Chang, KuoPing (2017): On Using RiskNeutral Probabilities to Price Assets.

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Abstract
This paper has used the Arbitrage Theorem under binomial case to show that in a complete market with no transaction costs and no arbitrage, for any asset, the current spot price is a function of the riskfree interest rate, the future possible prices and their probabilities. These probabilities are the actual world probabilities, not the socalled riskneutral probabilities. The paper also proves that for the levered firm, (i) under riskless debt, increasing the debtequity ratio increases the variance of the rate of return on equity and has no effect on the rate of return on debt; and (ii) under risky debt, increasing the debtequity ratio increases the variance of the rate of return on debt but does not affect the probability density function of the rate of return on equity. With the actual world probabilities, it can be shown that changes in the debtequity ratio do not affect the expected rate of return on the equity of the levered firm. These findings refute the ModiglianiMiller second proposition that the expected rate of return on the equity of the levered firm increases in proportion to the debtequity ratio. With the actual world probabilities, it is also found that increasing the variance of the underlying asset price may either increase or decrease the option prices.
Item Type:  MPRA Paper 

Original Title:  On Using RiskNeutral Probabilities to Price Assets 
English Title:  On Using RiskNeutral Probabilities to Price Assets 
Language:  English 
Keywords:  The Arbitrage Theorem, riskneutral probabilities, capital structure irrelevancy. 
Subjects:  G  Financial Economics > G1  General Financial Markets > G13  Contingent Pricing ; Futures Pricing G  Financial Economics > G3  Corporate Finance and Governance > G32  Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill 
Item ID:  96564 
Depositing User:  Professor KuoPing Chang 
Date Deposited:  25 Oct 2019 13:19 
Last Modified:  25 Oct 2019 13:19 
References:  Black, Fischer and Myron Scholes, 1973, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy 81, 637654. Brealey, Richard, Myers, Stewart and Allen, Franklin, 2017, Principles of Corporate Finance, McGrawHill, New York. Chang, KuoPing, 2016, “The ModiglianiMiller Second Proposition Is Dead; Long Live the Second Proposition,” Ekonomickomanažerské Spektrum 10, 2431; http://ssrn.com/abstract=2762158. Chang, KuoPing, 2015, The Ownership of the Firm, Corporate Finance, and Derivatives: Some Critical Thinking, Springer, New York. Chang, KuoPing, 2014, “Some Misconceptions in Derivative Pricing,” http://ssrn.com/abstract=2138357. Cox, John, Stephen Ross, and Mark Rubinstein, 1979, “Option Pricing: A Simplified Approach,” Journal of Financial Economics 7, 229263. Miller, Merton, 1988, “The ModiglianiMiller Propositions: After Thirty Years,” Journal of Economic Perspectives 2, 99120. Modigliani, Franco and Miller, Merton, 1958, “The Cost of Capital, Corporation Finance and the Theory of Investment,” American Economics Review 48, 261297. Ross, Sheldon, 1993, Introduction to Probability Models, Academic Press, New York. Ross, Stephen, Westerfield, Randolph, Jaffe, Jeffrey and Jordan, Bradford, 2016, Corporate Finance, McGrawHill, New York. Ross, Stephen, 1998, “The Mathematics of Finance: Pricing Derivatives,” Quarterly of Applied Mathematics 56, 695706. Wilmott, Paul, 2007, Paul Wilmott Introduces Quantitative Finance, John Wiley & Sons, West Sussex, England. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/96564 