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26 pages, 3783 KB

Open AccessArticle

Market Efficiency and Stability Under Short Sales Constraints: Evidence from a Natural Experiment with High-Frequency Resolution

by Lin-Kun Chan, Chin-Yang Lin and Jin-Huei Yeh

Mathematics 2025, 13(5), 816; https://doi.org/10.3390/math13050816 - 28 Feb 2025

Cited by 3 | Viewed by 901

Abstract

The six short-sales constraints (SSCs) regime changes from 2002 to 2009 in the Taiwan stock market provide “natural social” experiments to examine how different SSC intensities affect price adjustment efficiency and market stability. There are three main findings. Firstly, we derive the theoretical price with put–call parity from seven series index options. Using a “threshold error correction model” (TECM), we find a more efficient price adjustment to new equilibria for upward adjustments than for downward adjustments. The SSCs impede the price adjustment downward, especially during the financial crisis of 2008. Therefore, relaxing the short-sales constraints essentially improves price efficiency. Secondly, our findings also refute the claim that tighter SSCs can help stabilize the market since the tightening of the short-sales restriction leads to increases in both market volatility and downside risk even after controlling the investor fear gauge of the Taiwan volatility index (TVIX). These results hold even when market conditions and liquidity are controlled. Finally, the evidence from our counterfactual policy analysis suggests that tighter constraints help restore market confidence even though prices may fall more sharply without short-sales bans. As a result, policymakers may practically optimize to strike a balance between the benefits of restored emerging market order and the cost of elevated market volatility. Full article

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8 pages, 1445 KB

Open AccessCommunication

Exploring Implied Certainty Equivalent Rates in Financial Markets: Empirical Analysis and Application to the Electric Vehicle Industry

by Yifan He and Svetlozar Rachev

J. Risk Financial Manag. 2023, 16(7), 344; https://doi.org/10.3390/jrfm16070344 - 24 Jul 2023

Viewed by 1875

Abstract

In this paper, we mainly study the impact of the implied certainty equivalent rate on investment in financial markets. First, we derived the mathematical expression of the implied certainty equivalent rate by using put-call parity, and then we selected some company stocks and options; we considered the best-performing and worst-performing company stocks and options from the beginning of 2023 to the present for empirical research. By visualizing the relationship between the time to maturity, moneyness, and implied certainty equivalent rate of these options, we have obtained a universal conclusion—a positive implied certainty equivalent rate is more suitable for investment than a negative implied certainty equivalent rate, but for a positive implied certainty equivalent rate, a larger value also means a higher investment risk. Next, we applied these results to the electric vehicle industry, and by comparing several well-known US electric vehicle production companies, we further strengthened our conclusions. Finally, we give a warning concerning risk, that is, investment in the financial market should not focus solely on the implied certainty equivalent rate, because investment is not an easy task, and many factors need to be considered, including some factors that are difficult to predict with models. Full article

(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)

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17 pages, 453 KB

Open AccessArticle

Pricing and Hedging Bond Power Exchange Options in a Stochastic String Term-Structure Model

by Lloyd P. Blenman, Alberto Bueno-Guerrero and Steven P. Clark

Risks 2022, 10(10), 188; https://doi.org/10.3390/risks10100188 - 27 Sep 2022

Cited by 3 | Viewed by 2195

Abstract

We study power exchange options written on zero-coupon bonds under a stochastic string term-structure framework. Closed-form expressions for pricing and hedging bond power exchange options are obtained and, as particular cases, the corresponding expressions for call power options and constant underlying elasticity in strikes (CUES) options. Sufficient conditions for the equivalence of the European and the American versions of bond power exchange options are provided and the put-call parity relation for European bond power exchange options is established. Finally, we consider several applications of our results including duration and convexity measures for bond power exchange options, pricing extendable/accelerable maturity zero-coupon bonds, options to price a zero-coupon bond off of a shifted term-structure, and options on interest rates and rate spreads. In particular, we show that standard formulas for interest rate caplets and floorlets in a LIBOR market model can be obtained as special cases of bond power exchange options under a stochastic string term-structure model. Full article

(This article belongs to the Special Issue New Challenges in Mathematical Finance: From S(P)DEs to Machine Learning)

11 pages, 261 KB

Open AccessArticle

Risk-Neutral Pricing Method of Options Based on Uncertainty Theory

by Hong Huang and Yufu Ning

Symmetry 2021, 13(12), 2285; https://doi.org/10.3390/sym13122285 - 1 Dec 2021

Cited by 3 | Viewed by 2695

Abstract

In order to rationally deal with the belief degree, Liu proposed uncertainty theory and refined into a branch of mathematics based on normality, self-duality, sub-additivity and product axioms. Subsequently, Liu defined the uncertainty process to describe the evolution of uncertainty phenomena over time. This paper proposes a risk-neutral option pricing method under the assumption that the stock price is driven by Liu process, which is a special kind of uncertain process with a stationary independent increment. Based on uncertainty theory, the stock price’s distribution and inverse distribution function under the risk-neutral measure are first derived. Then these two proposed functions are applied to price the European and American options, and verify the parity relationship of European call and put options. Full article

(This article belongs to the Special Issue Fuzzy Set Theory and Uncertainty Theory)

12 pages, 269 KB

Open AccessArticle

Entropic Dynamics of Stocks and European Options

by Mohammad Abedi and Daniel Bartolomeo

Entropy 2019, 21(8), 765; https://doi.org/10.3390/e21080765 - 6 Aug 2019

Cited by 3 | Viewed by 4448

Abstract

We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. The objective of the paper is to lay down an alternative framework for modeling dynamics. An important information about the dynamics of a stock’s price is scale invariance. By imposing the scale invariant symmetry, we arrive at choosing the logarithm of the stock’s price as the proper variable to model. The dynamics of stock log price is derived using two pieces of information, the continuity of motion and the directionality constraint. The resulting model is the same as the Geometric Brownian Motion, GBM, of the stock price which is manifestly scale invariant. Furthermore, we come up with the dynamics of probability density function, which is a Fokker–Planck equation. Next, we extend the model to value the European Options on a stock. Derivative securities ought to be prices such that there is no arbitrage. To ensure the no-arbitrage pricing, we derive the risk-neutral measure by incorporating the risk-neutral information. Consequently, the Black–Scholes model and the Black–Scholes-Merton differential equation are derived. Full article

31 pages, 988 KB

Open AccessArticle

Equity Options During the Shorting Ban of 2008

by Nusret Cakici, Gautam Goswami and Sinan Tan

J. Risk Financial Manag. 2018, 11(2), 17; https://doi.org/10.3390/jrfm11020017 - 31 Mar 2018

Cited by 3 | Viewed by 4966

Abstract

The Securities and Exchange Commission’s 2008 emergency order introduced a shorting ban of some 800 financials traded in the US. This paper provides an empirical analysis of the options market around the ban period. Using transaction level data from OPRA (The Options Price Reporting Authority), we study the options volume, spreads, pricing measures and option trade volume informativeness during the ban. We also consider the put–call parity relationship. While mostly statistically significant, economic magnitudes of our results suggest that the impact of the ban on the equity options market was likely not as dramatic as initially thought. Full article

(This article belongs to the Special Issue Empirical Asset Pricing)

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