Exercise Price Research Articles

PARASIAN OVER PARISIAN, HOW MUCH EARLIER SHOULD ONE EXERCISE?

In this paper, an integral equation approach used for pricing American-style Parisian options is extended to pricing Parasian options, after overcoming an additional difficulty of losing the “reset” feature of the latter in addition to still dealing with the high nonlinearity associated with American-style exercises. More specifically, compared with an American Parisian option, the accumulative feature of the “tracking clock” time results in a pair of coupled three-dimensional (3D) Partial Differential Equation (PDE) systems instead of coupled two-dimensional (2D) and 3D PDE systems. Upon successfully establishing the couple integral equation systems, we have successfully computed the option price and the optimal exercise price and compared the results with those of its Parisian counterpart. Through the comparison, we can directly observe how the accumulativeness of the “tracking clock” time affects the option and the optimal exercise prices and provide some meaningful financial explanations.

Price optimization in supply chain agreements: a comparative analysis of buyback and put option contracts for inventory risk management

AbstractThis paper aims to provide a model of a supply chain in the integrated system and obtain its optimal decision variables. The paper introduces buyback and put option contracts to reduce inventory risk. These contracts were compared in three different cases via a numerical analysis approach. In the first case, the holding cost (h) of a retailer for surplus orders in the buyback contract is equal to the option price (o) in the put option model. The relationship between exercise price (e) in the put option model and buyback price (b) in the buyback contract was obtained by comparing the optimal values in the models. This study found that the exercise price in the put option contract will be greater than the buyback price. Furthermore, it is more likely that the retailer gave more benefits under the buyback agreement than the time the retailer chooses the put option contract. Therefore, it can be concluded that if the retailer chooses the buyback agreement in this situation, can gain more benefits. The study provides essential managerial insights to compare agreements and presents recommendations to choose a suitable contract.

The Controversy over Price Transparency: Patients and Plastic Surgeons Disagree.

The No Surprises Act (NSA) went into effect on January 1, 2022. This federal law is designed to minimize surprise bills for emergency care, out of network (OON) care, and care for uninsured or self-pay individuals. To achieve these goals, the NSA relies heavily on physicians providing cost estimates to patients prior to administering care. Because healthcare is often price-opaque, this study was conducted to assess physician and patient attitudes toward price transparency in plastic surgery and aesthetic/self-pay medicine. Two cohorts of providers received a survey asking whether and how their practice offers pricing information prior to a consultation and their views regarding the NSA. Patients who had previously used an online price estimator tool also received a survey regarding their experience and accuracy of estimates received online. Most surveyed providers do not share the costs of their services online, whereas patients had a positive experience when receiving estimates of medical services before consultation. Although many providers cited the inaccuracy of price estimator tools as a reason not to incorporate them into their website, most patients reported that their final cost of service was close to (or even less than) the estimate received online prior to the consultation. This study suggests that price transparency is a patient satisfier. Therefore, plastic surgeons should exercise price transparency to be compliant with federal law and to gain a competitive advantage in the market, as the decision to implement price transparency can be mutually beneficial to patients and providers.

Dual channel closed-loop supply chain coordination with exchange policy, sales efforts and green innovation under uncertain market

ABSTRACT This paper explores a dual-channel supply chain within an uncertain environment where a manufacturer produces a green product and a retailer makes sales efforts to attract a higher customer base. Moreover, we incorporate a reverse supply chain model in which the manufacturer retrieves end-of-used products from customers through a collection initiative. Simultaneously, the retailer gathers end-of-used products from customers by implementing an exchange policy facilitated through a coupon applied to the product’s selling price. Then, we explore centralized, manufacturer Stackelberg, option contracts and cost-sharing contracts strategies to maximize supply chain profits under various circumstances. Subsequently, a numerical example is undertaken to showcase the utility of the models and explore sensitivity that examines how different parameters impact the supply chain’s profit. Findings suggest that the supply chain members will be profitable if they engage in the option contract model under a suitable value of the option price and exercise price.

Stock and Structured Warrant Portfolio Optimization Using Black-Litterman Model and Binomial Method

In recent years, the number of Indonesian investors has rapidly increased during the COVID-19 pandemic which happened all around the world. There have been a massive number of influencers in social media who were promoting investment. Although stocks and warrants are interesting choices, mutual funds still become the main ones for beginners. Therefore, this research focuses on the development of a stock portfolio model using the Black-Litterman method which involves the investor’s views towards the stock returns. The research refers to one of the largest equity funds in Indonesia, that is Sucorinvest Equity Fund, by using the top ten of its stocks that are majority in the fund (as of April 28, 2023). Furthermore, this research also constructs a structured warrant portfolio, but it is separated from the initially constructed stock portfolio. Structured warrants could be an appropriate choice for low-budget investors. It was newly introduced in Indonesia in September 2022 so it is interesting to be observed. Based on the results and the implemented assumptions, the return obtained from the stock portfolio is superior to the observed fund’s return. Meanwhile, call structured warrant portfolio using the existing product in the market yields a negative return, because the exercise price and warrant offered price were too high. Thus, structured warrants could be considered overpriced at the moment, so the chance of obtaining profit is extremely small. Due to its similar properties to call and put options, we propose the warrant pricing and use it in simulations, so in the future, structured warrants may become an attractive instrument for the investors.

The Benefits and Potential Risks of Using Option Pricing for Investment in Chinas OTC Derivatives Market under the Black-Scholes Model

In this paper, based on the qualitative research and analysis of Chinas financial market, both the benefits and potential risks of using option pricing for investment in Chinas OTC derivatives market under the Black-Scholes model are obtained. In China, OTC derivatives mainly refer to the one-to-one contract trading between institutions, non-on-exchange financial derivatives, naturally, its environment is called OTC derivatives market; Black-Scholes model is a mathematical model for option pricing. Based on the assumption that stock price obeys geometric Brownian motion, it measures the relationship between option price and underlying asset price, term, interest rate, volatility and exercise price. Based on the above variables and their overall two aspects, the gains and losses of Chinas OTC derivatives market under the Black-Scholes pricing model are obtained. Some predictions and expectations are also expressed for the future of this field.

Firms’ discretion in the option exercise price adjustments during spinoffs

During corporate spinoffs, executives’ original options are converted to new options whose exercise price is reduced. The tax and financial regulations however do not provide specific guidance regarding the option conversion, giving firms considerable discretion over the extent of reduction in the exercise price. This paper finds evidence that firms indeed use discretion to reduce the new option’s exercise price to favor executives during corporate spinoffs. This paper examines two alternative explanations why firms make such discretionary adjustments. The results support that firms with weak corporate governance are more likely to use discretion to reduce exercise prices. The study also finds some evidence suggesting that boards might consider whether the spinoffs benefit shareholders when they make the discretionary reductions in exercise prices.

Binomial Method in Bermudan Option

The Bermudan option allows the contract holders to make and buy a hybrid contract between American and European options. Bermudan option contract can be executed at certain times until the due of the contract. The purpose of this research is to determine the price of the Bermudan option using the binomial method, and then to compare the binomial method result of n steps with the market option price. In determining stock prices at each point, there will be two branches of the binomial method: up and down branches. These branches represent the movement of stock prices in the market. The result shows the price of Bermudan option is convergent at a certain value when the binomial procedure is enlarged. The comparison of the Bermudan option price using a binomial method to the market price shows that the price of Bermudan option is an approach to the market price in certain conditions. Empirically, the price of Bermudan call option is in approach to the market option price or has a minimum error when the exercise price is below the current stock price. The price of Bermudan put option empirically is in approach to the market option price or having a minimum error when the exercise price is above the current stock price.

Coping with an unreliable supplier: An option contract with a backup supplier

AbstractThis study considers a channel with a retailer who satisfies demand by ordering from two suppliers: a low‐cost primary supplier whose production is subject to failure and an expensive reliable backup supplier. We develop a call option contract and evaluate the preference of each party through two negotiable scenarios: (i) the backup supplier only decides on option price and (ii) the backup supplier determines both option and exercise prices. We find that higher authority and flexibility of the backup supplier in making decisions in the second scenario results in a lower option price, yet more possibility of achieving channel coordination compared with the first scenario. While the backup supplier prefers the second scenario, the retailer would rather adopt the other one. The results also shed light on when/how the call option contract can be beneficial for each participant. Specifically, when the primary supplier is unable to supply the whole demand, the proposed option contract can be a win‐win Pareto‐improving profit‐sharing mechanism only if the likelihood of failure in the primary supplier's production is sufficiently low. Otherwise, the backup supplier may be a detrimental option for the retailer.

The origin of LYONs: A case study in financial innovation

The origin of LYONs: A case study in financial innovation

Managing Emergency Procurement Using Option Contract under Supply Disruption and Demand Uncertainty

Effective and flexible procurement and production strategies are capable of alleviating and mitigating supply disruption and demand risk. Considering the price fluctuation caused by environmental change, we investigate the optimal procurement and production strategies under supply disruption and demand uncertainty based on option contract in a two‐stage supply chain consisting of a retailer who has two procurement opportunities and a supplier who has the emergency production chance. We explore the value of option contract by comparing it with the optimal decision making under no option contract. The result shows that option ordering and emergency procurement can coordinate the optimal strategies under uncertain environment, improving the economic performance of whole supply chain. When the disruption probability is high or the price of emergency procurement is lower, the higher option price can stimulate the supplier to produce more products to satisfy the retailer’s emergency order at a low price, which is beneficial to both, and the value of option ordering is greater. Otherwise, the emergency procurement is worth more for the core enterprise. The moderate exercise price is conducive to the long‐term cooperation of the supplier and the retailer.

Pricing American options with stochastic volatility and small nonlinear price impact: A PDE approach

In this paper, transaction costs as small nonlinear price impact are introduced into American option pricing under the Heston stochastic volatility model, forming a gap between option prices of the holder and writer. Through the use of a dynamic hedging strategy together with a known option independent of transaction costs, we derive two different nonlinear pricing partial differential equation systems for the holder and writer, respectively. A numerical algorithm is designed to solve the systems so that American option prices as well as the optimal exercise boundary can be simultaneously obtained. Examples are presented to illustrate the effect of transaction costs on both option prices and optimal exercise prices.

Uncertain Currency Option Pricing Based on the Fractional Differential Equation in the Caputo Sense

The foreign exchange market comprises the largest global volume, so the pricing of foreign exchange options has always been a hot issue in the foreign exchange market. This paper treats the exchange rate as an uncertain process that is described by an uncertain fractional differential equation, and establishes a new uncertain fractional currency model. The uncertain process is driven by Liu process, and, with the application of the Mittag-Leffler function, the solution of the fractional differential equation in a Caputo sense is presented. Then, according to the uncertain fractional currency model, the pricing formulas of European and American currency options are given. Lastly, the two numerical examples of European and American currency options are given; the price of the currency option increased when p changed from 1.0 to 1.1, and prices with different p were all decreasing functions of exercise price K.

Hedging Performance of Protective Puts and Covered Calls Portfolio: A Study of NSE Nifty Options

This paper aims at analyzing the return and risk characteristics of covered call and protective puts portfolios based on NSE Nifty index and to find out the factors responsible for the variation in returns on covered call and protective put portfolios. The factors which have been considered as the main determinants of returns on covered call and protective put portfolios are: the return on unhedged portfolio based on NSE nifty; the extent to which option is in the money or out of the money; time to maturity of the option; number of contracts traded; and Open Interest. The results indicate that the performance of covered call and protective put portfolios is better than the performance of unhedged portfolio both in terms of risk and returns. When the performance of covered call portfolio is compared with the performance of protective put portfolio, the results indicate that covered call portfolio provides higher average returns than protective put portfolio but both the total risk as well as market risk of protective put portfolio is lower than that of covered call portfolio. The results of estimated regression models indicate that covered call portfolio provides higher rate of return if call option included in covered call portfolio: is written with higher exercise price; has shorter time to maturity; enjoys high degree of liquidity; and has less number of outstanding contracts. The protective put portfolio provides higher returns if put option included in protective put portfolio: is written with lower exercise price; has longer time to maturity; has low degree of-liquidity; and has large number of outstanding contracts.

On the Asymptotic Behavior of the Optimal Exercise Price Near Expiry of an American Put Option under Stochastic Volatility

The behavior of the optimal exercise price of American puts near expiry has been well studied under the Black–Scholes model as a result of a series of publications. However, the behavior of the optimal exercise price under a stochastic volatility model, such as the Heston model, has not been reported at all. Adopting the method of matched asymptotic expansions, this paper addresses the asymptotic behavior of American put options on a dividend-paying underlying with stochastic volatility near expiry. Through our analyses, we are able to show that the option price will be quite different from that evaluated under the Black–Scholes model, while the leading-order term of the optimal exercise price remains almost the same as the constant volatility case if the spot volatility is given the same value as the constant volatility in the Black–Scholes model. Results from numerical experiments also suggest that our analytical formulae derived from the asymptotic analysis are quite reasonable approximations for options with remaining times to expiry in the order of days or weeks.

Equity incentive plans and R&D investment manipulation: evidence from China

AbstractThis paper examines the issue of earning management in companies with equity incentives from two dimensions: management manipulation of the intensity of R&D and accounting treatment by using a sample of Shanghai and Shenzhen listed companies in China from 2014 to 2019. We find that in order to depress the benchmarks and exercise prices for the performance appraisal of the equity incentive covenants, managers not only conduct accrual earnings management by expensing R&D expenditure but also increase the intensity of R&D investment for real earnings management. We also find that companies with equity incentives where managers have more power are more inclined to opt for the more concealed means of real earnings management and try to avoid accrual earnings management, which may entail higher regulatory costs and greater litigation risk with tightening accounting regulations. Our findings contribute to expanding the literature on earnings management of companies with equity incentives and provide empirical evidence for regulators to implement ‘precision regulation’ on equity incentives and earnings management.

Coordinating a Three‐Level Fresh Agricultural Product Supply Chain considering Option Contract under Spot Price Uncertainty

We consider a three‐level fresh agricultural product supply chain consisting of a producer, a supplier, and a retailer, where the producer plants the initial fresh agricultural products with yield uncertainty, the supplier is the leader of the supply chain and the designer of the contracts, and the retailer sells processed products with random demand and spot price. This paper discusses coordination mechanism of wholesale price contracts or option contracts between the supplier and the retailer and wholesale price contracts between the supplier and the producer. Based on this, we not only explore the conditions for supply chain full coordination and Pareto improvement but also analyze the effect of the retailer’s spot market volatility by comparing two scenarios of the retailer with or without a random spot market. Results show that the wholesale price contract cannot coordinate the supply chain regardless of whether the retailer has a random spot market or not. The supply chain can be simultaneously fully coordinated and achieve Pareto improvement by setting reasonable option contract parameters, but the conditions for coordination are rigorous. When the expected value of reduction from the retailer’s spot market in unit shortage loss cost is greater, the total profit of supply chain will increase. Numerical analysis shows that the option exercise price must be set higher when the retailer has a spot market to achieve Pareto improvement. The loss rate in distribution process and other volatility risks will also affect the coordination of the agricultural supply chain.

Projection of the two-dimensional Black-Scholes equation for options with underlying stock and strike prices in two different currencies

The two-variable Black-Scholes equation is used to study the option exercise price of two different currencies. Due to the complexity of dealing with several variables, reduction methods have been implemented to deal with these problems. This paper proposes an alternative reduction by using the so-called Zwanzig projection method to one-dimension, successfully developed to study the diffusion in confined systems. In this case, the option price depends on the stock price and the exchange rate between currencies. We assume that the exchange rate between currencies will depend on the stock price through some model that bounds such dependence, which somehow influences the final option price.As a result, we find a projected one-dimensional Black-Scholes equation similar to the so-called Fick-Jacobs equation for diffusion on channels. This equation is an effective Black-Scholes equation with two different interest rates, whose solution gives rise to a modified Black-Scholes formula. The properties of this solution are shown and were graphically compared with previously found solutions, showing that the corresponding difference is bounded.

Optimal exercise of American puts with transaction costs under utility maximization

American option pricing plays an essential role in quantitative finance and has been extensively studied in the past. However, how transaction costs affect the American option price, particularly the most important feature of American options, the optimal exercise price, is much less investigated. It is primarily because such a study must be conducted under an incomplete market, which presents additional difficulties on top of an already difficult nonlinear mathematical problem. This paper attempts to provide a supplement study in this area by analyzing the optimal exercise price of an American option in addition to the option price itself in the presence of transaction costs through a utility-based approach. With a computationally efficient numerical scheme, we are able to demonstrate clearly how the optimal exercise price should be calculated and consequently how the option prices for the buyer and writer as well as the early exercise decision are affected by the inclusion of transaction cost.

Green supply chain management through call option contract and revenue-sharing contract to cope with demand uncertainty

Green supply chain management (GSCM) could be applied to enhance environmental and economic goals simultaneously; nevertheless, according to The University of Chicago Booth report, the overwhelming impacts of the COVID-19 epidemic have caused high fluctuations in market demand. Hence, green supply chain (SC) managers have faced challenges in the decision-making process. Motivated by this issue, we investigate a two-echelon SC network containing one retailer and two suppliers (a non-green supplier and a green supplier). The non-green supplier produces a customary product and has a limited production capacity. Inspired by Coors Brewery Company, the green supplier produces a recyclable product with sufficient production capacity; the retailer faces demand uncertainty and is responsible for bringing back the end-of-life products to the green supplier for the recycling process. In this study, besides decentralized and centralized decision scenarios, we survey two kinds of contracts, i.e., a call option contract and a revenue-sharing contract, which the green supplier offers as risk-sharing policies to motivate the retailer to increase its order quantity. We found that the two parties could agree to coordinate the channel by negotiating the optimal terms of the recommended contracts (i.e., call option contract terms: option price and exercise price, revenue-sharing contract term: wholesale price). Furthermore, our results show that both proposed contracts create a win–win situation for each member and heighten the profitability of the entire SC. By comparing the two contracts, we notice that the green supplier would like to offer the call option contract, and the retailer desires to accept the revenue-sharing contract in return.