In-the-Money Warrant Extensions

This paper examines the warrant price and stock price reactions to the extension of the expiration date of in-the-money warrants. The warrant prices increase significantly in response to the announcement, consistent with option pricing theory. Shareholders experience no significant abnormal returns at the announcement, contrary to the conjecture that an extension will transfer wealth from shareholders. There is support for the idea that firms extend warrant life because the existing assets' cash flow obviates the need for additional financing. The data show that both the stocks and the warrants perform poorly in the month following the extension announcement.     

The financing decisions of REITs: The case of warrant extensions

In this paper, we examine the warrant price and stock price reactions to the announcement of warrant life extensions by REITs. As predicted by option pricing theory, warrant prices increase in response to these extensions. The stocks of REITs making the extension announcements experience average abnormal returns that are not significantly different from zero. Thus, total firm value appears to increase, with the gains accruing primarily to the warrantholders.     

An extention of Samuelson's warrant valuation model and its application to Japanese data

It is well known among warrant traders that the Black & Scholes model cannot be directly used for warrant and convertible bond valuation. In this paper, a new warrant valuation model based on both the Samuelson and the Barone-Adesi & Whaley model is proposed, and the model is applied to convertible bond valuation. Our model is an extension of Samuelson's perpertual warrant model, whose parameters depend on stock price, volatility, term to maturity and interest rate.     

A Simple Formula for the Expected Rate of Return of an Option over a Finite Holding Period

Under conditions consistent with the Black-Scholes formula, a simple formula is developed for the expected rate of return of an option over a finite holding period possibly less than the time to expiration of the option. Under these conditions, surprisingly, the expected future value of a European option, even prior to expiration, is shown equal to the current Black-Scholes value of the option, except that the expected future value of the stock at the end of the holding period replaces the current stock price in the Black-Scholes formula and the future value of a riskless invesment of the striking price replaces the striking price. An extension of this result is used to approximate moments of the distribution of returns from an option portfolio.     

A Test for Price Pressure Effects in Tender Offer Stock Repurchases

The evidence in this paper supports the hypothesis that the previously documented stock price reversal following a tender offer announcement is consistent with a price pressure caused by a temporary shift in the security's demand curve. The authors came to this conclusion by redocumenting the price reversal, by finding an increase in trading volume around the tender offer announcement and expiration, by showing the increase in volume to be larger than expected from only an information effect, and by showing that short selling activity increases after the announcement and before the expiration of the tender offer.     

首日涨停板制度与IPO解禁效应——基于投机泡沫视角的分析

本文以2006—2016年上市的1397家公司为研究样本,实证检验了首日涨停板制度对新股解禁效应的影响。结果发现:首日涨停板制度实施期间发行的新股,解禁时有显著更差的市场表现,[-30,30]窗口期间的超额回报低至-8.43%,同时有更小的异常交易量和异常波动率;新股上市时股价高估程度越大、投资者情绪越高,首日涨停板制度对解禁效应的影响越强。上述结果支持了Hong et al.(2006)提出的“解禁与资产泡沫破灭”的理论,即首日涨停板制度导致新股发行后投机泡沫累积,投机泡沫破灭导致解禁时更大幅度的股价下跌。本文的研究结论补充了首日涨停板制度后果的文献,并对防范金融风险和完善新股市场化改革具有一定的政策参考价值。     

Option prices and stock market momentum: evidence from China

Option prices tend to be correlated to past stock market returns due to market imperfections. We unprecedentedly examine this issue on the SSE 50 ETF option in the Chinese derivatives market. To measure the price pressure in the options market, we construct an implied volatility spread based on pairs of the SSE 50 ETF option with identical expiration dates and strike prices. By regressing the implied volatility spread on past stock returns, we find that past stock returns exert a strong influence on the pricing of index options. Specifically, we find that SSE 50 ETF calls are significantly overvalued relative to SSE 50 ETF puts after stock price increases and the reverse is also true after the stock price decreases. Moreover, we validate the momentum effects in the underlying stock market to be responsible for the price pressure. These findings are both economically and statistically significant and have important implications.     

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.     

Modeling stock pinning

This paper investigates the effect of hedging strategies on the so-called pinning effect, i.e. the tendency of stock's prices to close near the strike price of heavily traded options as the expiration date nears. In the paper we extend the analysis of Avellaneda and Lipkin, who propose an explanation of stock pinning in terms of delta hedging strategies for long option positions. We adopt a model introduced by Frey and Stremme and show that, under the original assumptions of the model, pinning is driven by two effects: a hedging-dependent drift term that pushes the stock price toward the strike price and a hedging-dependent volatility term that constrains the stock price near the strike as it approaches it. Finally, we show that pinning can be generated by simulating trading in a double auction market. Pinning in the microstructure model is consistent with the Frey and Stremme model when both discrete hedging and stochastic impact are taken into account.     

VENTURE CAPITAL AND IPO LOCKUP EXPIRATION: AN EMPIRICAL ANALYSIS

Most initial public offerings (IPOs) feature “lockup” agreements, which bar insiders from selling the stock for a set period following the IPO, usually 180 days. We examine stock price behavior in the period surrounding lockup expiration for a sample of 2,529 firms from 1988 to 1997. We find that lockup expirations are, on average, associated with significant and negative abnormal returns, but the losses are concentrated in firms with venture capital backing. For the venture‐capital‐backed group, the largest losses occur for high‐tech firms and firms with the greatest post‐IPO stock price increases, the largest relative trading volume in the period surrounding expiration, and the highest quality underwriters. JEL classification: G14, G24     

WARRANT PRICING USING OBSERVABLE VARIABLES

The classical warrant pricing formula requires knowledge of the firm value and of the firm‐value process variance. When warrants are outstanding, the firm value itself is a function of the warrant price. Firm value and firm‐value variance are then unobservable variables. I develop an algorithm for pricing warrants using stock prices, an observable variable, and stock return variance. The method also enables estimation of firm‐value variance. A proof of existence of the solution is provided.     

股指期权合约规格设计研究——基于全球股指期权市场对比的视角

为了探索股指期权产品合约规格设计的一般规律,对全球主要市场中股指期权产品业务实践进行了调查、对比分析与总结。分析结果表明,全球主要市场的股指期权以欧式行权与现金交割的方式为主,注重近月合约月份,在行权价格间距、行权价格序列、合约乘数以及报价单位的设计上会综合考虑它们对流动性等因素的影响,合约编码主要采用交易代码、合约到期日、合约类型以及行权价格四个要素依次排列的结构。这些都为未来在境内市场推出股指期权产品,开展股指期权业务提供了重要参考。     

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.     

Adverse Information and Dealer Spreads: Evidence from Dutch Auction Repurchases

The Dutch auction repurchase has become an increasingly popular alternative to open market repurchases and self-tender offers for the distribution of earnings to shareholders. In a Dutch auction, the repurchase price is not determined by a managerial decision, but by shareholders. The extent to which a Dutch auction signals private information is tested by examining stock returns and bid-ask spreads. Stock prices increase and bid-ask spreads widen during the announcement of a Dutch auction; prices decrease and spreads narrow at expiration. Because of the uncertainty surrounding the final repurchase price, Dutch auctions initially increase the risk to which security dealers are exposed. As information asymmetry among managers, investors, and dealers is reduced at expiration, security dealers no longer need to protect themselves from information trades.     

A Reduced‐Form Model for Warrant Valuation

This paper studies warrant valuation using a reduced‐form model. Analogous to the credit risk literature, structural models require complete information about the asset value process and the firm’s liabilities. In contrast, reduced‐form models require only information about the firm’s stock price process. We introduce a reduced‐form model where the warrant holder is a price taker, and we relate our model to structural models appearing in the literature.     

Pricing Warrants: An Empirical Study of the Black-Scholes Model and Its Alternatives

This paper uses a sample of over 25,000 daily warrant prices to empirically investigate potential problems with the commonly used warrant pricing model proposed by Black and Scholes as an extension of their call option model. One problem seems to be especially important: the constant variance assumption of the dilution adjusted Black-Scholes model appears to cause biases in model prices for almost all warrants and over the entire sample period. We show that more accurate price forecasts are obtained with a specific form of the constant elasticity of variance model.     

Volatility spreads and earnings announcement returns

Prior research documents that volatility spreads predict stock returns. If the trading activity of informed investors is an important driver of volatility spreads, then the predictability of stock returns should be more pronounced during major information events. This paper investigates whether the predictability of equity returns by volatility spreads is stronger during earnings announcements. Volatility spreads are measured by the implied volatility differences between pairs of strike price and expiration date matched put and call options and capture price pressures in the option market. During a two-day earnings announcement window, the abnormal returns to the quintile that includes stocks with relatively expensive call options is more than 1.5% greater than the abnormal returns to the quintile that includes stocks with relatively expensive put options. This result is robust after measuring volatility spreads in alternative ways and controlling for firm characteristics and lagged equity returns. The degree of announcement return predictability is stronger when volatility spreads are measured using more liquid options, the information environment is more asymmetric, and stock liquidity is low.     

Asset Float and Speculative Bubbles

We model the relationship between asset float (tradeable shares) and speculative bubbles. Investors with heterogeneous beliefs and short‐sales constraints trade a stock with limited float because of insider lockups. A bubble arises as price overweighs optimists' beliefs and investors anticipate the option to resell to those with even higher valuations. The bubble's size depends on float as investors anticipate an increase in float with lockup expirations and speculate over the degree of insider selling. Consistent with the internet experience, the bubble, turnover, and volatility decrease with float and prices drop on the lockup expiration date.     

Fair Terms and Fair Pricing for Multiple Warrant Issues

Abstract

Some firms utilize one or more tranches of warrant issues to supplement their capital base. Unlike exchange-traded options, the exercise of warrants requires the issuance of stock by the company, resulting in a form of dilution. Some previous studies of warrant valuation relied on “the value of the firm,” which is nonobservable, making it difficult to apply the corresponding valuation formula. This paper derives closed-form formulas to value single and multiple tranches of warrants based on the underlying stock price, its volatility, and other known parameter values. The paper first establishes the equivalence of the Black-Scholes formula for both call options and warrants in the case of a single tranche. Thereafter, it considers the impact on the value of previously issued warrants that results when a new tranche of warrants is subsequently issued, showing in each case that fair treatment of the first-issued warrant holders requires an adjustment (due to dilution) in the terms of those warrants and a corresponding modification in the warrants’ value once a second tranche of warrants is issued. To promote such fair treatment, terms of a warrant indenture would specify the nature of the adjustment required when future warrants are issued or exercised, analogous to the antidilution terms related, for example, to stock dividends. Unlike multiple issues of traded options, which are valued independently of one another, multiple warrant issues will be shown to have prices dependent on other warrants outstanding. Also examined is the sensitivity of the fair-value adjustment to changes in the underlying variables, and the theoretical fair-value prices are compared with Black-Scholes prices and with market prices of warrants in the case of two publicly traded companies, each with two warrant issues outstanding. As warrant issues modify the equity structure of a firm, the methodology of valuing warrants presented here will be useful to investment actuaries in situations in which a comprehensive market value for all of a firm’s securities is called for. In addition, risk management practices may sometimes include the use of warrant transactions to hedge stock positions similar to the way that call options are used for that purpose. This may include hedging the risk in equity-linked insurance contracts when the equity position includes stock in companies that have one or more warrant issues that are traded. The methods developed here are also applicable to multiple issues of executive stock options (ESOs) or to combinations of warrant issues and ESOs.     

Employee Stock Options, Equity Valuation, and the Valuation of Option Grants Using a Warrant-Pricing Model

We investigate the use of a warrant‐pricing approach to incorporate employee stock options (ESOs) into equity valuation and to account for the dilutive effect of ESOs in the valuation of option grants for financial reporting purposes. Our valuation approach accounts for the jointly determined nature of ESO and shareholder values. The empirical results show that our stock price estimate exhibits lower prediction errors and higher explanatory powers for actual share price than does the traditional stock price estimate. We use our valuation approach to assess the implications of dilution on the fair‐value estimates of ESO grants. We find that the fair value is overstated by 6% if we ignore the dilutive feature of ESOs. Furthermore, this bias is larger for firms that are heavy users of ESOs, small, and R&D intensive, and for firms that have a broad‐based ESO compensation plan.