On Using Risk-Neutral Probabilities to Price Assets

22 Pages Posted: 10 Feb 2018

See all articles by Kuo-Ping Chang

Kuo-Ping Chang

National Tsing Hua University - Department of Quantitative Finance

Date Written: November 10, 2017

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 risk-free interest rate, the future possible prices and their probabilities. These probabilities are the actual world probabilities, not the so-called risk-neutral probabilities. The paper also proves that for the levered firm, (i) under riskless debt, increasing the debt-equity 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 debt-equity 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 debt-equity ratio do not affect the expected rate of return on the equity of the levered firm. These findings refute the Modigliani-Miller second proposition that the expected rate of return on the equity of the levered firm increases in proportion to the debt-equity 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.

Keywords: The Arbitrage Theorem, Risk-Neutral Probabilities, Capital Structure Irrelevancy

JEL Classification: G13, G32

Suggested Citation

Chang, Kuo-Ping, On Using Risk-Neutral Probabilities to Price Assets (November 10, 2017). Available at SSRN: https://ssrn.com/abstract=3114126 or http://dx.doi.org/10.2139/ssrn.3114126

Kuo-Ping Chang (Contact Author)

National Tsing Hua University - Department of Quantitative Finance ( email )

Hsin Chu, Taiwan 300
China
+886 3 574 2730 (Phone)
+886 3 571 5403 (Fax)

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