A market-induced mechanism for stock pinning

Abstract

We propose a model to describe stock pinning on option expiration dates. We argue that if the open interest on a particular contract is unusually large, delta-hedging in aggregate by floor market-makers can impact the stock price and drive it to the strike price of the option. We derive a stochastic differential equation for the stock price which has a singular drift that accounts for the price-impact of delta-hedging. According to this model, the stock price has a finite probability of pinning at a strike. We calculate analytically and numerically this probability in terms of the volatility of the stock, the time-to-maturity, the open interest for the option under consideration and a ‘price elasticity’ constant that models price impact.     

Optimal hedging in an extended binomial market under transaction costs

We develop an approach to optimal hedging of a contingent claim under proportional transaction costs in a discrete time financial market model which extends the binomial market model with transaction costs. Our model relaxes the binomial assumption on the stock price ratios to the case where the stock price ratio distribution has bounded support. Non-self-financing hedging strategies are studied to construct an optimal hedge for an investor who takes a short position in a European contingent claim settled by delivery. We develop the theoretical basis for our optimal hedging approach, extending results obtained in our previous work. Specifically, we derive a no-arbitrage option price interval and establish properties of the non-self-financing strategies and their residuals. Based on the theoretical foundation, we develop a computational algorithm for optimizing an investor relevant criterion over the set of admissible non-self-financing hedging strategies. We demonstrate the applicability of our approach using both simulated data and real market data.     

Price and volatility spillovers between exchange rates and stock indexes for the pre- and post-euro period

In this paper we explore the nature of the mean, volatility and causality transmission mechanism between stock and foreign exchange markets for the United States and some major European markets for the periods pre- and post-euro. The asymmetric volatility transmission is described by an extended Multivariate Exponential Generalized Autoregressive Conditionally Heteroskedastic (EGARCH) model. The results support the asymmetric and long-range persistence volatility spillover effect and show strong evidence of causality in the mean and variance between foreign exchange rate and stock price for both pre- and post-euro periods. However, the stock price has a more significant effect on foreign exchange rate for the two subsamples. These results are robust to the cross-correlation function test suggested by Cheung and Ng. The implication is particularly important for international portfolio managers when devising hedging and diversification strategies for their portfolios.     

基金经理更换、股票联动与股票价格

基金经理更换打破了基金共同持股投资组合中股票的关联性,降低了股票收益率相关性,进而影响了股票价格。本文基于基金共同持股和基金经理更换构建了对冲投资组合,获得0.1%的日超额收益率。基金投资组合中股票收益率相关性能够解释这种超额收益率,本文发现基金更换经理后,新基金经理重建投资组合,打破了原投资组合中股票间的关联,股票收益率相关性减弱,基金共同持股程度高的股票价格受到了更大影响。基金的被动流动性冲击不能解释本文的发现。本文的研究表明基金经理变更等基金管理行为通过股票收益率相关性对股票价格产生了重要影响。     

Pricing by hedging and no-arbitrage beyond semimartingales

We show that pricing a big class of relevant options by hedging and no-arbitrage can be extended beyond semimartingale models. To this end we construct a subclass of self-financing portfolios that contains hedges for these options, but does not contain arbitrage opportunities, even if the stock price process is a non-semimartingale of some special type. Moreover, we show that the option prices depend essentially only on a path property of the stock price process, viz. on the quadratic variation. We end the paper by giving no-arbitrage results even with stopping times for our model class.      

模糊厌恶下股指期货风险对冲策略设计及实证分析

投资者对股指期货与现货有着不同的模糊厌恶,本文首先将此假设条件引入带交易成本的Garleanu and Pederson (2013)投资模型中,并以指数基金对冲策略为例,构建了一个股指期货动态对冲的理论模型。与非对冲策略相比,基于上述模型设计的对冲策略投资绩效更好,动态最优成交额占目标交易额的比例更小,目标成交额对收益率预测因子的敏感性更大。借助上述模型,本文选取2010年4月至2021年6月的中国ETF指数基金和股指期货数据,并以2015年9月股指期货管理措施实施为界进行区间划分,实证研究发现:(1)中国A股市场的ETF投资组合进行股指期货对冲显著提升了投资绩效,但股指期货管理会削弱该作用;(2)投资绩效改善主要来源于交易成本的下降与目标成交额因子敏感性的提升,该机制受到股指期货管理的约束;(3)与Garleanu and Pederson (2013)、Zhang et al. (2017)相比,本文对冲策略保留“抗跌”特点的同时增加了“易涨”特性。本文研究结果表明,在当前大力发展机构投资者的背景下应不断丰富股指期货、股指期权产品谱系,降低股指期货交易成本并完善持仓约束。     

Why do convertible issuers simultaneously repurchase stock? An arbitrage-based explanation

Over recent years, a substantial fraction of US convertible bond issues have been combined with a stock repurchase. This paper explores the motivations for these combined transactions. We argue that convertible debt issuers repurchase their stock to facilitate arbitrage-related short selling. In line with this prediction, we show that convertibles combined with a stock repurchase are associated with lower offering discounts, lower stock price pressure, higher expected hedging demand, and lower issue-date short selling than uncombined issues. We also find that convertible arbitrage strategies explain both the size and the speed of execution of the stock repurchases.     

Portfolio Insurance Strategies when Hedging Affects Share Prices

Option-based portfolio insurance can result in coordinated buying and selling, which destabilizes markets such that hedgers fail to achieve their objective. Gennotte and Leland (1990) show portfolio insurance strategies can have an impact on price movements. Ramanlal and Mann (1996) show how price movements, in turn, can alter hedging strategies. In this paper, we combine these separate effects and develop an equilibrium, executable hedging strategy. This hedging strategy requires less rebalancing than traditional portfolio insurance; more important, it achieves downside protection with a less destabilizing impact on security prices.     

Consistent Variance Curve Models

We introduce a general approach to model a joint market of stock price and a term structure of variance swaps in an HJM-type framework. In such a model, strongly volatility-dependent contracts can be priced and risk-managed in terms of the observed stock and variance swap prices. To this end, we introduce equity forward variance term structure models and derive the respective HJM-type arbitrage conditions. We then discuss finite-dimensional Markovian representations of the fixed time-to-maturity forward variance swap curve and derive consistency results for both the standard case and for variance curves with values in a Hilbert space. For the latter, our representation also ensures non-negativity of the process. We then give a few examples of such variance curve functionals and briefly discuss completeness and hedging in such models. As a further application, we show that the speed of mean reversion in some standard stochastic volatility models should be kept constant when the model is recalibrated.     

The term structure of S&P 100 model-free volatilities

We develop an improved method to obtain the model-free volatility more accurately despite the limitations of a finite number of options and large strike price intervals. Our method computes the model-free volatility from European-style S&P 100 index options over a horizon of up to 450 days, the first time that this has been attempted, as far as we are aware. With the estimated daily term structure over the long horizon, we find that (i) changes in model-free volatilities are asymmetrically more positively impacted by a decrease in the index level than negatively impacted by an increase in the index level; (ii) the negative relationship between the daily change in model-free volatility and the daily change in index level is stronger in the near term than in the far term; and (iii) the slope of the term structure is positively associated with the index level, having a tendency to display a negative slope during bear markets and a positive slope during bull markets. These significant results have important implications for pricing and hedging index derivatives and portfolios.     

Determination of stock closing prices and hedging performance with stock indices futures

This paper examines the impact of the determination of stock closing prices on futures price efficiency and hedging effectiveness with stock indices futures. The empirical results indicate that the increase in the length of the batching period of the stock closing call improves price efficiency in the futures closing prices and then enhances hedging performance in terms of the hedging risks. Additionally, from a utility‐maximization point of view, hedging performance does not improve after the introduction of the 5 min stock closing call, which can be explained by an improvement in price efficiency at the futures market close.     

The impact of derivatives hedging on the stock market: Evidence from Taiwan’s covered warrants market

We examine the impact of derivatives hedging on the spot market using accurate hedge ratios of covered warrants traded in the Taiwan Stock Exchange (TWSE). Results present significant positive abnormal returns and trading volumes before the announcement of a warrant’s issuance, and the effect is stronger when the hedging demand is larger. Moreover, a significantly positive relationship exists between stock return volatility and the price elasticity of hedging demand. Finally, we observe a significantly negative price effect upon the underlying stock after a call warrant has expired in-the-money due to the liquidation of hedging portfolios.     

Multiperiod hedging in the presence of stochastic volatility

In this paper, we characterize the multiperiod minimum-risk hedge strategy within the stochastic volatility (SV) framework and compare it to other hedge strategies on the basis of hedging performance. Using crude oil markets as an example, we demonstrate that the SV model is appropriate in depicting price behaviour. However, ex ante and ex post comparisons indicate that the SV strategy is inferior to conventional hedging strategies. There is also evidence that the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) strategy may be better than the SV strategy, at least in terms of variance reduction.     

Firm Value and Hedging: Evidence from U.S. Oil and Gas Producers

This paper studies the hedging activities of 119 U.S. oil and gas producers from 1998 to 2001 and evaluates their effect on firm value. Theories of hedging based on market imperfections imply that hedging should increase the firm's market value (MV). To test this hypothesis, we collect detailed information on the extent of hedging and on the valuation of oil and gas reserves. We verify that hedging reduces the firm's stock price sensitivity to oil and gas prices. Contrary to previous studies, however, we find that hedging does not seem to affect MVs for this industry.     

备兑权证风险对冲策略分析

我国资本市场金融创新产品接连推出,备兑权证也再次被提上议程。在备兑权证的风险管理上,现有文献多集中于权证定价模型上的Delta对冲策略,却忽视了交易成本与间断交易,也没有深入分析影响该策略的各个因素。本文通过仿真实验Leland模型下的动态Delta对冲策略,发现交易成本、对冲间隔、行权价格以及波动率的变化都会显著影响对冲结果,但发行商仍有机会获取对冲收益,建议发行商略微溢价（5％）发行备兑权证,认为第三方对冲监管和差别对待的机制设计可确保市场繁荣。     

Revisiting the incentive effects of executive stock options

We develop a multiperiod framework to evaluate the incentive effects of executive stock options (ESOs). For a given increase in the grant-date firm stock price (and a concurrent increase in return volatility), the increment of total value at the vesting date acts as a proxy for the incentive effects of ESOs. If the option is attached to the existing contract without adjusting cash compensation, we suggest that a firm should not always fix the strike price to the grant-date stock price; instead, the strike price should vary with the length of the vesting period. We also show that, compared with at-the-money options, restricted stock generates greater incentives to increase stock prices in some scenarios, especially when equity-based awards are vested early. If the vesting period is long, the firm could grant options instead of restricted stock to maximize incentives.     

Insiders' hedging in a jump diffusion model

In this paper, we formulate the optimal hedging problem when the underlying stock price has jumps, especially for insiders who have more information than the general public. The jumps in the underlying price process depend on another diffusion process, which models a sequence of firm-specific information. This diffusion process is observed only by insiders. Nevertheless, the market is incomplete to insiders as well as to the general public. We use the local risk minimization method to find an optimal hedging strategy for insiders. We also numerically compare the value of the insider's hedging portfolio with the value of an honest trader's hedging portfolio for a simulated sample path of a stock price.     

Model misspecification analysis for bond options and Markovian hedging strategies

In this paper, we analyse the model misspecification risk of Markovian hedging strategies for discount bond options. We show how to decompose the Profit and Loss that results from model misspecification, and emphasize the importance of the position’s gamma in order to control it. We further provide mathematical results on the distribution of the forward Profit and Loss function for specific univariate term structure models. Finally, we run numerical simulations for options’ hedging strategies in order to examine the sensitivity of the forward Profit and Loss function with respect to the volatility of the forward rate curve, the frequency of the position rebalancing and the characteristics of the position being hedged.      

Selective hedging strategies for crude oil futures based on market state expectations

This paper studies the ex-ante selective hedging strategies of crude oil futures contracts based on market state expectations and compares the hedging performances to the traditional minimum variance routine hedging strategies. The main advantage of the proposed method is that it achieves a trade-off between return and risk, rather than hedges risk at all costs. Specifically, we first use a multi-input Hidden Markov Model(HMM) to identify the market state, assess the market’s herding impact, and then integrate the findings of identification and measurement to forecast the price trend. We offer an adjustment criterion for the hedge ratios driven by GARCH²-type models based on the anticipated market state. We conducted an empirical analysis to examine the hedging effect of WTI and Brent crude oil futures, the results indicate that the proposed state-dependent hedging strategies are superior to the traditional model-driven hedging strategies concerning the hedged portfolio based on four criteria. The robustness check reveals that the proposed hedging strategies still outperform in different market situation. The findings can help traders in the crude oil markets, and the methodology can be applied to other energy markets.     

Black swan events and safe havens: The role of gold in globally integrated emerging markets

There is evidence to suggest that gold acts as both a hedge and a safe haven for equity markets over recent years, and particularly during crises periods. Our work extends the recent literature on hedging and diversification roles of gold by analyzing its interaction with the stock markets of the leading emerging economies, the BRICS. While they generally exhibit a high growth rate, these economies still experience a pronounced vulnerability to external shocks, particularly to commodity price fluctuations. Using a multi-scale wavelet approach and a GARCH-based copula methodology, we mainly show evidence of: (i) the time-scale co-evolvement patterns between BRICS stock markets and gold market, with some profound regions of concentrated extreme variations; and (ii) a strong time-varying asymmetric dependence structure between those markets. These findings are essential for risk diversification and portfolio hedging strategies among the investigated markets.