, 48
While inspection of (25) shows that HT < 0 for d > 1 which agrees with the sign of GT for d > 1, H T can be either signed for d < 1 which does not agree with the positive sign on G
P. Samuelson (2015)
Proof that Properly Anticipated Prices Fluctuate Randomly
See Merton
R. Merton (2015)
Theory of Rational Option PricingWorld Scientific Reference on Contingent Claims Analysis in Corporate Finance
J. Cohen, F. Black, Myron Scholes (1972)
The Valuation of Option Contracts and a Test of Market EfficiencyJournal of Finance, 27
(1970)
Dynamic General Equilibrium Model of the Asset Market and and Its Application to the Pricing of the Capital Structure of the Firm
E. Fama (1970)
EFFICIENT CAPITAL MARKETS: A REVIEW OF THEORY AND EMPIRICAL WORK*Journal of Finance, 25
Of course, this assumption does not rule out serial dependence in the earnings of the firm. See Samuelson [10] for a discussion
Note, for example, that in the context of the Sharpe-Lintner-Mossin Capital Asset Pricing Model, g is equal to the ratio of the 'beta" of the bond to the "beta" of the firm
It is well known that '(x) + x(x) > 0 for -< x a<
For a rigorous discussion of Ito's Lemma, see McKean [4]. For references to its application in portfolio theory
10] where it is shown that f is a firstdegree homogeneous, convex function of V and B
M. Rothschild, J. Stiglitz (1970)
Increasing risk: I. A definitionJournal of Economic Theory, 2
F. Black, Myron Scholes (1973)
The Pricing of Options and Corporate LiabilitiesJournal of Political Economy, 81
P. Samuelson (1973)
Proof That Properly Discounted Present Values of Assets Vibrate RandomlyThe Bell Journal of Economics, 4
J. Stiglitz (1967)
A Re-Examination of the Modigliani Miller TheoremThe American Economic Review, 59
(1973)
" A Rational Theory of Option Pricing
I. I ntroduction T he value of a particular issue of corporate debt depends essentially on three items: (1) the required rate of return on riskless (in terms of default) debt (e.g., government bonds or very high grade corporate bonds); (2) the various provisions and restrictions contained in the indenture (e.g., maturity date, coupon rate, call terms, seniority in the event of default, sinking fund, etc.); (3) the probability that the firm will be unable to satisfy some or all of the indenture requirements (i.e., the probability of default). While a number of theories and empirical studies has been published on the term structure of interest rates (item 1), there has been no systematic development of a theory for pricing bonds when there is a significant probability of default. The purpose of this paper is to present such a theory which might be called a theory of the risk structure of interest rates. The use of the term “risk” is restricted to the possible gains or losses to bondholders as a result of (unanticipated) changes in the probability of default and does not include the gains or losses inherent to all bonds caused by (unanticipated) changes in interest
The Journal of Finance – Wiley
Published: May 1, 1974
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