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Journal articles on the topic 'Options Finance'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 July 2024

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1

Lambrecht, Bart M. "Real options in finance." Journal of Banking & Finance 81 (August 2017): 166–71. http://dx.doi.org/10.1016/j.jbankfin.2017.03.006.

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2

BRANGER, NICOLE, and CHRISTIAN SCHLAG. "OPTION BETAS: RISK MEASURES FOR OPTIONS." International Journal of Theoretical and Applied Finance 10, no. 07 (November 2007): 1137–57. http://dx.doi.org/10.1142/s0219024907004585.

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This paper deals with the problem of determining the correct risk measure for options in a Black–Scholes (BS) framework when time is discrete. For the purposes of hedging or testing simple asset pricing relationships previous papers used the "local", i.e., the continuous-time, BS beta as the measure of option risk even over discrete time intervals. We derive a closed-form solution for option betas over discrete return periods where we distinguish between "covariance betas" and "asset pricing betas". Both types of betas involve only simple Black–Scholes option prices and are thus easy to comput

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3

Kamińska, Barbara. "Options in Corporate Finance Management." Przedsiebiorczosc i Zarzadzanie 15, no. 1 (January 1, 2014): 69–81. http://dx.doi.org/10.2478/eam-2014-0005.

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Abstract Although there are many opinions critical of options, especially after the 2008 scandal, they are becoming increasingly popular in Poland again. Therefore, issues connected with options are not only the subject of interest in academic circles again but also arouse interest of economic entities, allowing enterprises to assess a variety of action strategies. Those instruments enable planning safeguards to protect against various negative future scenarios. Hence, it comes as no surprise that there has been an increase in the number and variety of enterprises that have accepted options as

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4

Ciurlia, Pierangelo, and Andrea Gheno. "Pricing and Applications of Digital Installment Options." Journal of Applied Mathematics 2012 (2012): 1–21. http://dx.doi.org/10.1155/2012/584705.

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For its theoretical interest and strong impact on financial markets, option valuation is considered one of the cornerstones of contemporary mathematical finance. This paper specifically studies the valuation of exotic options with digital payoff and flexible payment plan. By means of the Incomplete Fourier Transform, the pricing problem is solved in order to find integral representations of the upfront price for European call and put options. Several applications in the areas of corporate finance, insurance, and real options are discussed. Finally, a new type of digital derivative named superc

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5

Lambrecht, Bart M., and Grzegorz Pawlina. "Corporate Finance and the (In)efficient Exercise of Real Options." Multinational Finance Journal 14, no. 3/4 (December 1, 2010): 189–217. http://dx.doi.org/10.17578/14-3/4-2.

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6

CHANG, Kuo-Ping. "On Option Greeks and Corporate Finance." Journal of Advanced Studies in Finance 11, no. 2 (December 23, 2020): 183. http://dx.doi.org/10.14505//jasf.v11.2(22).09.

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This paper has proposed new option Greeks and new upper and lower bounds for European and American options. It shows that because of the put-call parity, the Greeks of put and call options are interconnected and should be shown simultaneously. In terms of the theory of the firm, it is found that both the Black-Scholes-Merton and the binomial option pricing models implicitly assume that maximizing the market value of the firm is not equivalent to maximizing the equityholders’ wealth. The binomial option pricing model implicitly assumes that further increasing (decreasing) the promised payment t

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7

DOKUCHAEV, NIKOLAI. "MULTIPLE RESCINDABLE OPTIONS AND THEIR PRICING." International Journal of Theoretical and Applied Finance 12, no. 04 (June 2009): 545–75. http://dx.doi.org/10.1142/s0219024909005348.

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We suggest a modification of an American option such that the option holder can exercise the option early before the expiration and can revert later this decision to exercise; it can be repeated a number of times. This feature gives additional flexibility and risk protection for the option holder. A classification of these options and pricing rules are given. We found that the price of some call options with this feature is the same as for the European call. This means that the additional flexibility costs nothing, similarly to the situation with American and European call options. For the mar

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8

LIU, YU-HONG. "VALUATION OF COMPOUND OPTION WHEN THE UNDERLYING ASSET IS NON-TRADABLE." International Journal of Theoretical and Applied Finance 13, no. 03 (May 2010): 441–58. http://dx.doi.org/10.1142/s021902491000584x.

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After Geske (1979), compound options — options on options — have been employed in many fields in which real options are applied. The formula for a compound option is convenient to use in real project investment, but it has one drawback — the assets that underlie the compound options are usually non-tradable. This article addresses this issue and proposes two new compound option pricing formulae to overcome this drawback.

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Tang, Han, and Wenfei Li. "Empirical study for uncertain finance." Journal of Intelligent & Fuzzy Systems 40, no. 5 (April 22, 2021): 9485–92. http://dx.doi.org/10.3233/jifs-201955.

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Interest rate, stock and option are all important parts of finance. This paper applies uncertain differential equation to the study of the evolution of interest rate and stock price separately. Based on actual observations, we estimate the parameters in uncertain differential equation with the method of moments. Using the introduced interest rate and stock models, we price European options and compare the results with actual observations. Finally, a paradox of the stochastic financial model is stated.

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10

Pechtl, Andreas. "Some applications of occupation times of Brownian motion with drift in mathematical finance." Journal of Applied Mathematics and Decision Sciences 3, no. 1 (January 1, 1999): 63–73. http://dx.doi.org/10.1155/s1173912699000048.

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In the last few years new types of path-dependent options called corridor options or range options have become well-known derivative instruments in European options markets. Since the payout profiles of those options are based on occupation times of the underlying security the purpose of this paper is to provide closed form pricing formulae of Black & Scholes type for some significant representatives. Alternatively we demonstrate in this paper a relatively simple derivation of the Black & Scholes price for a single corridor option – based on a static portfolio representation – which do

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11

Deng, Liubao, Hongye Tan, Fang Wei, and Yilin Wang. "Option Pricing for Uncertain Stock Model Based on Optimistic Value." Journal of Advanced Computational Intelligence and Intelligent Informatics 26, no. 6 (November 20, 2022): 1031–39. http://dx.doi.org/10.20965/jaciii.2022.p1031.

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Option pricing plays an important role in modern finance. This paper investigates the uncertain option pricing problems based on uncertainty theory by using the method to calculate the optimistic value of uncertain returns of options instead of the method of traditional expected value in the sense of the weighted average. The pricing formulas of the European and American options are derived for Liu’s uncertain stock model and Peng’s mean-reverting stock model which are two basic and representative uncertain stock models in uncertain finance. In the end, some numerical experiments are given to

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12

Dorion, Christian. "Option Valuation with Macro-Finance Variables." Journal of Financial and Quantitative Analysis 51, no. 4 (August 2016): 1359–89. http://dx.doi.org/10.1017/s0022109016000442.

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I propose a model in which the price of an option is partly determined by macro-finance variables. In an application using an index of current business conditions, the new model outperforms existing benchmarks in fitting underlying asset returns and in pricing options. The model performs particularly well when business conditions are deteriorating. Using the recent financial crisis as an out-of-sample experiment, the new model has option-pricing errors that are 18% below those of a nested 2-component volatility benchmark. Results are robust to using alternative business conditions proxies and

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13

Power, Jane. "Financing options for businesses in Ireland." Boolean: Snapshots of Doctoral Research at University College Cork, no. 2010 (January 1, 2010): 144–48. http://dx.doi.org/10.33178/boolean.2010.33.

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Starting a business is a complex process which requires multifaceted organisation and planning. Entrepreneurs begin with an idea which must immediately be tempered with the need to justify the creative concept, choose the business location, assess the competition and, most importantly, identify methods to finance it. This last task is the most crucial as, without capital, there will be no business. The majority of entrepreneurs face one fundamental problem; they rarely have the amount of capital required to see their ideas to fruition. Creating a business and executing a business plan requires

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Kammer, Alfred, Mohamed Norat, Marco Pinon, Ananthakrishnan Prasad, Christopher Towe, and Zeine Zeidane. "Islamic Finance: Opportunities, Challenges, and Policy Options." Staff Discussion Notes 15, no. 5 (2015): 1. http://dx.doi.org/10.5089/9781498325035.006.

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Ahmed, Qazi Masood, and Akhtar Lodhi. "Provincial Finance Commission: Options for Fiscal Transfers." Pakistan Development Review 47, no. 4II (December 1, 2008): 747–62. http://dx.doi.org/10.30541/v47i4iipp.747-762.

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The Provincial Finance Commissions were constituted in all four provinces of Pakistan in 2001. The Commissions were asked to formulate a formula for the distribution of resources among the districts in their respective province. The formula includes both transfers- the development transfer and current transfers. The purposes of the current transfers are to ensure the maintainability of existing services at the districts level and of the development grants to minimise the intradistrict poverty and inter-districts income differential. In this paper we compute the Rank Correlation between the exi

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16

Khare, Arvind, Sara Scherr, Augusta Molnar, and Andy White. "Forest Finance, Development Cooperation and Future Options." Review of European Community and International Environmental Law 14, no. 3 (November 2005): 247–54. http://dx.doi.org/10.1111/j.1467-9388.2005.00446.x.

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17

West, Jason. "Structured Islamic Finance Options for theResources Sector." Journal of Structured Finance 18, no. 3 (October 31, 2012): 91–101. http://dx.doi.org/10.3905/jsf.2012.18.3.091.

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18

Ramprasath, L. "Simpler proofs in finance and shout options." Applied Economics Letters 18, no. 2 (January 26, 2011): 173–78. http://dx.doi.org/10.1080/13504850903493189.

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19

Agliardi, Elettra, and Rossella Agliardi. "Pricing Multidimensional American Options." International Journal of Financial Studies 11, no. 1 (March 22, 2023): 51. http://dx.doi.org/10.3390/ijfs11010051.

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A new explicit form is provided for the solution of optimal stopping problems involving a multidimensional geometric Brownian motion. A free-boundary value approach is adopted and the value function is obtained via fundamental solution methods. There are many applications for the valuation of perpetual options of American style, which are of interest for finance and managerial decisions.

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20

LAU, KA WO, and YUE KUEN KWOK. "VALUATION OF EMPLOYEE RELOAD OPTIONS USING UTILITY MAXIMIZATION APPROACH." International Journal of Theoretical and Applied Finance 08, no. 05 (August 2005): 659–74. http://dx.doi.org/10.1142/s0219024905003189.

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The reload provision in an employee stock option is an option enhancement that allows the employee to pay the strike upon exercising the stock option using his owned stocks and to receive new "reload" stock options. The usual Black–Scholes risk neutral valuation approach may not be appropriate to be adopted as the pricing vehicle for employee stock options, due to the non-transferability of the ownership of the options and the restriction on short selling of the firm's stocks as hedging strategy. In this paper, we present a general utility maximization framework to price non-tradeable employee

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21

Efendi, Jap, Li-Chin Jennifer Ho, Jeffrey J. Tsay, and Yu Zhang. "Stock option expense management after SFAS 123R." Review of Accounting and Finance 13, no. 3 (August 5, 2014): 210–31. http://dx.doi.org/10.1108/raf-05-2012-0049.

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Purpose – The purpose of this paper is to examine whether firms manage the total value of stock option grants downward after the implementation of Statement of Financial Accounting Standards (SFAS) 123R to reduce their reported option expenses. Design/methodology/approach – All Standard & Poor’s (S&P) 1500 firms with available stock option data in 2004 and 2006 are included in the analysis. The authors analyze if the total value of options granted, the per share fair value of options granted, the number of options granted as well as each individual input assumption have changed from th

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22

Lin, Weili. "Supply Chain Finance: Brief Introduction of In-kind Finance and Factoring." Advances in Economics, Management and Political Sciences 18, no. 1 (September 13, 2023): 306–13. http://dx.doi.org/10.54254/2754-1169/18/20230089.

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Small and medium-size enterprises (SME) can sometimes find it difficult to acquire necessary cash flow from banks. It comes with a high cost to obtain necessary information for SMEs and assessing true financial situation for each individual suppliers can be both costly and time consuming. and other methods are needed to finance SMEs. The paper will talk about some of the most used supply chain financing options include in-kind finance, factoring and reverse factoring, and inventory-based financing. Based on findings, I concluded the benefit and risk of each method, and parties involved in thes

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23

McKeon, Ryan. "Empirical patterns of time value decay in options." China Finance Review International 7, no. 4 (November 20, 2017): 429–49. http://dx.doi.org/10.1108/cfri-09-2016-0108.

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Purpose The purpose of this paper is to conduct an empirical analysis of the pattern of time value decay in listed equity options, considering both call and put options and different moneyness and maturity levels. Design/methodology/approach The research design is empirical, with great attention paid to creating a standardized measure of time value that can be both tracked over time for an individual option contract and meaningfully compared across two or more different option contracts. Findings The author finds that moneyness classification at the beginning of the holding period is the key d

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24

RODRÍGUEZ, JESÚS F. "HEDGING SWING OPTIONS." International Journal of Theoretical and Applied Finance 14, no. 02 (March 2011): 295–312. http://dx.doi.org/10.1142/s021902491100636x.

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We study models for electricity pricing and derivatives in the context of a deregulated market setting. In particular we value swing options, since these are the electricity derivatives that attract the most attention from market participants. These are American style options in that they allow for multiple exercises subject to a set of constraints on the consumption process. Through the use of a penalty function, we generalize the problem by allowing for the consumption restrictions to be broken. We characterize the price function as a stochastic optimal control problem, and show that the opt

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25

Mo, Di, Neda Todorova, and Rakesh Gupta. "Implied volatility smirk and future stock returns: evidence from the German market." Managerial Finance 41, no. 12 (December 7, 2015): 1357–79. http://dx.doi.org/10.1108/mf-04-2015-0097.

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Purpose – The purpose of this paper is to investigate the relationship between option’s implied volatility smirk (IVS) and excess returns in the Germany’s leading stock index Deutscher-Aktien Index (DAX) 30. Design/methodology/approach – The study defines the IVS as the difference in implied volatility derived from out-of-the-money put options and at-the-money call options. This study employs the ordinary least square regression with Newey-West correction to analyse the relationship between IVS and excess DAX 30 index returns in Germany. Findings – The authors find that the German market adjus

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26

Blenman, Lloyd P., and Steven P. Clark. "Power exchange options." Finance Research Letters 2, no. 2 (June 2005): 97–106. http://dx.doi.org/10.1016/j.frl.2005.01.003.

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27

Ye, George L. "Asian options versus vanilla options: a boundary analysis." Journal of Risk Finance 9, no. 2 (February 29, 2008): 188–99. http://dx.doi.org/10.1108/15265940810853931.

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28

DIA, BAYE M. "A REGULARIZED FOURIER TRANSFORM APPROACH FOR VALUING OPTIONS UNDER STOCHASTIC DIVIDEND YIELDS." International Journal of Theoretical and Applied Finance 13, no. 02 (March 2010): 211–40. http://dx.doi.org/10.1142/s0219024910005747.

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This paper studies the option pricing problem in a class of models in which dividend yields follow a time-homogeneous diffusion. Within this framework, we develop a new approach for valuing options based on the use of a regularized Fourier transform. We derive a pricing formula for European options which gives the option price in the form of an inverse Fourier transform and propose two methods for numerically implementing this formula. As an application of this pricing approach, we introduce the Ornstein-Uhlenbeck and the square-root dividend yield models in which we explicitly solve the prici

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29

Heard, D. M., and S. J. Grenfell. "GROWTH, PROTECTION AND VALUE REALISATION USING DERIVATIVES." APPEA Journal 44, no. 1 (2004): 781. http://dx.doi.org/10.1071/aj03042.

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Oil and gas producers are familiar with the use of derivatives to hedge oil price risk.Beyond this, derivatives provide opportunities to enhance more general corporate finance activities.An example is raising finance for acquisitions or developments. When the maximum senior debt has been obtained, the choice between equity funding or other sources (such as subordinated debt) should also consider the up-front cash available from a structured derivative program—this may lower the overall cost of capital for the acquirer, and directly improve equity returns through lower dilution.A notable aspect

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Arora, Manpreet Kaur, and Manpreet Arora. "Influence of Behavioral Factors on Early Exercise of Employee Stock Option: A Literature Review." ECS Transactions 107, no. 1 (April 24, 2022): 6175–84. http://dx.doi.org/10.1149/10701.6175ecst.

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Employee Stock Option Plans (ESOPs) have gained prominence as a successful HR strategy that improves the employees’ performance and enables the company to have an economic and strategic advantage. However, the time at which employees decide to exercise their options determines the incentive that they derive from the stock options granted to them. It is one of the crucial financial decisions which can have immense implications for both employers and employees. According to the Black Scholes Model, an option's value is maximum when it is held until maturity. But most employees exercise their opt

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31

Ahlip, Rehez, Laurence A. F. Park, Ante Prodan, and Stephen Weissenhofer. "Forward start options under Heston affine jump-diffusions and stochastic interest rate." International Journal of Financial Engineering 08, no. 01 (March 2021): 2150005. http://dx.doi.org/10.1142/s2424786321500055.

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This paper presents a generalization of forward start options under jump diffusion framework of Duffie et al. [Duffie, D, J Pan and K Singleton (2000). Transform analysis and asset pricing for affine jump-diffusions, Econometrica 68, 1343–1376.]. We assume, in addition, the short-term rate is governed by the CIR dynamics introduced in Cox et al. [Cox, JC, JE Ingersoll and SA Ross (1985). A theory of term structure of interest rates, Econometrica 53, 385–408.]. The instantaneous volatilities are correlated with the dynamics of the stock price process, whereas the short-term rate is assumed to b

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32

Ang, Kian-Ping, Shafiqur Rahman, and Kok-Hui Tan. "Option Implied Moments: An Application to Nikkei 225 Futures Options." Review of Pacific Basin Financial Markets and Policies 05, no. 03 (September 2002): 301–20. http://dx.doi.org/10.1142/s0219091502000821.

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This paper proposes an integrated process to recover the moments of the risk-neutral distribution using a Gram-Charlier expansion series and Rubinstein's implied binomial tree approach. The advantage of using the implied tree approach is that it accounts for the possibility of early exercise of American options. We apply the method to American-style options on Nikkei 225 futures. We then demonstrate how to use the implied moments for trading options.

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33

Watson, Joel. "On the outside-option principle with one-sided options." Economics Letters 191 (June 2020): 109110. http://dx.doi.org/10.1016/j.econlet.2020.109110.

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34

Arnold, Tom, and Richard Shockley. "Real Options Analysis and the Assumptions of Corporate Finance: A Non-Technical Review." Multinational Finance Journal 14, no. 1/2 (June 1, 2010): 29–71. http://dx.doi.org/10.17578/14-1/2-2.

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35

Lindensjö, Kristoffer. "The End of the Month Option and Other Embedded Options in Futures Contracts." Asia-Pacific Financial Markets 23, no. 1 (February 16, 2016): 69–83. http://dx.doi.org/10.1007/s10690-016-9209-7.

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Dassios, Angelos, and Shanle Wu. "Double-Barrier Parisian Options." Journal of Applied Probability 48, no. 1 (March 2011): 1–20. http://dx.doi.org/10.1239/jap/1300198132.

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In this paper we study the excursion time of a Brownian motion with drift outside a corridor by using a four-state semi-Markov model. In mathematical finance, these results have an important application in the valuation of double-barrier Parisian options. We subsequently obtain an explicit expression for the Laplace transform of its price.

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Dassios, Angelos, and Shanle Wu. "Double-Barrier Parisian Options." Journal of Applied Probability 48, no. 01 (March 2011): 1–20. http://dx.doi.org/10.1017/s0021900200007592.

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In this paper we study the excursion time of a Brownian motion with drift outside a corridor by using a four-state semi-Markov model. In mathematical finance, these results have an important application in the valuation of double-barrier Parisian options. We subsequently obtain an explicit expression for the Laplace transform of its price.

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38

Ciccotello, Conrad, C. Terry Grant, and W. Mark Wilder. "Finance, Politics, and the Accounting for Stock Options." Journal of Applied Corporate Finance 17, no. 4 (September 2005): 125–33. http://dx.doi.org/10.1111/j.1745-6622.2005.00066.x.

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Aghion, Philippe, Patrick Bolton, and Jean Tirole. "Exit Options in Corporate Finance: Liquidity versus Incentives*." Review of Finance 8, no. 3 (January 1, 2004): 327–53. http://dx.doi.org/10.1007/s10679-004-2542-0.

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40

Swaroop, Vinaya. "The public finance of infrastructure: Issues and options." World Development 22, no. 12 (December 1994): 1909–19. http://dx.doi.org/10.1016/0305-750x(94)90182-1.

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41

Strand, Jon. "Mitigation incentives with climate finance and treaty options." Energy Economics 57 (June 2016): 166–74. http://dx.doi.org/10.1016/j.eneco.2016.05.003.

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42

Kraft, Evan. "Recasting Finance in Eastern Europe: Options and Possibilities." Review of Radical Political Economics 25, no. 3 (September 1993): 17–25. http://dx.doi.org/10.1177/048661349302500303.

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Šoltés, Michal, and Monika Harčariková. "Gold price risk management through Nova 3 option strategy created by barrier options." Investment Management and Financial Innovations 13, no. 1 (March 4, 2016): 49–0. http://dx.doi.org/10.21511/imfi.13(1).2016.04.

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The paper is focused on selected aspects of the hedging using of Nova 3 option strategy created by barrier options, which are appropriate tools widely used for risk management of high risk underlying assets. Financial risk management using option strategies is an effective solution for limiting the loss from underlying asset’s price development. The Nova 3 option strategy is suitable for hedging against increase in price of the underlying asset in case of its purchase in future. In our approach, European up and knock-in call options together with standard put and barrier put options are used f

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SOBEHART, JORGE R. "A FORWARD LOOKING, SINGULAR PERTURBATION APPROACH TO PRICING OPTIONS UNDER MARKET UNCERTAINTY AND TRADING NOISE." International Journal of Theoretical and Applied Finance 08, no. 05 (August 2005): 635–58. http://dx.doi.org/10.1142/s0219024905003165.

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In this article we examine the pricing of options when trading noise and uncertainty in the options markets invalidates the assumption that the price of the option depends solely on the price of the underlying security (or any set of underlying state variables). We show that the introduction of trading noise in the options market affects the call-put parity relationship, and can also contribute to generate implied volatility skews.

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BRODY, DORJE C., IRENE C. CONSTANTINOU, and BERNHARD K. MEISTER. "TERM STRUCTURE OF VANILLA OPTIONS." International Journal of Theoretical and Applied Finance 10, no. 08 (December 2007): 1323–37. http://dx.doi.org/10.1142/s0219024907004676.

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Every maturity-dependent derivative contract entails a term structure. For example, when the value of the portfolio consisting of a long position in a stock and a short position in a vanilla option is expressed in units of its instantaneous exercise value, the resulting quantity defines a discount function. Thus, the derivative of the discount function with respect to the time left until maturity defines a term structure density function, and the "hazard rate" associated with the discount function determines the forward rates for the vanilla option portfolio. The dynamics associated with these

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Goncalves-Pinto, Luis, Bruce D. Grundy, Allaudeen Hameed, Thijs van der Heijden, and Yichao Zhu. "Why Do Option Prices Predict Stock Returns? The Role of Price Pressure in the Stock Market." Management Science 66, no. 9 (September 2020): 3903–26. http://dx.doi.org/10.1287/mnsc.2019.3398.

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Stock and options markets can disagree about a stock’s value because of informed trading in options and/or price pressure in the stock. The predictability of stock returns based on this cross-market discrepancy in values is especially strong when accompanied by stock price pressure, and it does not depend on trading in options. We argue that option-implied prices provide an anchor for fundamental stock values that helps to distinguish stock price movements resulting from pressure versus news. Overall, our results are consistent with stock price pressure being the primary driver of the option p

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Tambingon, Desty A., Jullia Titaley, and Tohap Manurung. "Black-Scholes Model in Determining European Option Prices on Netflix,Inc." d'CARTESIAN 8, no. 2 (July 25, 2019): 80. http://dx.doi.org/10.35799/dc.8.2.2019.23960.

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Research has been conducted to compare the prices of European option on the Yahoo Finance website with prices obtained from the Black-Scholes model (theoretical price). Data was taken on January 31, 2019 which included the daily share price of Netflix, Inc. (NFLX) on February 14, 2018 - January 31, 2019 to obtain volatility, and NFLX options data due on January 17, 2020. Options with prices lower than theoretical prices are said to be underpriced, so the decision taken is to buy the options. Whereas options with prices higher than theoretical prices are said to be overpriced, so it has to be r

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EKSTRÖM, ERIK, and MARTIN VANNESTÅL. "AMERICAN OPTIONS AND INCOMPLETE INFORMATION." International Journal of Theoretical and Applied Finance 22, no. 06 (September 2019): 1950035. http://dx.doi.org/10.1142/s0219024919500353.

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We study the optimal exercise of American options under incomplete information about the drift of the underlying process, and we show that quite unexpected phenomena may occur. In fact, certain parameter values give rise to stopping regions very different from the standard case of complete information. For example, we show that for the American put (call) option it is sometimes optimal to exercise the option when the underlying process reaches an upper (lower) boundary.

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Trainor, William, and Richard Gregory. "Leveraged ETF option strategies." Managerial Finance 42, no. 5 (May 9, 2016): 438–48. http://dx.doi.org/10.1108/mf-12-2014-0305.

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Abstract:

Purpose – Leveraged exchange traded funds (ETFs) have become increasingly popular since their introduction in 2006. In recent years, options on leveraged ETFs have been promoted as a means of enhancing returns and reducing risk. The purpose of this paper is to examine the interchangeability of S & P 500 ETF options with leveraged S & P 500 ETF options and to what extent these options allow investors to manage their risk exposure. Design/methodology/approach – With increasing liquidity for these fund’s options, simple option strategies such as covered calls and protective puts can be im

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STOIKOV, SASHA F. "PRICING OPTIONS FROM THE POINT OF VIEW OF A TRADER." International Journal of Theoretical and Applied Finance 09, no. 08 (December 2006): 1245–66. http://dx.doi.org/10.1142/s0219024906004049.

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Abstract:

This paper is a contribution to the pricing and hedging of options in a market where the volatility is stochastic. The new concept of relative indifference pricing is further developed. This relative price is the price at which an option trader is indifferent to trade in an additional option, given that he is currently holding and dynamically hedging a portfolio of options. We find that the appropriate volatility risk premium depends on the trader's risk aversion coefficient and his portfolio position before selling or buying the additional option. We suggest two asymptotic expansions which re

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