No-Arbitrage in Financial Economics: Solution of the Mystery of Implied Volatility and S&P 500 Volatility Index  

作　　者：Valery V.Shemetov 

机构地区：[1]不详

出　　处：《Management Studies》2023年第3期125-168,共44页管理研究（英文版）

摘　　要：We have shown that classic works of Modigliani and Miller, Black and Scholes, Merton, Black and Cox, and Leland making the foundation of the modern asset pricing theory, are wrong due to misinterpretation of no arbitrage as the martingale no-arbitrage principle. This error explains appearance of the geometric Brownian model (GBM) for description of the firm value and other long-term assets considering the firm and its assets as self-financing portfolios with symmetric return distributions. It contradicts the empirical observations that returns on firms, stocks, and bonds are skewed. On the other side, the settings of the asset valuation problems, taking into account the default line and business securing expenses, BSEs, generate skewed return distributions for the firm and its securities. The Extended Merton model (EMM), taking into account BSEs and the default line, shows that the no-arbitrage principle should be understood as the non-martingale no arbitrage, when for sufficiently long periods both the predictable part of returns and the mean of the stochastic part of returns occur negative, and the value of the return deficit depends on time and the states of the firm and market. The EMM findings explain the problems with the S&P 500 VIX, the strange behavior of variance and skewness of stock returns before and after the crisis of 1987, etc.

关 键 词：geometric Brownian model Extended Merton model business securing expenses option and warrant pricing corporate debt default probability 

分 类 号：O17[理学—数学]