Option Buyer Research Articles

Pemodelan Matematika Opsi Saham Karyawan Menggunakan Metode Trinomial yang Memperhitungkan Efek Dilusi

Stock options are contracts involving two parties, namely the option seller (writer) and option buyer (holder), where the rights of the option buyer (holder) will be guaranteed by the option seller (writer) in selling or buying shares at an agreed price. (strike price) before or at maturity time. One type of development of stock options, namely Employee Stock Options (OSK) or commonly called Employee Stock Options, is an option where the beneficiary cannot sell or transfer the options given by the company because these options function as rewards and incentives for their employees so that in this case, employees has the right to stock options but has no obligation to buy them. 
 This study aims to model employee stock options that take into account the dilution effect. The dilution effect is a decrease in the percentage of share ownership due to an increase in the total number of shares, but the investor does not participate in the issuance of new shares. This study uses the trinomial method where stock price movements will be seen by calculating forward and determining the option value backwards. For this method, the stock price movement model has three possible events, namely the stock price moves up, stays, or falls. This research produces a mathematical model that is used in determining the price of employee stock options by taking into account the dilution effect.
 Keywords: Employee Stock Options, Trinomial Method, Dilution Effects

THE PRINCIPLE OF EXERCISING OPTIONS ON THE ELECTRICITY MARKET

Continual price fluctuations are possible to hedge by using various financial instruments, including options. An option buyer buys the right to the settlement price of an underlying asset such as electricity. Due to the volatility of the asset price, the buyer is not obliged to exercise the option. In such a case, the buyer’s only loss is the purchased right or the option premium, which is equal to the option price. Mathematical models for option pricing have been developed in the last hundred years. These models were very popular during the 1970s, owing to the application of the Black-Scholes formula for the calculation of theoretical option prices. In this article, options are distinguished according to various criteria, specific exercising methods are described and the historical development of option pricing models is reviewed. An example of option exercising with closing out of the margins on the largest Middle European electricity exchange, EEX, is presented.

The Use of Quasi Monte Carlo Method with Halton Random Number Sequence in Determining the Price of European Type Options: in PT Telekomunikasi Indonesia Stock’s

An investor must be wise in managing the funds he has to carry out investment activities. Investors can use options as an alternative to investing because they can increase profits and avoid investment risks. Options are one of the most widely used derivative products. The main problem when entering into an option contract is determining the right price to be paid by the option buyer to the option seller. This research was made to determine the price of European-type stock options. Case studies on PT Telekomunikasi Indonesia, Tbk shares in the 2021-2022 period. The analysis was performed using the Quasi-Monte Carlo method with Halton's random number sequence. Based on the results of this study, it is expected to be a consideration in deciding to buy European-type stock options at PT Telekomunikasi Indonesia, Tbk

Penalty method for indifference pricing of American option in a liquidity switching market

In this paper we develop a numerical method for pricing American options under regime-switching model, whose solutions are option buyer indifference prices. The problem is formulated as a nonlinear complementarity problem. We apply interior penalty method to approximate the differential complementarity problem, which results in a system of one degenerate parabolic equation and one ordinary differential equation, weakly coupled by nonlinear exponential term. We formulate the problems in variational form in appropriate spaces and prove comparison principle. Then, as a consequence, we derive estimates about the convergence rate of the interior penalty method.We discretize the penalized problem by fully implicit finite difference scheme and prove that the early exercise constraint is strictly satisfied. We establish comparison principle, uniqueness and boundedness of the numerical solution. To solve the nonlinear system of algebraic equations we use Newton method and partial Newton method. We present numerical results that confirm the theoretical statements. To improve the computational efficiency, we unfold the two-grid idea, combining both iteration processes – Newton method and partial Newton method. We illustrate the efficiency of this approach.

Delta-hedged gains of SSE 50 ETF options

ABSTRACT Using Chinese option market data, we construct a delta-neutral strategy for Shanghai Stock Exchange (SSE) 50ETF options and investigate the statistical properties of the strategy gains. The empirical results show that the delta-hedged gains are significantly negative, indicating that to hedge the volatility risk, the option buyer needs to pay a volatility risk premium to the option seller.

OPTION VALUE CALCULATION AFFECTED COMPONENTS

As the subprime credit crisis has attracted attention to financial derivative instruments, more frequently arises questions about fairvalue calculations. Over the time, different models had been introduced. All of those models take into account factors affectingprices. Mostly, factors used in calculations on the same type of financial instruments are approximately the same. Therefore questionarises, which factor affects price more and which less, with no matter which model would be used for fair value calculations. One offinancial derivative instrument types is options. Options are agreements, which give to option buyer rights to buy or sell underlyingasset. While the seller or writer of option has obligation to buy or sell underlying asset. This research aims to explore the impact offactors on option fair value calculations and evaluate most important ones from those, which could be chosen by option buyer orseller. To reach the aim of research following tasks are developed: 1) review of fair value calculation models; 2) compare results ofusage of different models and changes in affecting factors; 3) highlight differences between option price affecting factors, modelsused in calculations and results provided. Research includes literature review and analysis of option pricing results. Option pricecalculations are based on historical option prices, using black-Scholes and Binomial option pricing models. KEYWORDS: options, fair value models, strike price, exercise date. DOI: http://dx.doi.org/ 10.15181/rfds.v11i3.617

The Development of Option Market and The Role of Indonesia Financial Service Au-thority (OJK) In Indonesia Capital Market Period 2004-2019

The purpose of this paper is to describe several things related to the notion of options, stock options, transaction mechanisms, applicable legislation based on the study of literature, the previous research, and various information from financial sites related to the topic mentioned above. Therefore, the research questions that needs to be answered are as follows: 1. What are the developments in options markets in Indonesia? 2. What is the role of the Financial Services Authority (OJK) in developing options trading transactions related to the legal aspect in Indonesia Stock Exchange or capital market? Meanwhile, option is basically a contract between two parties that contains the right for the option buyer to buy or sell the underlying asset of the contract at the certain time and price agreed upon at the beginning of the contract. The discussion will be emphasized on the development of derivative transactions and the role of Financial Services Authority (OJK) in increasing the number of derivative transactions in Indonesia period 2004-2019 regarding the change of legal aspect.

Skew Preference in Energy Commodity Option Design

The pay-off profiles of an option buyer or seller, indeed the risks they bear, are skewed and asymmetric by design. A poorly designed option has a tendency for inadequate or excessive risk mitigation. Our objective in this paper is to develop an optimisation model for determining the mix and structure of energy commodity options, given alternative levels of skew preference and option premium budgets. Our modelling is particularly suitable to the setting of electric utility regulation involving multiple stakeholders with potentially diverse skew preferences. A regulated electric utility has a fiduciary duty to seek a prudent programme for fuel cost hedging, yet various stakeholders, including but not limited to corporate managers, regulators, and consumer advocates, are able to influence its configuration. We implement calibrations and simulations of our model for scenarios pertaining to skew preference, option premium budgets, and a representation of a California regulatory incentive system. We assess the economic consequences of mischaracterising the concept of skew in the design of natural gas options.

Pricing Average Price Advertising Options When Underlying Spot Market Prices Are Discontinuous

Advertising options have been recently studied as a special type of guaranteed contracts in online advertising, which are an alternative sales mechanism to real-time auctions. An advertising option is a contract which gives its buyer a right but not obligation to enter into transactions to purchase page views or link clicks at one or multiple pre-specified prices in a specific future period. Different from typical guaranteed contracts, the option buyer pays a lower upfront fee but can have greater flexibility and more control of advertising. Many studies on advertising options so far have been restricted to the situations where the option payoff is determined by the underlying spot market price at a specific time point and the price evolution over time is assumed to be continuous. The former leads to a biased calculation of option payoff and the latter is invalid empirically for many online advertising slots. This paper addresses these two limitations by proposing a new advertising option pricing framework. First, the option payoff is calculated based on an average price over a specific future period. Therefore, the option becomes path-dependent. The average price is measured by the power mean, which contains several existing option payoff functions as its special cases. Second, jump-diffusion stochastic models are used to describe the movement of the underlying spot market price, which incorporate several important statistical properties including jumps and spikes, non-normality, and absence of autocorrelations. A general option pricing algorithm is obtained based on Monte Carlo simulation. In addition, an explicit pricing formula is derived for the case when the option payoff is based on the geometric mean. This pricing formula is also a generalized version of several other option pricing models discussed in related studies.

A big data Bayesian approach to earnings profitability in the S&P 500

A big data Bayesian approach to earnings profitability in the S&P 500

The Tourinho model: neglected nugget or a receding relic?

This article evaluates Tourinho's (1979b) work as one of the earliest contributors to the real options literature. His model pioneered the application of risk neutrality to uncertain investments, but his originality of introducing an option-holding cost albeit to overcome the extraction paradox is rarely imitated. We claim that the combination of a convenience yield and an option-holding cost produces a more satisfying representation. Moreover, variations in the holding cost give rise to a host of investment decisions ranging from the standard real option solution for a zero-holding cost to a net present value solution for an infinite-holding cost. Not only does the holding cost mediate between these two poles, but it provides the option seller (usually a landowner or a government) with a policy instrument for influencing the extraction timing and thus the extraction profit of the option buyer. We derive the holding cost that optimizes the landowner's combined value of the option premium, holding costs and eventual royalties.

American Options under Proportional Transaction Costs: Pricing, Hedging and Stopping Algorithms for Long and Short Positions

American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale representations are presented for short (seller’s) and long (buyer’s) positions in an American option with an arbitrary payoff. This general approach extends the special cases considered in the literature concerned primarily with computing the prices of American puts under transaction costs by relaxing any restrictions on the form of the payoff, the magnitude of the transaction costs or the discrete market model itself. The largely unexplored case of pricing, hedging and stopping for the American option buyer under transaction costs is also covered. The pricing algorithms are computationally efficient, growing only polynomially with the number of time steps in a recombinant tree model. The stopping times realising the ask (seller’s) and bid (buyer’s) option prices can differ from one another. The former is generally a so-called mixed (randomised) stopping time, whereas the latter is always a pure (ordinary) stopping time.

Some optimal stopping problems with nontrivial boundaries for pricing exotic options

We solve the following three optimal stopping problems for different kinds of options, based on the Black-Scholes model of stock fluctuations. (i) The perpetual lookback American option for the running maximum of the stock price during the life of the option. This problem is more difficult than the closely related one for the Russian option, and we show that for a class of utility functions the free boundary is governed by a nonlinear ordinary differential equation. (ii) A new type of stock option, for a company, where the company provides a guaranteed minimum as an added incentive in case the market appreciation of the stock is low, thereby making the option more attractive to the employee. We show that the value of this option is given by solving a nonalgebraic equation. (iii) A new call option for the option buyer who is risk-averse and gets to choose, a priori, a fixed constant l as a ‘hedge’ on a possible downturn of the stock price, where the buyer gets the maximum of l and the price at any exercise time. We show that the optimal policy depends on the ratio of x/l, where x is the current stock price.

Some optimal stopping problems with nontrivial boundaries for pricing exotic options

We solve the following three optimal stopping problems for different kinds of options, based on the Black-Scholes model of stock fluctuations. (i) The perpetual lookback American option for the running maximum of the stock price during the life of the option. This problem is more difficult than the closely related one for the Russian option, and we show that for a class of utility functions the free boundary is governed by a nonlinear ordinary differential equation. (ii) A new type of stock option, for a company, where the company provides a guaranteed minimum as an added incentive in case the market appreciation of the stock is low, thereby making the option more attractive to the employee. We show that the value of this option is given by solving a nonalgebraic equation. (iii) A new call option for the option buyer who is risk-averse and gets to choose, a priori, a fixed constant l as a ‘hedge’ on a possible downturn of the stock price, where the buyer gets the maximum of l and the price at any exercise time. We show that the optimal policy depends on the ratio of x/l, where x is the current stock price.

The Russian Option: Reduced Regret

We propose a new put option where the option buyer receives the maximum price (discounted) that the option has ever traded at during the time period (which may be indefinitely long) between the purchase time and the exercise time, so that the buyer need look at the fluctuations only occasionally and enjoys having little or no regret that he did not exercise the option at an earlier time (except for the discounting). We give an exact simple formula for the optimal expected present value (fair price) that can be derived from the option and the (unique) optimal exercise strategy that achieves the optimum value under the assumption that the asset fluctuations follow the Black-Scholes exponential Brownian motion model, which is widely accepted. It is important to note that the discounting is necessary: If it is omitted or even if it is less than the Black-Scholes drift, then the value to the buyer under optimum performance is infinite. We also solve the same problem under a different model: the original Bachelier linear Brownian market with linear discounting. This model is no longer accepted, but of course the mathematics is consistent. To our knowledge no such regretless option is currently traded in any existing market despite its evident appeal. We call it the Russian option, partly to distinguish it from the American and European options, where the term of the option is prescribed in advance and where no exact formula for the value has been given.