Exercise Date Research Articles

An Optimal Selection of the basis Functions for the Valuation of Interest Rate Structured Notes

This paper examines which basis functions are efficient to employ a combined method of Hull and White (1990) with the Monte Carlo simulation when we price a callable range note or a callable bond. We use the Huge and Rom-Poulsen (2007) method which has modified the least squared Monte Carlo simulation proposed by Longstaff and Schwartz (2001) to reduce the estimation errors of the continuation value or the underlying assets. To use Monte carlo Simulation for pricing the early exercise premium, it is essential to accurately estimate the continuation value, because the investors will choose the higher value between the exercise and the continuation value at the possible early exercise dates. The main purpose of this paper is to analyze the estimation errors originating from the choice of the basis functions for the underlying asset and the continuation value estimation. We choose the callable bond and the callable range accrual note to show which basis functions are reliable to reduce the estimation errors. For this purpose, we replicate the callable range accrual note with a portfolio of a fixed rate bond and a delayed digital option. We use several basis functions such as a constant, the instantaneous interest rates, and the range in order to see which basis function is efficient for our purpose. We examine several combinations of the basis functions depending on which basis functions will be used for the underlying asset or the continuation value estimation. We show that the range which is an important determinant of the callable range accrual note is an effective basis function to accurately determine the underlying asset and the continuation value for the pricing of the callable range accrual note.

Pricing American put option on zero-coupon bond in a jump-extended CIR model

This paper presents a jump extension to the CIR model of the short interest rate with exponential distribution jumps. We derive an approximated price of an American put option on a defaultable-free, zero-coupon bond using the two-GJ approach based on combining an European put option and a Bermudan option with two possible exercise dates. Closed-form solutions for both the European put option and the Bermudan option are obtained by using multivariate Fourier transforms and characteristic functions. The accuracy and efficiency of the approximation are examined using the least-square Monte Carlo simulation as the benchmarks. Finally several numerical examples illustrating the results have been presented and the prices have been compared to the corresponding prices for American option in the pure diffusion model.

Primal–dual linear Monte Carlo algorithm for multiple stopping—an application to flexible caps

In this paper we consider the valuation of Bermudan callable derivatives with multiple exercise rights. We present in this context a new primal–dual linear Monte Carlo algorithm that allows for efficient simulation of the lower and upper price bounds without using nested simulations (hence the terminology). The algorithm is essentially an extension of the primal–dual Monte Carlo algorithm for standard Bermudan options proposed by Schoenmakers et al. [SIAM J. Finance Math., 2013, 4, 86–116] to the case of multiple exercise rights. In particular, the algorithm constructs upwardly a system of dual martingales to be plugged into the dual representation of Schoenmakers. At each level, the respective martingale is constructed via a backward regression procedure starting at the last exercise date. The thus constructed martingales are finally used to compute an upper price bound. The algorithm also provides approximate continuation functions that may be used to construct a price lower bound. The algorithm is applied to the pricing of flexible caps in a Hull and White model setup. The simple model choice allows for comparison of the computed price bounds with the exact price obtained by means of a trinomial tree implementation. As a result, we obtain tight price bounds for the considered application. Moreover, the algorithm is generically designed for multi-dimensional problems and is tractable to implement.

Self-Reported Versus Objectively Assessed Exercise Adherence

OBJECTIVE. We examined agreement of data between self-reported and objectively assessed exercise adherence among women with systemic lupus erythematosus. METHOD. Eleven participants completed weekly exercise logs on date and duration of exercise during a 10-wk Wii Fit™ home-based program. Afterward, exercise data from the log were compared with those recorded in the Wii console. RESULTS. Of the paired data, the mean duration of exercise recorded in the Wii was 29.5 min and that recorded in the log was 33.3 min. The composite intraclass correlation for exercise duration between exercise log and the Wii Fit was 0.4. The 95% limits of agreement indicated large between-subjects variability. CONCLUSION. Exercise logs exhibit a marginally acceptable agreement with Wii estimation of exercise duration at a group level. However, caution should be applied when using the exercise log as a measure of a person's exercise behavior because of the tendency to overreport.

Pricing Bermudan options using low-discrepancy mesh methods

This paper proposes a new simulation method for pricing Bermudan derivatives that is applicable to problems where the transition density of the underlying asset price process is known analytically. We assume that the owner can exercise the option at a finite, although possibly large, number of exercise dates. The method is computationally efficient for high-dimensional problems and is easy to apply. Its efficiency stems from our use of quasi-Monte Carlo techniques, which have proven effective in the case of European derivatives. The valuation of a Bermudan derivative hinges on the optimal exercise strategy. The optimal exercise decision can be reduced to the evaluation of a series of conditional expectations with respect to different distributions. These expectations can be approximated by sampling from just a single distribution at each exercise point. We provide a theoretical basis for the selection of this distribution and develop a simple approximation that has good convergence properties. We describe how to implement the method and confirm its efficiency using numerical examples involving Bermudan options written on multiple assets and options on a foreign asset with a stochastic interest rate.

An efficient pricing algorithm for swing options based on Fourier cosine expansions

Swing options give contract holders the right to modify amounts of future delivery of certain commodities, such as electricity or gas. We assume that these options can be exercised at any time before the end of the contract, and more than once. However, a recovery time between any two consecutive exercise dates is incorporated as a constraint to avoid continuous exercise. We introduce an efficient way of pricing these swing options, based on the Fourier cosine expansion method, which is especially suitable when the underlying is modeled by a Levy process.

A Real Option Perspective on Valuing Gas Fields

Real option theory has remained a fringe field; practitioners believe it is not practically applicable in complex real world environments. We show that this view is mistaken. We apply real option theory to a highly complex energy problem with unhedgeable risk, time varying volatilities and endogenous exercise dates (non-European options). Investment decisions in the energy industry are often undertaken sequentially and are sensitive to information on markets and geographic conditions. Information may arrive gradually over time and as a consequence of early stage decisions. Contrary to real option analysis (ROA), standard NPV-based frameworks are unsuitable because they do not allow for the fact that new information may change later stage decisions. We apply the approach to exploitation decisions for a Dutch cluster of gas fields, where gas prices and field reservoir size are the two main sources of uncertainty. Gas price returns show volatility clustering , which we model using a GARCH specification. Reservoir size uncertainty is unhedgeable, which necessitates an approach dealing with incomplete markets. Finally investment decisions can be postponed or delayed, which implies an non-European option setting, for which no analytical solutions exist. Correctly modeling the structure of volatility has a major impact: Option values shrink by 50% if the time varying nature of volatility is ignored. We also show that a high correlation between reservoir size at different locations creates large option values. The non-standard features of our approach have a major impact: option values are large so real options based valuations substantially exceed corresponding NPV calculations.

Czech Supreme Administrative Court on Taxation of Employee Stock Options

On 30 January 2012, the Czech Supreme Administrative Court issued a decision on the timing of the crystallization of taxable income in regard to employee stock options. In the absence of specific rules in the Czech Income Taxes Act, this decision confirms that the taxable event is the date of exercise of the options.

An efficient algorithm for Bermudan barrier option pricing

An efficient option pricing method based on Fourier-cosine expansions was presented by Fang and Oosterlee for European options in 2008, and later, this method was also used by them to price early-exercise options and barrier options respectively, in 2009. In this paper, this method is applied to price discretely American barrier options in which the monitored dates are many times more than the exercise dates. The corresponding algorithm is presented to practical option pricing. Numerical experiments show that this algorithm works very well and efficiently for different exponential Levy asset models.

Acceleration of option pricing technique on graphics processing units

SUMMARYThe acceleration of an option pricing technique based on Fourier cosine expansions on the graphics processing unit (GPU) is reported. European options, in particular with multiple strikes, and Bermudan options will be discussed. The influence of the number of terms in the Fourier cosine series expansion, the number of strikes, as well as the number of exercise dates for Bermudan options is explored. We also give details about the different ways of implementing on a GPU. Numerical examples include asset price processes on the basis of a Lévy process of infinite activity and the stochastic volatility Heston model. Furthermore, we discuss the issue of precision on the present GPU systems. Copyright © 2012 John Wiley & Sons, Ltd.

A censored quantile regression analysis of employee stock options substitution for debt and the impact of SFAS 123R

PurposeThis paper aims to examine whether the substitution of employee stock options (ESOs) for debt occurs for firms with different tax status classifications throughout the conditional distribution of interest expense before and after the implementation of Statement of Financial Accounting Standard 123R (SFAS 123R).Design/methodology/approachThis study uses Censored Quantile Regression (CQR) to assess whether the substitution effect is dependent on firms' position in the conditional distribution of interest expense. Our sample firms are categorized into two groups: one group (tax‐sensitive) that is sensitive to additional deductions due to a moderate income level and the other group (tax‐insatiable) that is not sensitive because of very high income level.FindingsThe substitution effect is not present for firms with below medium level of interest expense. Only tax‐sensitive firms substitute at medium levels of interest expense while both tax‐sensitive and tax‐insatiable firms substitute at high levels of interest expense. Tax‐insatiable firms with very high levels of interest expense also substitute; however, tax‐sensitive firms with very high levels of interest expense only substitute after SFAS 123R required firms to report ESO expense in financial statements. We attribute the substitution patterns revealed by the CQR analysis to a positive relationship between interest expense and cost of debt.Originality/valueTo the authors' knowledge, this is the first paper to analyze firms' tax status classification impact on the substitution of ESO expense for interest expense across different levels of interest expense. Our application of CQR should benefit researchers who are interested in examining explanatory variables' impact at various points in the conditional distribution of the dependent variable. This study also refines the conjecture that ESOs are substitutes for debt by demonstrating that such relationship is dependent on the level of interest expense and tax status. Furthermore, the finding of firms substituting ESOs for debt provides accounting standard setters a reason to begin requiring firms to re‐measure the value of ESOs after the grant date until the exercise date.

An Accurate FFT-Based Algorithm for Bermudan Barrier Option Pricing

An efficient and accurate numerical method, which is called the CONV method, was proposed by Lord et al in [1] to price Bermudan options. In this paper, this method is applied to price Bermudan barrier options in which the monitored dates may be many times more than the exercise dates. The corresponding algorithm is presented to practical option pricing. Numerical experiments show that this algorithm works very well for different exponential Lévy asset models.

On the stability the least squares Monte Carlo

Consider least squares Monte Carlo (LSM) algorithm, which is proposed by Longstaff and Schwartz (Rev Financial Studies 14:113–147, 2001) for pricing American style securities. This algorithm is based on the projection of the value of continuation onto a certain set of basis functions via the least squares problem. We analyze the stability of the algorithm when the number of exercise dates increases and prove that, if the underlying process for the stock price is continuous, then the regression problem is ill-conditioned for small values of the time parameter.

What drives the dating game of executive options exercise? Evidence from Taiwan

AbstractExamining Taiwanese firms from 2002 to 2008, this paper investigates the motivations behind backdating the exercising of executive stock options. The probability of suspect exercises (backdating) is positively related to the firm’s stock return, the value of the option, tax savings, institutional ownership and the extent of CEO equity ownership and negatively related to firm‐specific risk and the use of Big Four accounting firms. Tax incentives motivate executives to backdate the exercise date, implying that the greater the potential for larger tax savings, the greater the likelihood of backdating. Backdating usually occurs in firms that have heavy ownership by the CEO, have more claims to executive stock options and are not family‐run, confirming the presence of the agency cost problem.

No More Scandals: A Simple Model For Valuing Employee Stock Options

<p class="MsoNormal" style="text-align: justify; margin: 0in 34.2pt 0pt 0.5in;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">The escalating size of compensation packages to senior managers and investor disillusionment have resulted in growing calls for the expensing of employee stock options (ESO).<span style="mso-spacerun: yes;">  </span>While initially slow to respond, the FASB has now mandated the expensing of ESO.<span style="mso-spacerun: yes;">  </span>The two primary methods used to value ESO, the Black-Scholes closed form equation and the lattice model, suffer from several deficiencies<span style="mso-spacerun: yes;">  </span>.A Simple model for valuing ESO that marks the option expense to market in succeeding financial statement dates and allows for the staggered exercise dates of option holders is available. The model is easy to understand, would have a low cost of implementation, and offers a superior estimate of the true cash flow effects associated with the opportunity cost to shareholders of ESO exercise.</span></span></p>

Accounting For Stock Options: Comparison Of Alternative Approaches

<p>The Financial Accounting Standards Board in Standard No. 123 requires the disclosure of the annual option expense assuming a market based static model is used to measure the option "value" at issue data. This study reviews and tests alternative measures of accounting for stock options that were previously proposed by the Board. Our results suggest the exercise date model provides a measure of option expense which more consistently reflexes the changes in the market value of the option.</p>

GAAP/Tax Differences In Accounting For Nonqualified Employee Stock Options: The Gathering Storm

<p class="MsoNormal" style="text-align: justify; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">The escalating size of compensation packages to senior managers and investor disillusionment resulted in the issuance of FAS 123(R). Under the current rules, the grant date fair value of employee stock options (ESO) are expensed over the vesting period. The two primary methods used to value ESO are the Black-Scholes closed form equation and the lattice model. Several studies suggested an alternative Simple model for valuing ESO that marks the option expense to market in succeeding financial statement dates and allows for the staggered exercise dates of option holders. This approach is easy to understand, would have a low cost of implementation, and offers a superior estimate of the true cash flow effects and economic injury associated with the opportunity cost to shareholders of ESO exercise. Moreover, the Simple model would head off another threat to the legitimacy of the FASB that is unfolding in the U.S. Congress as Senator Carl Levin holds hearings on ESO in the Senate Permanent Subcommittee on Investigations to decide what to do about the multi-billion dollar gap between what companies report to stockholders as ESO expense and what they deduct on their tax returns. In addition, this gap results in highly controversial rules of accounting and reporting for the favorable impact of the deductions in the financial statements.</span></span></p>

A simple model of deferred callability in defaultable debt

Banks and other financial institutions issue hybrid capital as part of their risk capital. Hybrid capital has no maturity, but, similarly to most corporate debt, includes an embedded issuer’s call option. To obtain acceptance as risk capital, the first possible exercise date of the embedded call is contractually deferred by several years, generating a protection period. We value the call feature as a European option on perpetual defaultable debt. We do this by first modifying the underlying asset process to incorporate a time-dependent bankruptcy level before the expiration of the embedded option. We identify a call option on debt as a fixed number of put options on a modified asset, which is lognormally distributed, as opposed to the market value of debt. To include the possibility of default before the expiration of the option we apply barrier options results. The formulas are quite general and may be used for valuing both embedded and third-party options. All formulas are developed in the seminal and standard Black–Scholes–Merton model and, thus, standard analytical tools such as ‘the greeks’, are immediately available.

Research culture and New Zealand’s performance-based research fund: some insights from bibliographic compilations of research outputs

Year-on-year trends in research outputs show increases in research activity as the date of the research assessment exercise—in New Zealand the Performance-Based Research Fund (PBRF)—looms. Moreover, changes with time in the number and types of conference presentation indicate that the vehicle of publication is also being influenced by the PBRF. Within New Zealand business schools, relating the published journal articles to the Australian Business Deans Council rankings list shows a trend towards more publications of lower rank, raising doubts about whether the rhetoric about the PBRF raising the quality of research is really justified. This ‘drive’ towards increasing numbers of research outputs is also fostered by an increasing trend towards co-authorship in publishing across all disciplines.

The Manipulation of Executive Stock Option Exercise Strategies: Information Timing and Backdating

ABSTRACTI identify three option exercise strategies executives engage in, including (i) exercising with cash and immediately selling the shares, (ii) exercising with cash and holding the shares, and (iii) delivering some shares to the company to cover the exercise costs and holding the remaining shares. Stock price patterns suggest executives manipulate option exercises. They use private information to increase the profitability of all three strategies, and likely backdated some exercise dates in the pre‐Sarbanes‐Oxley period to enhance the profitability of the latter two strategies, where the executive's company is the only counterparty. Backdating is associated with reporting of internal control weaknesses.