Chooser Options Research Articles

A Study of Asian Chooser Options in a General Two-Period Binomial Model

Asian options are also known as average price options, and their strike price is the average price of the stock in the market half a day before the strike. Binomial model is a good model to identify the value of options, The paper develops the theory of Asian chooser options in the two-period binomial model. There are Asian call options, and Asian put options. We first derive the binomial model of the Asian option and get the portfolio function. After that, we get the number of bond and stock, Nb and Ns. We study the problem via five different cases in the two-period Binomial model. In these five cases, we choose the maximum value between Asian put and call options. Then, we decide whether they are call options or put options. Then, we calculate the number of portfolios in these five cases in the two-period binomial model. Finally, we implemented the whole project with Python.

Valuation of chooser options with state-dependent risks

In this study, the underlying stock price dynamics and the forward interest rate processes are, respectively, driven by a Markovian regime-switching jump-diffusion model and a state-dependent Heath-Jarrow-Morton model. Furthermore, we employ the regime-switching Esscher transform to identify a risk-neutral martingale measure, which is used to derive integral expressions on prices of European-style chooser options. Eventually, numerical examples are provided and discussed.

Research on the Valuation of Chooser Options: Case of AAPL

The financial market is becoming increasingly sophisticated as the economy grows. Since the majority of investors are looking for the best investment to decrease risks and increase returns, the flexibility that chooser options offer is very appealing. This article provides a detailed analysis of the chooser options, emphasizing their significance and usefulness in financial markets. Since determining the precise value of options is relatively challenging, the essay involves both the qualitative and quantitative aspects of pricing chooser options, which implies a wide variety of applications in various market circumstances. Explanations in this article focus on how chooser options are applied in practice, including options’ essential properties, exotic options’ role in the financial markets, introduction to chooser options, and the valuation process. By using Monte-Carlo simulation, the paper investigates variables influencing the value of AAPL's chooser options. It aids in explaining how uncertainty and risks affect predicting and forecasting models by estimating the potential outcomes of an uncertain event. According to the calculations used in this article, Apple Inc.'s (AAPL) price is tightly connected with the selected period and less correlated with volatility and its strike price at one-year maturity. With chooser options, the investor has the discretion of deciding in advance if the option is a put or a call. In this way, this article contributes to the comprehension of investing choices.

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.

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.

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.

Pricing Bounds for Volatility Derivatives via Duality and Least Squares Monte Carlo

Derivatives on the Chicago Board Options Exchange volatility index have gained significant popularity over the last decade. The pricing of volatility derivatives involves evaluating the square root of a conditional expectation which cannot be computed by direct Monte Carlo methods. Least squares Monte Carlo methods can be used, but the sign of the error is difficult to determine. In this paper, we propose a new model-independent technique for computing upper and lower pricing bounds for volatility derivatives. In particular, we first present a general stochastic duality result on payoffs involving convex (or concave) functions. This result also allows us to interpret these contingent claims as a type of chooser options. It is then applied to volatility derivatives along with minor adjustments to handle issues caused by the square root function. The upper bound involves the evaluation of a variance swap, while the lower bound involves estimating a martingale increment corresponding to its hedging portfolio. Both can be achieved simultaneously using a single linear least square regression. Numerical results show that the method works very well for futures, calls and puts under a wide range of parameter choices.

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.

A Forward Monte Carlo Method for American Options Pricing

This study proposes a forward Monte Carlo method for the pricing of American options. The main advantage of this method is that it does not use backward induction as required by other methods. Instead, the proposed approach relies on a wise determination about whether a simulated stock price has entered the exercise region. The validity of the proposed method is supported by the mathematical proofs for the vanilla cases. With some adaption, it is shown that this forward method can be extended to price other American style options such as chooser and exchange options. This study demonstrates the effectiveness of the proposed approach using a series of numerical examples, revealing significant improvements in numerical efficiency and accuracy in contrast with the standard regression‐based method of Longstaff and Schwartz (2001). © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 33:369‐395, 2013

IT'S YOUR CHOICE: A UNIFIED APPROACH TO CHOOSER OPTIONS

We propose a unified framework for the pricing and hedging of chooser options on lognormal assets. This includes e.g. exchange or inflation rates under stochastic interest rates or equities under stochastic interest rates and dividend yields. This extends and includes chooser options under deterministic interest rates by a multidimensional model of an international economy with correlated stochastic processes. In this framework we derive closed form solutions of the arbitrage price for different specifications of chooser options. Also different hedge strategies are derived and their properties compared.

Real options in service investments: scenarios from defence

This paper addresses the theme of investment under uncertainty in services. We specifically apply principles of contingent-claims analysis to underline the value of flexibility, i.e., the real options, embedded in service level agreements (SLAs) and maintenance & repair investments in the context of aerospace and defence. We focus on path-dependent and complex contingent-claims, to show how the design of 'exotic' type options in service investments can provide valuable insurance policies against operational and financial risks for the customer, in addition to enhancing providers' incentives from superior service performance. For illustration, we highlight examples of barrier, lookback, compound, chooser and extendible options as flexibility clauses/alternatives for service provision in defence contracts.

American chooser options

This paper examines the valuation of American chooser options, i.e., American-style contracts written on the maximum of an American put and an American call. The structure of the immediate exercise region is examined. The early exercise premium representation of the chooser's price is derived and used to construct a system of coupled recursive integral equations for a pair of boundary components. Numerical implementations of the model based on this system are carried out and used to examine the boundary properties and the price behavior.

It's Your Choice: Currency Chooser Options under Stochastic Interest Rates

It's Your Choice: Currency Chooser Options under Stochastic Interest Rates

The pricing of dual-expiry exotics

This paper develops a new technique for pricing a class of exotic options that are characterized by two expiry dates. Examples of such exotics include compound options, chooser options, extendable options, shout options, partial barrier options and others. The method, based on the partial differential equation approach to option pricing, however requires no formal solution of such equations. Instead, the method exploits the observation that dual expiry options have payoffs that can be perfectly replicated by a particular set of first and second order binary options. Hence, in order to avoid arbitrage, the exotic option prices are obtained by static replication with respect to this family of binaries. The representation of prices in terms of these binaries is also quite general and does not depend on any particular underlying asset price dynamics. Closed form expressions agreeing with published results are given for the case of log-normal asset price dynamics and standard Black–Scholes assumptions.

Pricing contingent claims in incomplete markets when the holder can choose among different payoffs

We suggest a valuation principle to price general claims giving the holder the right to choose (in a predefined way) among several random payoffs in an incomplete financial market. Examples are so-called “chooser options” and American options with finitely many possible exertion times but also some life insurance contracts. Our premium is defined by the minimal amount the writer must receive at time zero such that for all possible decision functions of the holder, the writer’s utility is at least as big as the utility he would have if he did not offer this contingent claim. The valuation principle is consistent with no-arbitrage and can be interpreted as a generalization of Schweizer’s indifference principle (Schweizer [Insurance: Mathematics and Economics 28 (2001) 31–47]). We show that in a complete financial market or, in general, if the writer has an exponential utility function, our premium is the supremum over all “utility-indifference premiums” related to all fixed random payoffs we get by fixing the decision function of the holder. For every other utility function our premium can be even larger than this supremum.