Academic literature on the topic 'Options (Finance) – Valuation – Mathematical models'
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Journal articles on the topic "Options (Finance) – Valuation – Mathematical models"
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Loerx, Andre, and Ekkehard W. Sachs. "Model Calibration in Option Pricing." Sultan Qaboos University Journal for Science [SQUJS] 16 (April 1, 2012): 84. http://dx.doi.org/10.24200/squjs.vol17iss1pp84-102.
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We consider calibration problems for models of pricing derivatives which occur in mathematical finance. We discuss various approaches such as using stochastic differential equations or partial differential equations for the modeling process. We discuss the development in the past literature and give an outlook into modern approaches of modelling. Furthermore, we address important numerical issues in the valuation of options and likewise the calibration of these models. This leads to interesting problems in optimization, where, e.g., the use of adjoint equations or the choice of the parametrization for the model parameters play an important role.
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HUEHNE, FLORIAN. "DEFAULTABLE LÉVY LIBOR RATES AND CREDIT DERIVATIVES." International Journal of Theoretical and Applied Finance 10, no. 03 (May 2007): 407–35. http://dx.doi.org/10.1142/s0219024907004172.
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We introduce the intensity-based defaultable Lévy Libor model, which generalizes the default-free Lévy Libor model introduced by Eberlein and Özkan in [The defaultable Lévy term structure: Ratings and restructuring, Mathematical Finance13(2) (2003) 277–300], and the intensity-based defaultable model presented by Bielecki and Rutkowski in [Credit Risk: Modeling, Valuation and Hedging, Springer Finance (Springer-Verlag, 2002)] by embedding it in the defaultable HJM framework introduced by Eberlein and Özkan in [The defaultable Lévy term structure: Ratings and restructuring, Mathematical Finance13(2) (2003) 277–300]. We also derive some additional results for defaultable HJM models such as the dynamics of credit spreads. We then go on and model the default-free Libor rates and credit spreads as the primal variable and derive the dynamics of the defaultable Libor rates under the defaultable forward measure. Finally, we derive an explicit formula for options on credit default swaps, using an idea introduced by Raible in [Lévy Processes in finance: Theory, numerics and empirical facts, PhD thesis, University of Freiburg i. Brsg. (2000)].
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Giribone, Pier Giuseppe, and Roberto Revetria. "Certificate pricing using Discrete Event Simulations and System Dynamics theory." Risk Management Magazine 16, no. 2 (August 18, 2021): 75–93. http://dx.doi.org/10.47473/2020rmm0092.
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The study proposes an innovative application of Discrete Event Simulations (DES) and System Dynamics (SD) theory to the pricing of a certain kind of certificates very popular among private investors and, more generally, in the context of wealth management. The paper shows how numerical simulation software mainly used in traditional engineering, such as industrial and mechanical engineering, can be successfully adapted to the risk analysis of structured financial products. The article can be divided into three macro-sections: in the first part a synthetic overview of the most widespread option pricing models in the quantitative finance branch is given to the readers together with the fundamental technical-instrumental background of the implemented DES and SD simulator. After dealing with some of the most popular models adopted for Equity and Equity index options, which are the most common underlying assets for the certificates structuring, we move, in the second part, to describe how the mathematical models can be integrated into a general simulation environment able to provide both DES and SD extensively used in the engineering field. The core stochastic differential equation (SDE) will therefore be translated, together with all its input parameters, into a visual block model which allows an immediate quantitative analysis of how market parameters and the other model variables can change over time. The possibility for the structurer to observe how the variables evolve day-by-day gives a strong sensitivity to evaluate how the price and the associated risk measures can be directly affected. The third part of the study compares the results obtained from the simulator designed by the authors with the more traditional pricing approaches, which consist in programming Matlab® codes for the numerical integration of the core stochastic dynamics through a Euler-Maruyama scheme. The comparison includes a price check using the Bloomberg® DLIB pricing module and a check directly against the valuation provided by the counterparty. In this section, real market cases will therefore be examined with a complete quantitative analysis of two of the most widespread categories of certificates in wealth management: Multi-asset Barrier Reverse Convertible with Issuer Callability and Multi-asset Express Certificate with conditional memory fixed coupon.
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LORENZO, MERCURI. "PRICING ASIAN OPTIONS IN AFFINE GARCH MODELS." International Journal of Theoretical and Applied Finance 14, no. 02 (March 2011): 313–33. http://dx.doi.org/10.1142/s0219024911006371.
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We derive recursive relationships for the m.g.f. of the geometric average of the underlying within some affine Garch models [Heston and Nandi (2000), Christoffersen et al. (2006), Bellini and Mercuri (2007), Mercuri (2008)] and use them for the semi-analytical valuation of geometric Asian options. Similar relationships are obtained for low order moments of the arithmetic average, that are used for an approximated valuation of arithmetic Asian options based on truncated Edgeworth expansions, following the approach of Turnbull and Wakeman (1991). In both cases the accuracy of the semi-analytical procedure is assessed by means of a comparison with Monte Carlo prices. The results are quite good in the geometric case, while in the arithmetic case the proposed methodology seems to work well only in the Heston and Nandi case.
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CHU, CHI CHIU, and YUE KUEN KWOK. "VALUATION OF GUARANTEED ANNUITY OPTIONS IN AFFINE TERM STRUCTURE MODELS." International Journal of Theoretical and Applied Finance 10, no. 02 (March 2007): 363–87. http://dx.doi.org/10.1142/s0219024907004160.
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We propose three analytic approximation methods for numerical valuation of the guaranteed annuity options in deferred annuity pension policies. The approximation methods include the stochastic duration approach, Edgeworth expansion, and analytic approximation in affine diffusions. The payoff structure in the annuity policies is similar to a quanto call option written on a coupon-bearing bond. To circumvent the limitations of the one-factor interest rate model, we model the interest rate dynamics by a two-factor affine interest rate term structure model. The numerical accuracy and the computational efficiency of these approximation methods are analyzed. We also investigate the value sensitivity of the guaranteed annuity option with respect to different parameters in the pricing model.
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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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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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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 a way to plan for their future. The article provides a brief presentation of options. It also describes one of their pricing methods. Light of the foregoing has been hypothesized that 'valuation of options using mathematical calculators using the binomial model is an effective tool for supporting management positions in futures instruments’.
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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 supercash option is introduced and some payment schemes are also presented.
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ZEGHAL, AMINA BOUZGUENDA, and MOHAMED MNIF. "OPTIMAL MULTIPLE STOPPING AND VALUATION OF SWING OPTIONS IN LÉVY MODELS." International Journal of Theoretical and Applied Finance 09, no. 08 (December 2006): 1267–97. http://dx.doi.org/10.1142/s0219024906004037.
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In this paper, we extend the results of Carmona and Touzi [6] for an optimal multiple stopping problem to a market where the price process is allowed to jump. We also generalize the problem of valuation swing options to the context of a Lévy market. We prove the existence of multiple exercise policies under an additional condition on Snell envelops. This condition emerges naturally in the case of Lévy processes. Then, we give a constructive solution for perpetual put swing options when the price process has no negative jumps. We use the Monte Carlo approximation method based on Malliavin calculus in order to solve the finite horizon case. Numerical results are given in the last two sections. We illustrate the theoretical results of the perpetual case and give the numerical solution for the finite horizon case.
Dissertations / Theses on the topic "Options (Finance) – Valuation – Mathematical models"
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Mimouni, Karim. "Three essays on volatility specification in option valuation." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103274.
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Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the empirical shortcomings of this model. In the first essay, we investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources. We first use realized volatilities to assess the properties of the SQR model and to guide us in the search for alternative specifications. We then estimate the models using maximum likelihood on a long sample of S& P500 returns. Finally, we employ nonlinear least squares on a time series of cross sections of option data. In the estimations on returns and options data, we use the particle filtering technique to retrieve the spot volatility path. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. Overall, the best of alternative volatility specifications is a model we refer to as the VAR model, which is of the GARCH diffusion type.<br>In the second essay, we estimate the Constant Elasticity of Variance (CEV) model in order to study the level of nonlinearity in the volatility dynamic. We also estimate a CEV process combined with a jump process (CEVJ) and analyze the effects of the jump component on the nonlinearity coefficient. Estimation is performed using the particle filtering technique on a long series of S&P500 returns and on options data. We find that both returns data and returns-and-options data favor nonlinear specifications for the volatility dynamic, suggesting that the extensive use of linear models is not supported empirically. We also find that the inclusion of jumps does not affect the level of nonlinearity and does not improve the CEV model fit.<br>The third essay provides an empirical comparison of two classes of option valuation models: continuous-time models and discrete-time models. The literature provides some theoretical limit results for these types of dynamics, and researchers have used these limit results to argue that the performance of certain discrete-time and continuous-time models ought to be very similar. This interpretation is somewhat contentious, because a given discrete-time model can have several continuous-time limits, and a given continuous-time model can be the limit for more than one discrete-time model. Therefore, it is imperative to investigate whether there exist similarities between these specifications from an empirical perspective. Using data on S&P500 returns and call options, we find that the discrete-time models investigated in this paper have the same performance in fitting the data as selected continuous-time models both in and out-of-sample.
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Dharmawan, Komang School of Mathematics UNSW. "Superreplication method for multi-asset barrier options." Awarded by:University of New South Wales. School of Mathematics, 2005. http://handle.unsw.edu.au/1959.4/30169.
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The aim of this thesis is to study multi-asset barrier options, where the volatilities of the stocks are assumed to define a matrix-valued bounded stochastic process. The bounds on volatilities may represent, for instance, the extreme values of the volatilities of traded options. As the volatilities are not known exactly, the value of the option can not be determined. Nevertheless, it is possible to calculate extreme values. We show that these values correspond to the best and the worst case scenarios of the future volatilities for short positions and long positions in the portfolio of the options. Our main tool is the equivalence of the option pricing and a certain stochastic control problem and the resulting concept of superhedging. This concept has been well known for some time but never applied to barrier options. First, we prove the dynamic programming principle (DPP) for the control problem. Next, using rather standard arguments we derive the Hamilton-Jacobi-Bellman equation for the value function. We show that the value function is a unique viscosity solution of the Hamilton-Jacobi-Bellman equation. Then we define the super price and superhedging strategy for the barrier options and show equivalence with the control problem studied above. The superprice price can be found by solving the nonlinear Hamilton-Jacobi-Equation studied above. It is called sometimes the Black-Scholes-Barenblatt (BSB) equation. This is the Hamilton-Jacobi-Bellman equation of the exit control problem. The sup term in the BSB equation is determined dynamically: it is either the upper bound or the lower bound of the volatility matrix, according to the convexity or concavity of the value function with respect to the stock prices. By utilizing a probabilistic approach, we show that the value function of the exit control problem is continuous. Then, we also obtain bounds for the first derivative of the value function with respect to the space variable. This derivative has an important financial interpretation. Namely, it allows us to define the superhedging strategy. We include an example: pricing and hedging of a single-asset barrier option and its numerical solution using the finite difference method.
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Wang, Yintian 1976. "Three essays on volatility long memory and European option valuation." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=102851.
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This dissertation is in the form of three essays on the topic of component and long memory GARCH models. The unifying feature of the thesis is the focus on investigating European index option evaluation using these models.<br>The first essay presents a new model for the valuation of European options. In this model, the volatility of returns consists of two components. One of these components is a long-run component that can be modeled as fully persistent. The other component is short-run and has zero mean. The model can be viewed as an affine version of Engle and Lee (1999), allowing for easy valuation of European options. The model substantially outperforms a benchmark single-component volatility model that is well established in the literature. It also fits options better than a model that combines conditional heteroskedasticity and Poisson normal jumps. While the improvement in the component model's performance is partly due to its improved ability to capture the structure of the smirk and the path of spot volatility, its most distinctive feature is its ability to model the term structure. This feature enables the component model to jointly model long-maturity and short-maturity options.<br>The second essay derives two new GARCH variance component models with non-normal innovations. One of these models has an affine structure and leads to a closed-form option valuation formula. The other model has a non-affine structure and hence, option valuation is carried out using Monte Carlo simulation. We provide an empirical comparison of these two new component models and the respective special cases with normal innovations. We also compare the four component models against GARCH(1,1) models which they nest. All eight models are estimated using MLE on S&P500 returns. The likelihood criterion strongly favors the component models as well as non-normal innovations. The properties of the non-affine models differ significantly from those of the affine models. Evaluating the performance of component variance specifications for option valuation using parameter estimates from returns data also provides strong support for component models. However, support for non-normal innovations and non-affine structure is less convincing for option valuation.<br>The third essay aims to investigate the impact of long memory in volatility on European option valuation. We mainly compare two groups of GARCH models that allow for long memory in volatility. They are the component Heston-Nandi GARCH model developed in the first essay, in which the volatility of returns consists of a long-run and a short-run component, and a fractionally integrated Heston-Nandi GARCH (FIHNGARCH) model based on Bollerslev and Mikkelsen (1999). We investigate the performance of the models using S&P500 index returns and cross-sections of European options data. The component GARCH model slightly outperforms the FIGARCH in fitting return data but significantly dominates the FIHNGARCH in capturing option prices. The findings are mainly due to the shorter memory of the FIHNGARCH model, which may be attributed to an artificially prolonged leverage effect that results from fractional integration and the limitations of the affine structure.
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Endekovski, Jessica. "Pricing multi-asset options in exponential levy models." Master's thesis, Faculty of Commerce, 2019. http://hdl.handle.net/11427/31437.
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This dissertation looks at implementing exponential Levy models whereby the un- ´ derlyings are driven by Levy processes, which are able to account for stylised facts ´ that traditional models do not, in order to price basket options more efficiently. In particular, two exponential Levy models are implemented and tested: the multi- ´ variate Variance Gamma (VG) model and the multivariate normal inverse Gaussian (NIG) model. Both models are calibrated to real market data and then used to price basket options, where the underlyings are the constituents of the KBW Bank Index. Two pricing methods are also compared: a closed-form (analytical) approximation of the price, derived by Linders and Stassen (2016) and the standard Monte Carlo method. The convergence of the analytical approximation to Monte Carlo prices was found to improve as the time to maturity of the option increased. In comparison to real market data, the multivariate NIG model was able to fit the data more accurately for shorter maturities and the multivariate VG model for longer maturities. However, when looking at Monte Carlo prices, the multivariate VG model was found to outperform the results of the multivariate NIG model, as it was able to converge to Monte Carlo prices to a greater degree.
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Glover, Elistan Nicholas. "Analytic pricing of American put options." Thesis, Rhodes University, 2009. http://hdl.handle.net/10962/d1002804.
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American options are the most commonly traded financial derivatives in the market. Pricing these options fairly, so as to avoid arbitrage, is of paramount importance. Closed form solutions for American put options cannot be utilised in practice and so numerical techniques are employed. This thesis looks at the work done by other researchers to find an analytic solution to the American put option pricing problem and suggests a practical method, that uses Monte Carlo simulation, to approximate the American put option price. The theory behind option pricing is first discussed using a discrete model. Once the concepts of arbitrage-free pricing and hedging have been dealt with, this model is extended to a continuous-time setting. Martingale theory is introduced to put the option pricing theory in a more formal framework. The construction of a hedging portfolio is discussed in detail and it is shown how financial derivatives are priced according to a unique riskneutral probability measure. Black-Scholes model is discussed and utilised to find closed form solutions to European style options. American options are discussed in detail and it is shown that under certain conditions, American style options can be solved according to closed form solutions. Various numerical techniques are presented to approximate the true American put option price. Chief among these methods is the Richardson extrapolation on a sequence of Bermudan options method that was developed by Geske and Johnson. This model is extended to a Repeated-Richardson extrapolation technique. Finally, a Monte Carlo simulation is used to approximate Bermudan put options. These values are then extrapolated to approximate the price of an American put option. The use of extrapolation techniques was hampered by the presence of non-uniform convergence of the Bermudan put option sequence. When convergence was uniform, the approximations were accurate up to a few cents difference.
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Song, Na, and 宋娜. "Mathematical models and numerical algorithms for option pricing and optimal trading." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50662168.
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Research conducted in mathematical finance focuses on the quantitative modeling of financial markets. It allows one to solve financial problems by using mathematical methods and provides understanding and prediction of the complicated financial behaviors. In this thesis, efforts are devoted to derive and extend stochastic optimization models in financial economics and establish practical algorithms for representing and solving problems in mathematical finance.
An option gives the holder the right, but not the obligation, to buy or sell an underlying asset at a specified strike price on or before a specified date. In this thesis, a valuation model for a perpetual convertible bond is developed when the price dynamics of the underlying share are governed by Markovian regime-switching models. By making use of the relationship between the convertible bond and an American option, the valuation of a perpetual convertible bond can be transformed into an optimal stopping problem. A novel approach is also proposed to discuss an optimal inventory level of a retail product from a real option perspective in this thesis. The expected present value of the net profit from selling the product which is the objective function of the optimal inventory problem can be given by the actuarial value of a real option. Hence, option pricing techniques are adopted to solve the optimal inventory problem in this thesis.
The goal of risk management is to eliminate or minimize the level of risk associated with a business operation. In the risk measurement literature, there is relatively little amount of work focusing on the risk measurement and management of interest rate instruments. This thesis concerns about building a risk measurement framework based on some modern risk measures, such as Value-at-Risk (VaR) and Expected Shortfall (ES), for describing and quantifying the risk of interest rate sensitive instruments. From the lessons of the recent financial turmoils, it is understood that maximizing profits is not the only objective that needs to be taken into account. The consideration for risk control is of primal importance. Hence, an optimal submission problem of bid and ask quotes in the presence of risk constraints is studied in this thesis. The optimal submission problem of bid and ask quotes is formulated as a stochastic optimal control problem.
Portfolio management is a professional management of various securities and assets in order to match investment objectives and balance risk against performance. Different choices of time series models for asset price may lead to different portfolio management strategies. In this thesis, a discrete-time dynamic programming approach which is flexible enough to deal with the optimal asset allocation problem under a general stochastic dynamical system is explored. It’s also interesting to analyze the implications of the heteroscedastic effect described by a continuous-time stochastic volatility model for evaluating risk of a cash management problem. In this thesis, a continuous-time dynamic programming approach is employed to investigate the cash management problem under stochastic volatility model and constant volatility model respectively.<br>published_or_final_version<br>Mathematics<br>Doctoral<br>Doctor of Philosophy
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Lee, Mou Chin. "An empirical test of variance gamma options pricing model on Hang Seng index options." HKBU Institutional Repository, 2000. http://repository.hkbu.edu.hk/etd_ra/263.
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Zhao, Jing Ya. "Numerical methods for pricing Bermudan barrier options." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2592939.
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Cisneros-Molina, Myriam. "Mathematical methods for valuation and risk assessment of investment projects and real options." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491350.
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In this thesis, we study the problems of risk measurement, valuation and hedging of financial positions in incomplete markets when an insufficient number of assets are available for investment (real options). We work closely with three measures of risk: Worst-Case Scenario (WCS) (the supremum of expected values over a set of given probability measures), Value-at-Risk (VaR) and Average Value-at-Risk (AVaR), and analyse the problem of hedging derivative securities depending on a non-traded asset, defined in terms of the risk measures via their acceptance sets. The hedging problem associated to VaR is the problem of minimising the expected shortfall. For WCS, the hedging problem turns out to be a robust version of minimising the expected shortfall; and as AVaR can be seen as a particular case of WCS, its hedging problem is also related to the minimisation of expected shortfall. Under some sufficient conditions, we solve explicitly the minimal expected shortfall problem in a discrete-time setting of two assets driven by correlated binomial models. In the continuous-time case, we analyse the problem of measuring risk by WCS, VaR and AVaR on positions modelled as Markov diffusion processes and develop some results on transformations of Markov processes to apply to the risk measurement of derivative securities. In all cases, we characterise the risk of a position as the solution of a partial differential equation of second order with boundary conditions. In relation to the valuation and hedging of derivative securities, and in the search for explicit solutions, we analyse a variant of the robust version of the expected shortfall hedging problem. Instead of taking the loss function $l(x) = [x]^+$ we work with the strictly increasing, strictly convex function $L_{\epsilon}(x) = \epsilon \log \left( \frac{1+exp\{−x/\epsilon\} }{ exp\{−x/\epsilon\} } \right)$. Clearly $lim_{\epsilon \rightarrow 0} L_{\epsilon}(x) = l(x)$. The reformulation to the problem for L_{\epsilon}(x) also allow us to use directly the dual theory under robust preferences recently developed in [82]. Due to the fact that the function $L_{\epsilon}(x)$ is not separable in its variables, we are not able to solve explicitly, but instead, we use a power series approximation in the dual variables. It turns out that the approximated solution corresponds to the robust version of a utility maximisation problem with exponential preferences $(U(x) = −\frac{1}{\gamma}e^{-\gamma x})$ for a preferenes parameter $\gamma = 1/\epsilon$. For the approximated problem, we analyse the cases with and without random endowment, and obtain an expression for the utility indifference bid price of a derivative security which depends only on the non-traded asset.
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Welihockyj, Alexander. "The cost of using misspecified models to exercise and hedge American options on coupon bearing bonds." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/20532.
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This dissertation investigates the cost of using single-factor models to exercise and hedge American options on South African coupon bearing bonds, when the simulated market term structure is driven by a two-factor model. Even if the single factor models are re-calibrated on a daily basis to the term structure, we find that the exercise and hedge strategies can be suboptimal and incur large losses. There is a vast body of research suggesting that real market term structures are in actual fact driven by multiple factors, so suboptimal losses can be largely reduced by simply employing a well-specified multi-factor model.
Books on the topic "Options (Finance) – Valuation – Mathematical models"
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Gibson, Rajna. Option valuation: Analyzing and pricing standardized option contracts. Genève: Georg, 1988.
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Option valuation: Analyzing and pricing standardized option contracts. New York: McGraw-Hill, 1991.
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Option valuation: An introduction to financial mathematics. Boca Raton: Taylor & Francis, 2012.
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Option valuation in the presence of market imperfections. Frankfurt am Main: P. Lang, 1993.
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An introduction to financial option valuation: Mathematics, stochastics, and computation. New York: Cambridge University Press, 2004.
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1957-, Srivastava Sanjay, ed. Option valuation and Option tutor. Cincinnati, Ohio: South-Western College, 1995.
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John, O'Brien. Investments: A visual approach. Cincinnati, Ohio: South-Western Pub, 1995.
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Real options valuation: The importance of interest rate modelling in theory and practice. 2nd ed. Heidelberg: Springer, 2010.
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Beliefs-preferences gauge symmetry group and replication of contingent claims in a general market environment. Research Triangle Park, NC: IES Press, 1998.
Find full textBook chapters on the topic "Options (Finance) – Valuation – Mathematical models"
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Eberlein, Ernst, Kathrin Glau, and Antonis Papapantoleon. "Analyticity of the Wiener–Hopf Factors and Valuation of Exotic Options in Lévy Models." In Advanced Mathematical Methods for Finance, 223–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18412-3_8.
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Bordag, Ljudmila A. "On Option-Valuation in Illiquid Markets: Invariant Solutions to a Nonlinear Model." In Mathematical Control Theory and Finance, 71–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-69532-5_5.
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Biancardi, Marta, and Giovanni Villani. "A Robustness Analysis of Least-Squares Monte Carlo for R&D Real Options Valuation." In Mathematical and Statistical Methods for Actuarial Sciences and Finance, 27–30. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05014-0_6.
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Smit, Han, and Thras Moraitis. "Option Games Valuation." In Playing at Acquisitions. Princeton University Press, 2015. http://dx.doi.org/10.23943/princeton/9780691140001.003.0006.
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Valuing uncertainty in strategy requires the development of quantitative models reflecting the conceptual options games view on strategy. The application of fresh ideas based on two major strands in the existing literature—real options and game theory—has attracted increased interest, both to academia and to acquisition strategy practitioners. Despite the mathematical elegance of option game models, the key metrics and tools for implementation have not yet been fully developed, especially with regard to providing relevant managerial guidance. This chapter presents an in-depth examination of Xstrata's Falconbridge acquisition through option and game lenses in order to provide insights into the implementation of these new and effective quantitative real option models in practice, as well as pointing out their limitations.
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Davis, Mark H. A. "3. The classical theory of option pricing." In Mathematical Finance: A Very Short Introduction, 30–60. Oxford University Press, 2019. http://dx.doi.org/10.1093/actrade/9780198787945.003.0003.
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‘The classical theory of option pricing’ explains the theory of arbitrage pricing, which is closely related to the Dutch Book Arguments, but which brings in a new factor: prices in financial markets evolve over time and participants are able to trade at any time, instead of just taking bets and awaiting the result. In addition to the general theory, pricing models and methods have been developed for specific markets—foreign exchange, interest rates, and credit. The binomial and continuous-time mathematical models for stock prices are introduced along with the Black–Scholes formula, the volatility surface, the difference between European and American options, and the Fundamental Theorem of Asset Pricing.