Chooser Option Research Articles

Chooser Option Pricing based on Black-Scholes Model and Monte-Carlo Simulations

Since February 2022, the intensification of the Ukrainian conflict has triggered significant impacts on financial market. Huge changes in supply and demand have led to a spike in stock volatility, which resulted in the growth in risk aversion among investors. The gold is regarded as a safe haven asset and has hedge function in the stock markets. In this study, a Monte-Carlo pricing simulation based on Black-Scholes model for chooser option was investigated using the underlying asset of gold. The gold price and volatility index were sourced from Yahoo Finance website and the Chicago Board Options Exchange (CBOE). According to the analysis, the present value of the average return for one-month chooser option is simulated as $58.91, using the initial gold price of $1965.10 and the strike price of $1977.3. The present value of the average return for one-month chooser option is significantly higher than traditional call or put options. According to the sensitivity analysis, the return of chooser option under the pricing model adopted is not sensitive to the changes in volatility and time, which indicates that this pricing model is able to resist to risks and play a better role in a high-volatility market. These results shed light on the optimization of investment portfolio under complex situations. The utilization of a new pricing method paved a path for the research of exotic options and the state-of-art applications of them in the financial innovation procedures.

Evaluation of chooser option evidence from Alibaba

Due to the financial market’s globalization, it has resulted in the growingly fierce competition and the international financial system’s volatility in current financial market. This implies that it is growingly necessary to analyze the financial derivatives market’s trend. To assess chooser option, Alibaba is selected. The way of trading a majority of the exotic options is generally determined by the financial organizations based on the customers’ specific demands. Exotic options have three common types which are respectively lookback options, chooser options and binary options. In this proposed study, the Brown Motion Theory can be used to determine the prices of assets through applying Geometric Brownian Motion to simulate the prices of Alibaba’s financial assets in order to calculate the financial assets’ future value. This study offers valuable insights with both financial institutions and investors respectively creating more proper exotic options and making more appropriate investment decisions.

Pricing of Chooser Option Based on Black-Scholes Model: Case of AAPL Company

Financial derivatives traded in the markets are becoming more complex and investors' complicated situations also should be responsible for this trend. This study examines the Black-Scholes Model theoretically and practically. By using the information of AAPL company, the simulation of stock price is calculated with related parameter, in the comparison of the straddle, the chooser option has a relatively high potential profit. The paper also gives sensitivity analysis and the conclusion of variables, the result is that the volatility has the largest impact on the stock price, followed by maturity period and date chosen period. Finally, this paper introduces wider application scenarios of our study, it can be used to estimate whether the future is bullish or bearish to obtain higher returns, to predict stock volatility, and to evaluate the value of growing companies, which fill the vacancy in past researches of financial market and gives suggestions for investors.

Exploration of JPMorgan Chooser Option Pricing

As the development of the capital market, the derivatives of financial instruments have been active in the financial market. Investors can trade customized derivatives designed to manage increasingly complex risk exposures. Examples of exotic options satisfying demands include the chooser option. Most contracts require the holder to commit to a particular payoff profile at the outset, which may often be unattractive for some potential investors. Therefore, we choose the stocks of JPMorgan and use the Black-Scholes model to simulate the value of the chooser option. This article suggests approximating the value on two periods and aims to set the value of the chooser option of JPMorgan, constructs the reasonable expectation for investors, and enables them to make the proper decision on the chooser options. We provide reliable option values and retains the flexibility of simulation, in that it allows great freedom in decision date when the investors decide which type of option for the underlying assets or a joint process for the asset price, its volatility, and other asset prices. From the simulation results, we conclude that although the chooser option is the same as the traditional option in nature, the chooser option puts off the decision date and makes the payoff less volatile to the movement of the stock market, thus partly hedge the risks of the stock market.

Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model

Based on the modification of some assumptions in the traditional Black-Scholes option pricing model, we construct a model that is closer to the real financial market in this paper. That is to say, in order to make up for the shortages of using the standard Brownian motion to describe the underlying asset price, we use fractional Brownian motion to replace the standard Brownian motion in the traditional Black-Scholes model. At the same time, we assume that the interest rate satisfies the Vasicek interest rate model under fractional Brownian motion. Under the above market model, we use the stochastic analysis method under fractional Brownian motion to obtain the pricing formulae of European simple option and complex option, which generalize the existing conclusions. It is not only can be closer to the actual financial market but also make the research more practical. In addition, since the sensitivity analysis of options refers to the sensitivity or response of options to the change of its determinants, we use numerical methods to analyze the impact of the stock initial price, the chooser date and Hurst parameter on the price of European complex chooser option, which not only verifies the rationality of the pricing formula but also has guiding value for option trading.

Pricing exotic option under stochastic volatility model

Exotic options are called “customer tailored options” or “special purpose option” because they are flexible to be tailored to the specific needs of investors. Strategies based on exotic options are often employed to hedge the specific risk exposures from the financial markets. Because exotic options are more efficient and less expensive than their standard counterparts, they are playing a significant hedging role in cost effective ways. Unlike the vanilla call and put options, exotic options are either variation on the payoff patterns of plain vanilla options or they are totally different kinds of derivatives with other features. While simple vanilla call and put options are traded in the exchanges, most of the exotic options are traded in the over-the-counter markets. Supershare option and chooser option are two typical kinds of exotic options which suggest a broad range of usage and application in different financial market conditions. Supershare option is one type of Binary option. Unlike the binary option which has only one boundary, a supershare option has an upper and lower boundary.

MATHEMATICAL PROPERTIES OF AMERICAN CHOOSER OPTIONS

The American chooser option is a relatively new compound option that has the characteristic of offering exceptional risk reduction for highly volatile assets. This has become particularly significant since the start of the global financial crisis. In this paper, we derive mathematical properties of American chooser options. We show that the two optimal stopping boundaries for American chooser options with finite horizon can be characterized as the unique solution pair to a system formed by two nonlinear integral equations, arising from the early exercise premium (EEP) representation. The proof of EEP representation is based on the method of change-of-variable formula with local time on curves. The key mathematical properties of American chooser options are proved, specifically smooth-fit, continuity of value function and continuity of free-boundary among others. We compare the performance of the American chooser option against the American strangle option. We also conduct numerical experiments to illustrate our results.

Optimization of Water Resource Management Using Chooser Option Contracts under Uncertainty

Optimization of water resource management is very important to reduce water shortage risk and increase economic benefit. Water option can be used as a flexible instrument in water resource management. In this study, chooser options are designed for water managers to buy additional water in drought periods and sell redundant water in wet periods. To make optimal decisions under uncertainties including probability distributions and intervals, an inexact two-stage mixed-integer programming (ITSMIP) model is applied. To illustrate the role of chooser options in water resource management, a case study is presented. Factors which influence the willingness of buying the chooser options are analyzed and the optimal water allocation plans are also provided. The results demonstrate that chooser options can help water managers mitigate the impact of water shortage and increase utilization efficiency of water resource greatly.

Using real options for urban infrastructure adaptation under climate change

Climate uncertainties pose a problem for decision makers as they cannot choose and implement an effective adaptation strategy in infrastructure. An effective adaptation strategy can be derived only when the potential damage induced by climate change is well understood. This study proposed a decision-making model to evaluate the economic feasibility of the adaptation projects in an urban area. The climate scenarios and the economic and technical factors were used to calculate the volatility that reflects the potential damage reduction of an urban area. The model relies on a type of real options, called the “chooser option”, to consider managerial flexibility for long-term management of urban infrastructure. The proposed model can estimate the economic value of investment with reasonable accuracy based on the representative concentration pathway (RCP) climate scenarios. A case study involving a disaster prevention facility in Seoul, Korea was conducted to demonstrate the model’s applicability. The model is expected to provide guidance for the development of effective adaptation strategies for urban infrastructure.

Speculative Futures Trading under Mean Reversion

This paper studies the problem of trading futures with transaction costs when the underlying spot price is mean-reverting. Specifically, we model the spot dynamics by the Ornstein–Uhlenbeck, Cox–Ingersoll–Ross, or exponential Ornstein–Uhlenbeck model. The futures term structure is derived and its connection to futures price dynamics is examined. For each futures contract, we describe the evolution of the roll yield, and compute explicitly the expected roll yield. For the futures trading problem, we incorporate the investor’s timing option to enter or exit the market, as well as a chooser option to long or short a futures upon entry. This leads us to formulate and solve the corresponding optimal double stopping problems to determine the optimal trading strategies. Numerical results are presented to illustrate the optimal entry and exit boundaries under different models. We find that the option to choose between a long or short position induces the investor to delay market entry, as compared to the case where the investor pre-commits to go either long or short.

The right to choose: political decisions and environmental investments

Incorporating real option modelling into the valuation of ecological investments and decisions has become widely accepted in recent years. This welcome broadening suffers from one limitation as all papers assume that the decision-maker knows which option he or she has at his or her disposal: an investment option or an abandonment option. Environmental related investment decisions depend very often on political decisions which will be made on a specific date in the future and may change the general direction of environmental policy. From the investor's viewpoint, it is not clear how this decision will affect his investment, as it is possible that he must invest or disinvest after the political decision. Therefore, the aim of this paper is twofold: first, the structure of such investment decisions will be discussed, and second, a chooser option model will be presented and analysed for the first time.

Speculative Futures Trading Under Mean Reversion

This paper studies the problem of trading futures with transaction costs when the underlying spot price is mean-reverting. Specifically, we model the spot dynamics by the Ornstein-Uhlenbeck (OU), Cox-Ingersoll-Ross (CIR), or exponential Ornstein-Uhlenbeck (XOU) model. The futures term structure is derived and its connection to futures price dynamics is examined. For each futures contract, we describe the evolution of the roll yield, and compute explicitly the expected roll yield. For the futures trading problem, we incorporate the investor's timing option to enter or exit the market, as well as a chooser option to long or short a futures upon entry. This leads us to formulate and solve the corresponding optimal double stopping problems to determine the optimal trading strategies. Numerical results are presented to illustrate the optimal entry and exit boundaries under different models. We find that the option to choose between a long or short position induces the investor to delay market entry, as compared to the case where the investor pre-commits to go either long or short.

MODIFICATION OF DELTA FOR CHOOSER OPTIONS

Correctly used financial derivatives can help investors increase their expected returns and minimize their exposure to risk. To ensure the specific needs of investors, a large number of different types of non-standard exotic options is used. Chooser option is one of them. It is an option that gives its holder the right to choose at some predetermined future time whether the option will be a standard call or put with predetermined strike price and maturity time. Although the chooser options are more expensive than standard European-style options, in many cases they are a more suitable instrument for investors in hedging their portfolio value. For an effective use of the chooser option as a hedging instrument, it is necessary to check the values of the Greek parameters delta and gamma for the options. Especially, if the value of the parameter gamma is too large, hedging of the portfolio value using only parameter delta is insufficient and brings high transaction costs because the portfolio has to be reviewed relatively often. Therefore, in this article, a modification of delta-hedging as well as using the value of parameter gamma is suggested. Error of the delta modification is analyzed and compared with the error of widely used parameter delta. Typical patterns for the modified hedging parameter variation with various time to choose time for chooser options are also presented in this article.

Normalized particle swarm optimization for complex chooser option pricing on graphics processing unit

An option is a financial instrument that derives its value from an underlying asset, for example, a stock. There are a wide range of options traded today from simple and plain (European options) to exotic (chooser options) that are very difficult to evaluate. Both buyers and sellers continue to look for efficient algorithms and faster technology to price options for better profit and to beat the competition. There are mathematical models like the Black---Scholes---Merton model used to price options approximately for simple and plain options in the form of closed form solution. However, the market is flooded with various styles of options, which are difficult to price, and hence there are many numerical techniques proposed for pricing. The computational cost for pricing complex options using these numerical techniques is exorbitant for reasonable accuracy in pricing results. Heuristic approaches such as particle swarm optimization (PSO) have been proposed for option pricing, which provide same or better results for simple options than that of numerical techniques at much less computational cost. In this study, we first map the PSO parameters to option pricing parameters. Analyzing the characteristics of PSO and option pricing, we propose a strategy to normalize some of the parameters, which helps in better understanding of the sensitivity of these and other parameters on option pricing results. We then avail of the inherent concurrency of the PSO algorithm while searching for an optimum solution, and design an algorithm for implementation on a modern state-of-the-art graphics processor unit (GPU). Our implementation makes use of the architectural features of GPU in accelerating the computing performance while maintaining accuracy on the pricing results.

EXOTIC OPTIONS: A CHOOSER OPTION AND ITS PRICING

Financial instruments traded in the markets and investors’ situation in such markets are getting more and more complex. This leads to more complex derivative structures used for hedging that are harder to analyze and which risk is harder managed. Because of the complexity of these instruments, the basic characteristics of many exotic options may sometimes be not clearly understood. Most scientific studies have been focused on developing models for pricing various types of exotic options, but it is important to study their unique characteristics and to understand them correctly in order to use them in proper market situations. The paper examines main aspects of options, emphasizing the variety of exotic options and their place in financial markets and risk management process. As the exact valuation of exotic options is quite difficult, the article deals with the theoretical and practical aspects of pricing of chooser options that suggest a broad range of usage and application in different market conditions. The calculations made in the article showed that the price of the chooser is closely correlated with the choice time and low correlated with its strike price. So the first mentioned factor should be taken into consideration when making appropriate hedging and investing decisions.

Dynamic market entry and the value of flexibility in transitional international joint ventures

The purpose of this study is to formalize the optimal choice of market entry strategy for an individual multinational enterprise (MNE) from a dynamic perspective. It is argued that incorporating a suitable treatment of irreversibility, uncertainty and flexibility related to an MNE's investment decision gives further insights into the expansion, dissolvement, and optimal timing of international joint ventures (IJVs). In most cases, the initial entry strategy serves as a platform allowing the firm to make subsequent investments to exploit host-country advantages and capabilities. We allow for this by taking a three-step expansion strategy explicitly into account. The evolutionary process of the value of the foreign direct investment can be interpreted as a compound complex chooser option. The results suggest that uncertainty, size of equity share and future investment/divestment opportunities play an important role when it comes to transit from export to the first phase of the foreign direct investment commitment. The paper underscores the importance of modeling the dynamics of market entry and helps to refine the application of real options in the alliance context by providing a closed-form solution in continuous time to value the overall strategic flexibility.

Evolving economy bank asset‐liability and risk management under uncertainty with hierarchical objectives and nonlinear pricing

AbstractQuantitative modelling of the asset‐liability management (ALM) problem faced by banking institutions is reexamined in this paper. The model presented here joins stochastic programming with non‐linear goal programming (SNGP). A bank optimization model with multiple objectives, multiple non‐linear economic relationships and a complex options hedge is proposed as an extension to the contemporary model structure now used by most financial institutions. The model structure is particularly well suited to solve the ALM decision problem in evolving economies where shareholder value maximization is often stated across a multiple goal hierarchy. The result of solving the SNGP provided significant evidence that the method is viable for efficient bank management under quasi‐planned economics. Stating the non‐linear demand and supply relationships within the two‐stage representation of the stochastic decision environment proved to be an effective method for resolving complex pricing policy issues. Finally, the SNGP model extends prior ALM models by simultaneously hedging interest rate risk under uncertainty through the incorporation of a complex chooser option. The complex chooser option, a hedge with a known pay‐off, was chosen to assist an inexperienced management team with an effective risk‐abatement tool. Copyright © 2003 John Wiley & Sons, Ltd.

Penalty methods for American options with stochastic volatility

The American early exercise constraint can be viewed as transforming the original linear two dimensional stochastic volatility option pricing PDE into a PDE with a nonlinear source term. Several methods are described for enforcing the early exercise constraint by using a penalty source term in the discrete equations. The resulting nonlinear algebraic equations are solved using an approximate Newton iteration. The solution of the Jacobian is obtained using an incomplete LU (ILU) preconditioned conjugate gradient-like (PCG) method. Some example computations are presented for option pricing problems based on a stochastic volatility model, including an exotic American chooser option written on a put and call with discrete double knockout barriers and discrete dividends.