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Journal articles on the topic 'American Options'

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Published: 4 June 2021

Last updated: 20 February 2023

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1

KE, ZIWEI, and JOANNA GOARD. "PENALTY AMERICAN OPTIONS." International Journal of Theoretical and Applied Finance 22, no. 02 (March 2019): 1950001. http://dx.doi.org/10.1142/s0219024919500018.

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We present a new American-style option whereby on the event of exercise before expiry, the holder pays the writer a fee (which will be referred to as a ‘penalty’). The valuation of the option is not straightforward as it involves determining when it is optimal for the holder to exercise the option, leading to a free boundary problem. As most options in the traded markets have short maturities, accurate and fast valuations of such options are important. We derive analytic approximations for the value of the option with short times to expiry (up to [Formula: see text] months) and its optimal exercise boundary. Some properties of the option, such as the put–call relationship, are explored as well. Numerical experiments suggest that our solutions both for the optimal exercise boundary and option value provide very accurate results.

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2

QIU, SHI, and SOVAN MITRA. "MATHEMATICAL PROPERTIES OF AMERICAN CHOOSER OPTIONS." International Journal of Theoretical and Applied Finance 21, no. 08 (December 2018): 1850062. http://dx.doi.org/10.1142/s0219024918500620.

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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.

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3

Qiu, Shi. "American Strangle Options." Applied Mathematical Finance 27, no. 3 (May 3, 2020): 228–63. http://dx.doi.org/10.1080/1350486x.2020.1825968.

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4

Chesney, Marc, and Laurent Gauthier. "American Parisian options." Finance and Stochastics 10, no. 4 (August 11, 2006): 475–506. http://dx.doi.org/10.1007/s00780-006-0015-3.

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5

Detemple, Jérôme, Souleymane Laminou Abdou, and Franck Moraux. "American step options." European Journal of Operational Research 282, no. 1 (April 2020): 363–85. http://dx.doi.org/10.1016/j.ejor.2019.09.009.

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6

Klein, Peter, and Jun Yang. "Vulnerable American options." Managerial Finance 36, no. 5 (April 20, 2010): 414–30. http://dx.doi.org/10.1108/03074351011039436.

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7

Detemple, Jérôme, and Thomas Emmerling. "American chooser options." Journal of Economic Dynamics and Control 33, no. 1 (January 2009): 128–53. http://dx.doi.org/10.1016/j.jedc.2008.05.004.

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8

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 market model with zero interest rate, the price of put options with this feature is also the same as for the standard European put options. Therefore, these options can be more competitive than the standard American options.

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9

Barone, Gaia. "European Compound Options Writtenon Perpetual American Options." Journal of Derivatives 20, no. 3 (February 28, 2013): 61–74. http://dx.doi.org/10.3905/jod.2013.20.3.061.

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10

Chung, San-Lin, and Hsieh-Chung Chang. "Generalized Analytical Upper Bounds for American Option Prices." Journal of Financial and Quantitative Analysis 42, no. 1 (March 2007): 209–27. http://dx.doi.org/10.1017/s0022109000002258.

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AbstractThis paper generalizes and tightens Chen and Yeh's (2002) analytical upper bounds for American options under stochastic interest rates, stochastic volatility, and jumps, where American option prices are difficult to compute with accuracy. We first generalize Theorem 1 of Chen and Yeh (2002) and apply it to derive a tighter upper bound for American calls when the interest rate is greater than the dividend yield. Our upper bounds are not only tight, but also converge to accurate American call option prices when the dividend yield or strike price is small or when volatility is large. We then propose a general theorem that can be applied to derive upper bounds for American options whose payoffs depend on several risky assets. As a demonstration, we utilize our general theorem to derive upper bounds for American exchange options and American maximum options on two risky assets.

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11

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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12

Ibáñez, Alfredo, and Ioannis Paraskevopoulos. "The Sensitivity of American Options to Suboptimal Exercise Strategies." Journal of Financial and Quantitative Analysis 45, no. 6 (September 21, 2010): 1563–90. http://dx.doi.org/10.1017/s002210901000058x.

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AbstractThe value of American options depends on the exercise policy followed by option holders. Market frictions, risk aversion, or a misspecified model, for example, can result in suboptimal behavior. We study the sensitivity of American options to suboptimal exercise strategies. We show that this measure is given by the Gamma of the American option at the optimal exercise boundary. More precisely, “ifBis the optimal exercise price, but exercise is eitherbrought forward whenordelayed untila priceB̃has been reached, the cost of suboptimal exercise is given by ½ ×Γ(B) × (B−B̃)2, whereΓ(B) denotes the American option Gamma.” Therefore, the cost of suboptimal exercise is second-order in the bias of the exercise policy and depends on Gamma. This result provides new insights on American options.

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13

KIMURA, TOSHIKAZU. "ALTERNATIVE RANDOMIZATION FOR VALUING AMERICAN OPTIONS." Asia-Pacific Journal of Operational Research 27, no. 02 (April 2010): 167–87. http://dx.doi.org/10.1142/s0217595910002624.

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This paper deals with randomization methods for valuing American options written on dividend-paying assets, which are based on the idea of treating the maturity date as a random variable. In the randomization method introduced by Carr in 1998, he used the Erlangian distributed random variable to develop a recursive algorithm starting from the so-called Canadian option with an exponentially distributed random maturity. The purposes of this paper are (i) to provide much simpler pricing formulas for the Canadian option; (ii) to interpret the Gaver–Stehfest method developed for inverting Laplace transforms as an alternative randomization method in the context of valuing American options; and (iii) to evaluate the performance of the Gaver–Stehfest method in details with theoretical and numerical views. Numerical experiments indicate that the Gaver–Stehfest method works well to generate accurate approximations for the early exercise boundary as well as the option value.

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14

Chevalier, Etienne, Vathana Ly Vath, and Mohamed Mnif. "Path-dependent American options." Journal of Computational Finance 23, no. 1 (2019): 61–95. http://dx.doi.org/10.21314/jcf.2019.369.

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15

Baptista, Alexandre M. "Spanning with American options." Journal of Economic Theory 110, no. 2 (June 2003): 264–89. http://dx.doi.org/10.1016/s0022-0531(03)00037-1.

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16

Dai, Min, and Yue Kuen Kwok. "Knock-in American options." Journal of Futures Markets 24, no. 2 (2003): 179–92. http://dx.doi.org/10.1002/fut.10101.

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17

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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18

Alobaidi, Ghada, and Roland Mallier. "ASYMPTOTICS FOR AMERICANS: AMERICAN OPTIONS CLOSE TO EXPIRY." Far East Journal of Mathematical Sciences (FJMS) 99, no. 12 (June 24, 2016): 1883–96. http://dx.doi.org/10.17654/ms099121883.

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19

Gao, Shuai, and Jun Zhao. "Pricing 50ETF in the Way of American Options Based on Least Squares Monte Carlo Simulation." Applied Finance and Accounting 2, no. 2 (June 3, 2016): 71. http://dx.doi.org/10.11114/afa.v2i2.1657.

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50ETF appears on the Chinese stock market on 9th February,2015, the contracts are European Options and the options are priced by B-S model.50ETF is the only one option that can be traded, there are no American Options in Chinese stock market. This paper studies 50ETF pricing analysis in accordance with the way of American Option. We use Least Squares Monte Carlo Simulation to price 50ETF and analyze them, give the numerical results by matlab program. This issue is worth studying, because the paper studies 50ETF, and price it in the way of American Options, we try to employ Monte Carlo Simulation to solve this problem in china and the results of the paper can enrich the option products in the stock market of China.

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20

Gaspar, Raquel M., Sara D. Lopes, and Bernardo Sequeira. "Neural Network Pricing of American Put Options." Risks 8, no. 3 (July 2, 2020): 73. http://dx.doi.org/10.3390/risks8030073.

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In this study, we use Neural Networks (NNs) to price American put options. We propose two NN models—a simple one and a more complex one—and we discuss the performance of two NN models with the Least-Squares Monte Carlo (LSM) method. This study relies on American put option market prices, for four large U.S. companies—Procter and Gamble Company (PG), Coca-Cola Company (KO), General Motors (GM), and Bank of America Corp (BAC). Our dataset is composed of all options traded within the period December 2018 until March 2019. Although on average, both NN models perform better than LSM, the simpler model (NN Model 1) performs quite close to LSM. Moreover, the second NN model substantially outperforms the other models, having an RMSE ca. 40% lower than the presented by LSM. The lower RMSE is consistent across all companies, strike levels, and maturities. In summary, all methods present a good accuracy; however, after calibration, NNs produce better results in terms of both execution time and Root Mean Squared Error (RMSE).

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21

Alobaidi, Ghada, and Roland Mallier. "Asymptotic analysis of American call options." International Journal of Mathematics and Mathematical Sciences 27, no. 3 (2001): 177–88. http://dx.doi.org/10.1155/s0161171201005701.

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American call options are financial derivatives that give the holder the right but not the obligation to buy an underlying security at a pre-determined price. They differ from European options in that they may be exercised at any time prior to their expiration, rather than only at expiration. Their value is described by the Black-Scholes PDE together with a constraint that arises from the possibility of early exercise. This leads to a free boundary problem for the optimal exercise boundary, which determines whether or not it is beneficial for the holder to exercise the option prior to expiration. However, an exact solution cannot be found, and therefore by using asymptotic techniques employed in the study of boundary layers in fluid mechanics, we find an asymptotic expression for the location of the optimal exercise boundary and the value of the option near to expiration.

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22

Goard, Joanna, and Mohammed AbaOud. "Analytic Approximation for American Straddle Options." Mathematics 10, no. 9 (April 22, 2022): 1401. http://dx.doi.org/10.3390/math10091401.

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This paper looks at adapting a recent approach found in the literature for pricing short-term American options to price American straddle options with two free boundaries. We provide a series solution in which explicit formulas for the coefficients are given. Hence, no complicated, recursive systems or nonlinear integral equations need to be solved, and the method efficiently provides fast solutions. We also compare the method with a numerical method and find that it gives very accurate prices not only for the option value, but also for the critical stock prices.

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23

HAUG, ESPEN GAARDER. "CLOSED FORM VALUATION OF AMERICAN BARRIER OPTIONS." International Journal of Theoretical and Applied Finance 04, no. 02 (April 2001): 355–59. http://dx.doi.org/10.1142/s0219024901001012.

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Closed form formulae for European barrier options are well known from the literature. This is not the case for American barrier options, for which no closed form formulae have been published. One has therefore had to resort to numerical methods. Lattice models like a binomial or a trinomial tree, for valuation of barrier options are known to converge extremely slowly, compared to plain vanilla options. Methods for improving the algorithms have been described by several authors. However, these are still numerical methods that are quite computer intensive. In this paper we show how some American barrier options can be valued analytically in a very simple way. This speeds up the valuation dramatically as well as give new insight into barrier option valuation.

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24

Iron, Yonatan, and Yuri Kifer. "Error Estimates for Binomial Approximations of Game Put Options." ISRN Probability and Statistics 2014 (January 30, 2014): 1–26. http://dx.doi.org/10.1155/2014/743030.

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A game or Israeli option is an American style option where both the writer and the holder have the right to terminate the contract before the expiration time. Kifer (2000) shows that the fair price for this option can be expressed as the value of a Dynkin game. In general, there are no explicit formulas for fair prices of American and game options and approximations are used for their computations. The paper by Lamberton (1998) provides error estimates for binomial approximation of American put options and here we extend the approach of Lamberton (1998) in order to obtain error estimates for binomial approximations of game put options which is more complicated as it requires us to deal with two free boundaries corresponding to the writer and to the holder of the game option.

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25

Wang, Guanying, Xingchun Wang, and Zhongyi Liu. "PRICING VULNERABLE AMERICAN PUT OPTIONS UNDER JUMP–DIFFUSION PROCESSES." Probability in the Engineering and Informational Sciences 31, no. 2 (December 14, 2016): 121–38. http://dx.doi.org/10.1017/s0269964816000486.

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This paper evaluates vulnerable American put options under jump–diffusion assumptions on the underlying asset and the assets of the counterparty. Sudden shocks on the asset prices are described as a compound Poisson process. Analytical pricing formulae of vulnerable European put options and vulnerable twice-exercisable European put options are derived. Employing the two-point Geske and Johnson method, we derive an approximate analytical pricing formula of vulnerable American put options under jump–diffusions. Numerical simulations are performed for investigating the impacts of jumps and default risk on option prices.

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26

Goard, Joanna, and Mohammed AbaOud. "Pricing European and American Installment Options." Mathematics 10, no. 19 (September 25, 2022): 3494. http://dx.doi.org/10.3390/math10193494.

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This paper derives accurate and efficient analytic approximations for the prices of both European and American continuous-installment call and put options. The solutions are in the form of series in time-to-expiry with explicit formulae for the coefficients provided. Unlike other solutions for installment options, no Laplace inverses are needed, and there is no need to solve complex, recursive systems or integral equations. The formulae provided fast yield and accurate solutions not just for the prices, but also for the critical boundaries. We also compare the solutions with those obtained using an existing method and show that it surpasses it delivering more correct option prices and critical stock prices.

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27

Gukhal, Chandrasekhar Reddy. "The compound option approach to American options on jump-diffusions." Journal of Economic Dynamics and Control 28, no. 10 (September 2004): 2055–74. http://dx.doi.org/10.1016/j.jedc.2003.06.002.

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28

Salvador, Beatriz, Cornelis W. Oosterlee, and Remco van der Meer. "Financial Option Valuation by Unsupervised Learning with Artificial Neural Networks." Mathematics 9, no. 1 (December 28, 2020): 46. http://dx.doi.org/10.3390/math9010046.

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Artificial neural networks (ANNs) have recently also been applied to solve partial differential equations (PDEs). The classical problem of pricing European and American financial options, based on the corresponding PDE formulations, is studied here. Instead of using numerical techniques based on finite element or difference methods, we address the problem using ANNs in the context of unsupervised learning. As a result, the ANN learns the option values for all possible underlying stock values at future time points, based on the minimization of a suitable loss function. For the European option, we solve the linear Black–Scholes equation, whereas for the American option we solve the linear complementarity problem formulation. Two-asset exotic option values are also computed, since ANNs enable the accurate valuation of high-dimensional options. The resulting errors of the ANN approach are assessed by comparing to the analytic option values or to numerical reference solutions (for American options, computed by finite elements). In the short note, previously published, a brief introduction to this work was given, where some ideas to price vanilla options by ANNs were presented, and only European options were addressed. In the current work, the methodology is introduced in much more detail.

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29

Bae, Kwangil. "Analytical Approximations of American Call Options with Discrete Dividends." Journal of Derivatives and Quantitative Studies 26, no. 3 (August 31, 2018): 283–310. http://dx.doi.org/10.1108/jdqs-03-2018-b0001.

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In this study, we assume that stock prices follow piecewise geometric Brownian motion, a variant of geometric Brownian motion except the ex-dividend date, and find pricing formulas of American call options. While piecewise geometric Brownian motion can effectively incorporate discrete dividends into stock prices without losing consistency, the process results in the lack of closed-form solutions for option prices. We aim to resolve this by providing analytical approximation formulas for American call option prices under this process. Our work differs from other studies using the same assumption in at least three respects. First, we investigate the analytical approximations of American call options and examine European call options as a special case, while most analytical approximations in the literature cover only European options. Second, we provide both the upper and the lower bounds of option prices. Third, our solutions are equal to the exact price when the size of the dividend is proportional to the stock price, while binomial tree results never match the exact option price in any circumstance. The numerical analysis therefore demonstrates the efficiency of our method. Especially, the lower bound formula is accurate, and it can be further improved by considering second order approximations although it requires more computing time.

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30

Kim, Young Shin. "Sample Path Generation of the Stochastic Volatility CGMY Process and Its Application to Path-Dependent Option Pricing." Journal of Risk and Financial Management 14, no. 2 (February 15, 2021): 77. http://dx.doi.org/10.3390/jrfm14020077.

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This paper proposes the sample path generation method for the stochastic volatility version of the CGMY process. We present the Monte-Carlo method for European and American option pricing with the sample path generation and calibrate model parameters to the American style S&P 100 index options market, using the least square regression method. Moreover, we discuss path-dependent options, such as Asian and Barrier options.

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31

Simozar, Saied. "Near Exact Calculation of American Options." Applied Economics and Finance 7, no. 3 (March 18, 2020): 55. http://dx.doi.org/10.11114/aef.v7i3.4681.

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A new practical approach for the analysis of American (bond) options is developed which is a combination of the closed form solutions and binomial lattice models. The model is calibrated to the observed term structure of rates and traded volatilities and is arbitrage free. The convergence is very fast, but numerically intensive. By extrapolation the near exact premium of an American (bond) option can be calculated.

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32

Deng, Dongya, and Cuiye Peng. "New Methods with Capped Options for Pricing American Options." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/176306.

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We propose two new methods: improved binomial methods and improved least square MonteCarlo methods (LSM), for pricing American options. These two methods are developed using the nice capped options which have closed-form formulas. Numerical examples are provided to verify that these two new methods are pretty efficient.

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33

Shoude, Huang, and Xunxiang Guo. "A Shannon Wavelet Method for Pricing American Options under Two-Factor Stochastic Volatilities and Stochastic Interest Rate." Discrete Dynamics in Nature and Society 2020 (April 9, 2020): 1–8. http://dx.doi.org/10.1155/2020/8531959.

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In the paper, the pricing of the American put options under the double Heston model with Cox–Ingersoll–Ross (CIR) interest rate process is studied. The characteristic function of the log asset price is derived, and thereby Bermuda options are well evaluated by means of a state-of-the-art Shannon wavelet inverse Fourier technique (SWIFT), which is a robust and highly efficient pricing method. Based on the SWIFT method, the price of American option can be approximated by using Richardson extrapolation schemes on a series of Bermudan options. Numerical experiments show that the proposed pricing method is efficient, especially for short-term American put options.

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34

Whaley, Robert E. "On Valuing American Futures Options." Financial Analysts Journal 42, no. 3 (May 1986): 49–59. http://dx.doi.org/10.2469/faj.v42.n3.49.

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35

Zaevski, Tsvetelin S. "Pricing discounted American capped options." Chaos, Solitons & Fractals 156 (March 2022): 111833. http://dx.doi.org/10.1016/j.chaos.2022.111833.

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36

Chockalingam, Arun, and Kumar Muthuraman. "American Options Under Stochastic Volatility." Operations Research 59, no. 4 (August 2011): 793–809. http://dx.doi.org/10.1287/opre.1110.0945.

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37

Xing, Xiaoyu, and Hailiang Yang. "American type geometric step options." Journal of Industrial & Management Optimization 9, no. 3 (2013): 549–60. http://dx.doi.org/10.3934/jimo.2013.9.549.

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38

BUFFINGTON, JOHN, and ROBERT J. ELLIOTT. "AMERICAN OPTIONS WITH REGIME SWITCHING." International Journal of Theoretical and Applied Finance 05, no. 05 (August 2002): 497–514. http://dx.doi.org/10.1142/s0219024902001523.

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A Black-Scholes market is considered in which the underlying economy, as modeled by the parameters and volatility of the processes, switches between a finite number of states. The switching is modeled by a hidden Markov chain. European options are priced and a Black-Scholes equation obtained. The approximate valuation of American options due to Barone-Adesi and Whaley is extended to this setting.

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39

Mallier, Roland, and Ghada Alobaidi. "Laplace transforms and American options." Applied Mathematical Finance 7, no. 4 (December 2000): 241–56. http://dx.doi.org/10.1080/13504860110060384.

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40

Smith, Adam T. "American options under uncertain volatility." Applied Mathematical Finance 9, no. 2 (June 2002): 123–41. http://dx.doi.org/10.1080/13504860210136730.

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41

Montero, Miquel. "Perpetual American options within CTRWs." Physica A: Statistical Mechanics and its Applications 387, no. 15 (June 2008): 3936–41. http://dx.doi.org/10.1016/j.physa.2008.01.054.

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42

Paxson, Dean A. "Sequential American Exchange Property Options." Journal of Real Estate Finance and Economics 34, no. 1 (March 6, 2007): 135–57. http://dx.doi.org/10.1007/s11146-007-9003-4.

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43

Cheng, Jun, and Jin E. Zhang. "Analytical pricing of American options." Review of Derivatives Research 15, no. 2 (January 17, 2012): 157–92. http://dx.doi.org/10.1007/s11147-011-9073-6.

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44

Dai, Min, and Yue Kuen Kwok. "American Options with Lookback Payoff." SIAM Journal on Applied Mathematics 66, no. 1 (January 2005): 206–27. http://dx.doi.org/10.1137/s0036139903437345.

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45

Achdou, Yves, Govindaraj Indragoby, and Olivier Pironneau. "Volatility calibration with American options." Methods and Applications of Analysis 11, no. 4 (2004): 533–56. http://dx.doi.org/10.4310/maa.2004.v11.n4.a6.

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46

Kourtis, Apostolos, and Raphael N. Markellos. "Traded American options are Bermudan." Managerial Finance 37, no. 11 (September 27, 2011): 978–84. http://dx.doi.org/10.1108/03074351111167884.

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47

Pun, Chi Seng, and Hoi Ying Wong. "CEV asymptotics of American options." Journal of Mathematical Analysis and Applications 403, no. 2 (July 2013): 451–63. http://dx.doi.org/10.1016/j.jmaa.2013.02.036.

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48

Rakic, Biljana, and Tamara Radjenovic. "Real options methodology in public-private partnership projects valuation." Ekonomski anali 59, no. 200 (2014): 91–113. http://dx.doi.org/10.2298/eka1400091r.

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PPP offers numerous benefits to both public and private partners in delivery of infrastructure projects. However this partnership also involves great risks which have to be adequately managed and mitigated. Private partners are especially sensitive to revenue risk, since they are mostly interested in the financial viability of the project. Thus they often expect public partners to provide some kind of risk-sharing mechanism in the form of Minimum Revenue Guarantees or abandonment options. The objective of this paper is to investigate whether the real option of abandoning the project increases its value. Therefore the binominal option pricing model and risk-neutral probability approach have been implemented to price the European and American abandonment options for the Build-Operate-Transfer (BOT) toll road investment. The obtained results suggest that the project value with the American abandonment option is greater than with the European abandonment option, hence implying that American options offer greater flexibility and are more valuable for private partners.

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49

Yu, Xisheng, and Li Yang. "Pricing American Options Using a Nonparametric Entropy Approach." Discrete Dynamics in Nature and Society 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/369795.

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This paper studies the pricing problem of American options using a nonparametric entropy approach. First, we derive a general expression for recovering the risk-neutral moments of underlying asset return and then incorporate them into the maximum entropy framework as constraints. Second, by solving this constrained entropy problem, we obtain a discrete risk-neutral (martingale) distribution as the unique pricing measure. Third, the optimal exercise strategies are achieved via the least-squares Monte Carlo algorithm and consequently the pricing algorithm of American options is obtained. Finally, we conduct the comparative analysis based on simulations and IBM option contracts. The results demonstrate that this nonparametric entropy approach yields reasonably accurate prices for American options and produces smaller pricing errors compared to other competing methods.

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Li, Shuang, Yanli Zhou, Xinfeng Ruan, and B. Wiwatanapataphee. "Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/236091.

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Abstract:

We study the pricing of American options in an incomplete market in which the dynamics of the underlying risky asset is driven by a jump diffusion process with stochastic volatility. By employing a risk-minimization criterion, we obtain the Radon-Nikodym derivative for the minimal martingale measure and consequently a linear complementarity problem (LCP) for American option price. An iterative method is then established to solve the LCP problem for American put option price. Our numerical results show that the model and numerical scheme are robust in capturing the feature of incomplete finance market, particularly the influence of market volatility on the price of American options.

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