Exercise Price Research Articles

Joint order and pricing decisions for fresh produce with put option contracts

This paper investigates a newsvendor problem for fresh produce with put option contracts, in which the stochastic demand is price sensitive. The newsvendor can obtain products by ordering from a firm and return unsold products by purchasing and exercising put options. The fresh produce incurs a circulation loss in quantity during its transportation. The optimal joint order and pricing decisions for the newsvendor are analytically derived in the presence of put option contracts and circulation loss. Moreover, combined with numerical analysis, the optimal order quantity and selling price of the newsvendor are found to decrease with option price, but increase with exercise price and circulation loss, whereas the maximum expected profit is found to decrease with option price and circulation loss, but increase with exercise price. Furthermore, the newsvendor with put option contracts can deal with the risks that caused by demand uncertainty and high circulation loss of fresh produce.

Non-structural approach to implied moments extraction

Moments of future prices and returns are not observable, but it is possible to measure them indirectly. A set of option prices with the same maturity but with different exercise prices are used to extract implied probability distribution of the underlying asset at the expiration date. The aim is to obtain market expectations from options and to investigate which non-structural model for estimating implied probability distribution gives the best fit. Non-structural models assume that only dynamics in prices is known. Mixture of two log-normals (MLN), Edgeworth expansions and Shimko’s model (representatives of parametric, semiparametric and nonparametric approaches respectively) are compared. Previous researches are inconclusive about the superiority of one approach over the others. This article contributes to finding which approach dominates. The best fit model is used to describe moments of the implied probability distribution. The sample covers one-year data for DAX index options. The results are compared through models and maturities. All models give better short-term forecasts. In pairwise comparison, MLN is superior to other approaches according to mean squared errors and Diebold-Mariano test in the observed period for DAX index options.

Planos de Opções de Compra de Ações, Oportunidades de Crescimento e Desempenho: Evidências na BMF&Bovespa

This paper aims to analyze how Growth Opportunities can influence the relationship between Employee Stock Options Plans (ESOP) and company development. The theoretical line of this study comes from the search to mitigate agency conflicts, thus mechanisms are necessary for the alignment of interests between organization managers (agents) and stockholders (principal), in order to guarantee company valuation. This article replies to and extends studies by Perobelli, Lopes and Silveira (2012) and Hutchinson and Gul (2006). Given this paper’s aim, the work method analyzes companies which had their stocks negotiated on at least 90% of the days when there was trading on the stock market exchange. The sample comprises 115 companies, between 2012 and 2014. The data were extracted from the Reference Forms (FR), available in CVM, and from the database Com Dinheiro. To estimate the models, panel data analysis method was used. Research hypothesis 1, in which companies use ESOP with a view to maximizing their development, was refuted. The tests showed that whether or not ESOP is used alone wealth is not generated for the stockholder, but quality in plan structuring, that is, when there is a distance between the exercise price and the stock price on the grant date (out-of-money stocks). Research hypothesis 2, which affirms that the effect of the presence of ESOP is influenced by Growth Opportunities, was accepted. Consistent data were found that performance calculated according to stock returns are positively influenced by Growth Opportunities. Further, the presence of ESOP, its Quality (QESOP) and Corporate Management (GC) expand amplify this effect.

If I Leave Here Tomorrow: An Option View of Migration When Labor Market Quality Declines

In this article, we provide a framework for determining when it is optimal to move when labor market opportunities are declining. We model the decision to migrate as akin to owning a financial option in which the exercise price is the fixed cost of moving. We show that a higher fixed cost associated with moving and a higher standard deviation of the quality of the labor market reduce the incentive to migrate. We then empirically examine whether the standard deviation of indicators of labor market quality reduce the likelihood of migration. Our findings strongly support this hypothesis, and imply that for the relatively mobile population of high‐skilled workers the counterfactual outmigration rates that would obtain if future labor‐market quality were known with certainty are more than twice observed rates.

20000000 200000 (Kospi200 Futures Price and Implied Volatility Smile of Kospi200 Options)

Korean Abstract: 코스피200 주가지수 선물과 코스피200 주가지수 옵션은 선물-풋-콜 패리티로 연결되어 있다. 본 연구는 비교적 장기간 선물 및 옵션의 거래 자료를 분석하여 선물의 가격이 행사가격별 옵션의 내재변동성에 차별적으로 미치는 영향을 분석하였다. 분석한 결과는 다음과 같다. 첫째, 선물가격이 고평가될수록 상대적으로 Call의 내재변동성은 상승하고 Put의 내재변동성은 하락하였고, 선물가격이 저평가될수록 상대적으로 Put의 내재변동성은 상승하고 Call의 내재변동성은 하락하였다. 이러한 선물의 영향력은 변동성이 낮은 경우에 더 높게 나타났다. 둘째, 선물가격의 영향력은 내가격옵션에서 더 크게 나타났다. 선물가격의 영향에 따라 옵션시장에서 변동성 스큐 모양과 변동성 스머크 모양이 나타났다. 셋째, 옵션의 잔존만기가 감소함에 따라 선물가격의 영향력이 증가하고 특히 내가격옵션의 내재변동성에 더 큰 영향을 주었다. 잔존만기가 감소함에 따라 변동성 스큐 현상과 변동성 스머크 현상이 심화되기도 하고 새로 발생하기도 하였다. 코스피200 주가지수 선물과 코스피200 주가지수 옵션시장처럼 동일한 기초자산을 갖는 파생상품의 가격은 서로 연결되어 있으며 영향을 준다는 사실을 가지고 옵션시장의 변동성 스마일 현상을 상당히 설명할 수 있었다. English Abstract: The KOSPI200 stock index futures and the KOSPI200 stock index options are linked to futures-put-call parity. This study analyzes the effect of the futures price on the implied volatility of option by exercise price by analyzing the long - term futures and options trading data. The results of the analysis are as follows. First, as the futures price is overvalued, the implied volatility of the call increases and the implied volatility of the put decreases, while the implied volatility of the put increases and the implied volatility of the call decreases as the futures price becomes undervalued. The influence of these futures is higher when the volatility is low. Second, the influence of futures prices is greater in ITM options. The volatility skew shape and the volatility smirk shape appeared in the option market depending on the influence of the futures price. Third, as the remaining maturity of the option decreases, the influence of futures price increases, especially the implied volatility of ITM options. As the remaining maturity decreases, the volatility skew and the volatility smirk shape become more severe and new. The fact that the prices of derivatives with the same underlying assets, like the KOSPI200 stock index futures and the KOSPI200 stock index options market, are linked and influenced, could explain the volatility smile of the option market considerably.

Stock Options and Management Timing:Evidence from China

This paper empirically tests management timing in the listed companies when the mangers are awarded stock options. It comes to the results as follows:firstly, interval pricing samples award the management timing stock options to reduce exercise prices; secondly, interval and daily pricing samples have timing good information disclosure after the pricing benchmark date to increase the value of stock options; thirdly, with large power of the management, lower-degree corporate governance and state-owned ultimate controllers, the probability of simultaneous timing stock options and information disclosure by the management is higher and the proportion of intangible assets&firm size reduce the probability abovementioned. It enriches and extends existing management timing research, and is of great significance to effective promotion of management stock options plan and the inhibition on management timing behavior.

Crop price insurance in China: pricing and hedging using futures market

PurposeThe purpose of this paper is to demonstrate how crop price insurance premium can be calculated using an option pricing model and how insurers can transfer underwriting risks in the futures market.Design/methodology/approachBased on data from spot and futures market in China, this paper develops an improved B-S model for the calculation of crop price insurance premium and tests the possibility of hedging underwriting risks by insurance firms in the futures market.FindingsThe authors find that spot price of crops in China can be estimated with agricultural commodity futures prices, and can be taken as the insured price for crop price insurance. The authors also find that improved B-S model yields better estimation of crop price insurance premium than traditional B-S model when spot price does not follow geometric Brownian motion. Finally, the authors find that hedging can be one good alternative for insurance firms to manage underwriting risks.Originality/valueThis paper develops an improved B-S model that is data-driven in nature. Insured price of the crop price insurance, or the exercise price used in the B-S model, is estimated from a co-integration model built on spot and futures market price series. Meanwhile, distributional patterns of spot price series, one important factor determining the applicability of B-S model, is factored into the improved B-S model so that the latter is more robust and friendly to data with varied distributions. This paper also verifies the possibility of hedging of underwriting risks by insurance firms in the futures market.

A new integral equation formulation for American put options

In this paper, a completely new integral equation for the price of an American put option as well as its optimal exercise price is successfully derived. Compared to existing integral equations for pricing American options, the new integral formulation has two distinguishable advantages: (i) it is in a form of one-dimensional integral, and (ii) it is in a form that is free from any discontinuity and singularities associated with the optimal exercise boundary at the expiry time. These rather unique features have led to a significant enhancement of the computational accuracy and efficiency as shown in the examples.

Pricing of American Options.

In this paper, we present somewhat alternative point of view on early exercised American options. The standard valuation of the American options the exercise moment is defined as one, which guarantees the maximum value of the option. We discuss the standard approach in the first two sections of the paper. The standard approach was initially presented in the papers [3]-[7]. Our idea is that the exercise moment of the American call/put options is defined by maximum/minimum value of underlying. It was shown that at this moment exercise and sell prices are equal.

Efficient valuation and exercise boundary of American fractional lookback option in a mixed jump-diffusion model

This study presents an efficient method for pricing the American fractional lookback option in the case where the stock price follows a mixed jump diffusion fraction Brownian motion. By using It ô formula and Wick–It ô–Skorohod integral, a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.

Research on the indexed stock options’ quadratic hedging under jump-diffusion settings

This paper studied the hedging of European indexed stock options, whose exercise price is a variable varying with the market index. Firstly, using the expectation of the squared error between option’s terminal value and hedging portfolio to measure market risk , and with the constraint of self-financing, a squared hedge decision model was built; Then, by using the Dynamic Programming Principle and backward recursion method, the optimal hedging positions’ analytical expressions were acquired; Lastly, all hedging results with different option maturities and different position rebalancing frequencies show that there is dependent relationship between hedging positions and option’s maturity time limit; hedging positions also rely on the relative variation of the underlying asset price.

Valuing Employee Stock Options with Exogenous and Endogenous Early Exercise

This paper examines how forfeiture, vesting, and early exercise affect the value of employee stock options. The forfeiture and exogenous exercise of the options are modeled as two Poisson processes with constant intensity. Rational exercise by the employee due to the option's American feature is modeled as endogenous exercise. The Crank-Nicholson numerical method is used to solve for the resulting value of employee stock options. Results are consistent with the findings that the employee stock options are worth substantially less than the Black-Scholes formula value. The model demonstrates that the option holder would rationally exercise the option early even when the underlying stock pays no dividend. The model also provides results on the expected time to exercise of employee stock options and the expected exercise price relative to strike price. The method used in this paper is proposed as an alternative to the Black-Scholes formula for measuring fair market value of employee stock options for accounting and regulation purposes.

Outsource planning with asymmetric supply cost information through a menu of option contracts

AbstractThis paper investigates a supply contract design by a dominant manufacturer who faces a stochastic demand during a selling season. The manufacturer has several estimations of the supplier's cost with corresponding probabilities, that is, asymmetric cost information. The manufacturer designs a menu of call option contracts that include three variables: a supply order, an option, and an exercise price. We determine the optimal negative correlation between option and exercise prices as well as closed‐form formulas for the optimal supply orders. The results show that in the optimal menu of contracts either the option or the exercise price may be omitted from the menu, whereas the supply orders should always be customized for each supplier type. We show that in this problem, optimal profit assignment between contract partners under put and bidirectional option contracts is the same as call option contract studied. Numerical analysis including managerial insights is presented.

Pricing American-style Parisian up-and-out call options

In this paper, we propose an integral equation approach for pricing an American-style Parisian up-and-out call option under the Black–Scholes framework. The main difficulty of pricing this option lies in the determination of its optimal exercise price, which is a three-dimensional surface, instead of a two-dimensional (2-D) curve as is the case for a “one-touch” barrier option. In our approach, we first reduce the 3-D pricing problem to a 2-D one by using the “moving window” technique developed by Zhu and Chen (2013, Pricing Parisian and Parasian options analytically. Journal of Economic Dynamics and Control, 37(4): 875-896), then apply the Fourier sine transform to the 2-D problem to obtain two coupled integral equations in terms of two unknown quantities: the option price at the asset barrier and the optimal exercise price. Once the integral equations are solved numerically by using an iterative procedure, the calculation of the option price and the hedging parameters is straightforward from their integral representations. Our approach is validated by a comparison between our results and those of the trusted finite difference method. Numerical results are also provided to show some interesting features of the prices of American-style Parisian up-and-out call options and the behaviour of the associated optimal exercise boundaries.

Temporary employment contracts in academia: a real option view

This paper examines the strategic use of temporary employment contracts in dealing with supply uncertainty in the form of employee ability that is slow to reveal itself, for example in academia where there exist significant time lags in demonstration of research ability. A temporary contract is modeled as a real option, specifically as a combination of put option and stock, known as a protective put. The option price is modeled as relief from project work, e.g. teaching, and the exercise price is modeled as a target value, e.g. requisite number of publications. The model provides an explanation for contrasting use of temporary contracts in research and in teaching intensive institutions, and for teaching only and research only staff. The model has relevance in other employment situations where there is a time-lag between recruitment and revelation of employee ability, for example in young professional, top executive and political positions.

PENENTUAN HARGA OPSI BELI TIPE ASIA DENGAN METODE MONTE CARLO-CONTROL VARIATE

Option is a contract between the writer and the holder which entitles the holder to buy or sell an underlying asset at the maturity date for a specified price known as an exercise price. Asian option is a type of financial derivatives which the payoff taking the average value over the time series of the asset price. The aim of the study is to present the Monte Carlo-Control Variate as an extension of Standard Monte Carlo applied on the calculation of the Asian option price. Standard Monte Carlo simulations 10.000.000 generate standard error 0.06 and the option price convergent at Rp.160.00 while Monte Carlo-Control Variate simulations 100.000 generate standard error 0.01 and the option price convergent at Rp.152.00. This shows the Monte Carlo-Control Variate achieve faster option price toward convergent of the Monte Carlo Standar.

Optimal Exercise Boundary of American Fractional Lookback Option in a Mixed Jump-Diffusion Fractional Brownian Motion Environment

A new framework for pricing the American fractional lookback option is developed in the case where the stock price follows a mixed jump-diffusion fraction Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.

Using Sectoral Indexes to Discount the Exercise Price of Employee Stock Options

Abstract Employee stock options (ESOs) are an instrument in compensating top management of corporations. In the literature, they are described as a variable component of remuneration of a long-term character (Borkowska, 2012). There are six characteristic elements of the ESO: a grant date, the ESO plan duration, employees entitled to receive options, vesting criteria, a vesting period, and an exercise price. The article refers to the exercise price. The remuneration of employees is determined by the option’s intrinsic value, i.e. the difference between the current stock price and the exercise price. This difference affects the costs incurred by a company in relation with their incentive stock option plan. In this connection, the exercise price of stock options needs to be analysed. The literature shows that usually the strike price is equal to the stock market’s value at the time the option is granted. The options issued with an exercise price equal to the market value of the company’s stock on the date of the grant usually lead to at-the-money options. Walker (2009) mentions that almost all options issued by US firms have been such type of options. Hence, the options with exercise prices less than the prices of the underlying assets have been rarely observed. One of the solutions can be discounting the exercise price by using sectoral indexes, which are sensitive to changes on a particular market. The purpose of this paper is to address several aspects of specifying the exercise price in ESOs. The research shows how sector indexes can be used to discount it. Using sectoral indexes in determining the exercise price can partly limit the unreasonably high profits from the ESO. The literature does not provide ready-made formulas of exercise prices based on specific variables. The aim of the research is to present and apply the formula of the exercise prices in which sectoral indices are used to discount. The data are from the Warsaw Stock Exchange (WSE) and include those companies that revealed the information concerning their incentive programs in 1999–2013. The relevant data come from annual reports, current reports, supervisory boards’ resolutions, and press announcements.

Perbandingan Efek Dilusi pada Nilai Waran dengan Menggunakan Metode Black-Scholes, Dilusi Black-Scholes, dan Pengamatan Variabel

Warrant is a financial derivative product issued by a firm on its own equity. Warrant is different from call options because the exercise price is paid to the firm and increases its assets and new shares of stock are issued at exercise. In this paper, warrant pricing is obtained using three methods; Black-Scholes, diluted Black-Scholes, and observable variables. Specifically, effect of dilution of warrant pricing would be compared each other with different characteristics of contract. Keywords: warrant, dilution, Black-Scholes, diluted Black-Scholes, observable variables

Mixing LSMC and PDE Methods to Price Bermudan Options

We develop a mixed least square Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options with assets whose dynamics are driven by latent variables. The algorithm is formulated for an arbitrary number of assets and volatility processes, and its probabilistic convergence is established. Our numerical examples focus on the Heston model and we compare our hybrid algorithm with a full LSMC approach. Using Fourier methods we are able to derive efficient FFT based solutions, and we demonstrate that our algorithm greatly reduces the variance in the computed prices and optimal exercise boundaries. We also compare the early exercise boundaries and prices computed by our hybrid algorithm with those produced by finite difference methods and find excellent agreement.