Relevant bibliographies by topics / Options (Finance) Australia Mathematical models

Academic literature on the topic 'Options (Finance) Australia Mathematical models'

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Published: 10 December 2022
Last updated: 29 January 2023

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Journal articles on the topic "Options (Finance) Australia Mathematical models"

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CARMONA, RENÉ, and SERGEY NADTOCHIY. "TANGENT MODELS AS A MATHEMATICAL FRAMEWORK FOR DYNAMIC CALIBRATION." International Journal of Theoretical and Applied Finance 14, no. 01 (February 2011): 107–35. http://dx.doi.org/10.1142/s0219024911006280.

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Motivated by the desire to integrate repeated calibration procedures into a single dynamic market model, we introduce the notion of a "tangent model" in an abstract set up, and we show that this new mathematical paradigm accommodates all the recent attempts to study consistency and absence of arbitrage in market models. For the sake of illustration, we concentrate on the case when market quotes provide the prices of European call options for a specific set of strikes and maturities. While reviewing our recent results on dynamic local volatility and tangent Lévy models, we present a theory of tangent models unifying these two approaches and construct a new class of tangent Lévy models, which allows the underlying to have both continuous and pure jump components.
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Dubey, Rajesh P., S. Samarawickrama, P. P. Gunaratna, L. Halgahawatta, K. P. P. Pathirana, K. Raveenthiran, K. Subasingha, Bitanjaya Das, and T. A. N. Sugandika. "Mathematical Model Studies for River Regulatory Measures for the Improvement of Draft in Hoogly Estuary, India." International Journal of Engineering and Technologies 2 (October 1, 2014): 1–12. http://dx.doi.org/10.56431/p-740099.

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The Haldia port is situated in the Hooghly estuary, 104 km downstream of Kolkata Port. As a result of high sedimentation, the navigational channel to the Haldia Port is maintained with great amount of dredging (25 MCM per Annum). The paper presents a study carried out to find a solution to improve the channel depth together with minimum maintenance dredging. A desk study was carried out to identify the historical formation of the estuary and the remedial measures implemented in the past. A detailed field investigation was carried out to obtain the relevant data for the calibration of numerical models. 1D (MIKE 11) river hydrodynamic modelling was carried out using the available bathymetric data to supply upstream boundary conditions for the 2D (MIKE 21) and 3D (MIKE 3) numerical models. Number of possible scenarios were tested through MIKE 21 hydrodynamic modelling to select more feasible options. Selected options were further assessed through morphodynamic and 3D hydrodynamic modelling to examine the long term sustainability of the proposed solutions. Finally, the option which comprise of; approach channel through Balari Passage & closure of the Shore Attached Channel was selected as the best option. The selected option was further studied taking navigational aspects, dredging efforts and construction sequence into consideration.
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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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Fernández, Lexuri, Peter Hieber, and Matthias Scherer. "Double-barrier first-passage times of jump-diffusion processes." mcma 19, no. 2 (July 1, 2013): 107–41. http://dx.doi.org/10.1515/mcma-2013-0005.

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Abstract. Required in a wide range of applications in, e.g., finance, engineering, and physics, first-passage time problems have attracted considerable interest over the past decades. Since analytical solutions often do not exist, one strand of research focuses on fast and accurate numerical techniques. In this paper, we present an efficient and unbiased Monte-Carlo simulation to obtain double-barrier first-passage time probabilities of a jump-diffusion process with arbitrary jump size distribution; extending single-barrier results by [Journal of Derivatives 10 (2002), 43–54]. In mathematical finance, the double-barrier first-passage time is required to price exotic derivatives, for example corridor bonus certificates, (step) double barrier options, or digital first-touch options, that depend on whether or not the underlying asset price exceeds certain threshold levels. Furthermore, it is relevant in structural credit risk models if one considers two exit events, e.g., default and early repayment.
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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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Gardini, Matteo, Piergiacomo Sabino, and Emanuela Sasso. "Correlating Lévy processes with self-decomposability: applications to energy markets." Decisions in Economics and Finance 44, no. 2 (October 8, 2021): 1253–80. http://dx.doi.org/10.1007/s10203-021-00352-9.

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AbstractBased on the concept of self-decomposability, we extend some recent multidimensional Lévy models built using multivariate subordination. Our aim is to construct multivariate Lévy processes that can model the propagation of the systematic risk in dependent markets with some stochastic delay instead of affecting all the markets at the same time. To this end, we extend some known approaches keeping their mathematical tractability, study the properties of the new processes, derive closed-form expressions for their characteristic functions and detail how Monte Carlo schemes can be implemented. We illustrate the applicability of our approach in the context of gas, power and emission markets focusing on the calibration and on the pricing of spread options written on different underlying commodities.
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Abraham, Rebecca, and Hani El-Chaarani. "A Mathematical Formulation of the Valuation of Ether and Ether Derivatives as a Function of Investor Sentiment and Price Jumps." Journal of Risk and Financial Management 15, no. 12 (December 8, 2022): 591. http://dx.doi.org/10.3390/jrfm15120591.

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The purpose of this study was to create quantitative models to value ether, ether futures, and ether options based upon the ability of cryptocurrencies to transform existing intermediary-verified payments to non-intermediary-based currency transfers, the ability of ether as a late mover to displace bitcoin as the first mover, and the valuation of ether in the context of investor irrationality models. The risk-averse investor’s utility function is a combination of expectations of the performance of ether, expectations of cryptocurrencies’ transformative power, and expectations of ether superseding bitcoin. The moderate risk-taker’s utility function is an alt-Weibull distribution, along with a gamma distribution. Risk-takers have a utility function in the form of a Bessel function. Ether price functions consist of a Levy jump process. Ether futures are valued as the combination of current spot prices along with term prices. The value of spot prices is the product of a spot premium and a lognormal distribution of spot prices. The value of term prices is equal to the product of a term premium, and the Levy jump process of price fluctuations during the delivery period. For ether options, a less risky ether option portfolio offsets ether’s risk by a fixed-income trading strategy.
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Eissa, Mahmoud A., and M. Elsayed. "Improve Stock Price Model-Based Stochastic Pantograph Differential Equation." Symmetry 14, no. 7 (July 1, 2022): 1358. http://dx.doi.org/10.3390/sym14071358.

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Although the concept of symmetry is widely used in many fields, it is almost not discussed in finance. This concept appears to be relevant in relation, for example, to mathematical models that can predict stock prices to contribute to the decision-making process. This work considers the stock price of European options with a new class of the non-constant delay model. The stochastic pantograph differential equation (SPDE) with a variable delay is provided in order to overcome the weaknesses of using stochastic models with constant delay. The proposed model is constructed to improve the evaluation process and prediction accuracy for stock prices. The feasibility of the proposed model is introduced under relatively weak conditions imposed on its volatility function. Furthermore, the sensitivity of time lag is discussed. The robust stochastic theta Milstein (STM) method is combined with the Monte Carlo simulation to compute asset prices within the proposed model. In addition, we prove that the numerical solution can preserve the non-negativity of the solution of the model. Numerical experiments using real financial data indicate that there is an increasing possibility of prediction accuracy for the proposed model with a variable delay compared to non-linear models with constant delay and the classical Black and Scholes model.
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Aghabeygi, Mona, Kamel Louhichi, and Sergio Gomez y Paloma. "Impacts of fertilizer subsidy reform options in Iran: an assessment using a Regional Crop Programming model." Bio-based and Applied Economics 11, no. 1 (July 20, 2022): 55–73. http://dx.doi.org/10.36253/bae-10981.

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The aim of this paper is to assess the potential impacts of different fertilizer subsidy reform options on the performance of the Iranian crops production sector. This is achieved using a Regional Crop Programming (RCP) model, based on Positive Mathematical Programming, which includes in total 14 crop activities and encompasses 31 administrative regions. The RCP model is a collection of micro-economic models, working with exogenous prices, each representing the optimal crop allocation at the regional level. The model is calibrated against observed data on crop acreage, yield responses to nitrogen application, and exogenous supply elasticities. Simulation results show that a total removal of nitrogen fertilizer subsidies would affect the competitiveness of crops with the highest nitrogen application rates and lead to a slight reduction of national agricultural income, at approximately 1%. This effect, which is more pronounced at the regional level, is driven by area reallocation rather than land productivity. The reallocation of nitrogen fertilizer subsidy to only strategic crops boost their production and income but increase disparity among regions and affects negatively welfare compared to the current universal fertilizer program. The transfer efficiency analysis shows that both target and universal simulated options are inefficient with an efficiency score below one.
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Dziatkovskii, Anton, and Uladzimir Hryneuski. "The possibilities of ensuring the security of the software product in the conditions of unauthorized access." Economic Annals-ХХI 189, no. 5-6(1) (June 10, 2021): 90–100. http://dx.doi.org/10.21003/ea.v189-09.

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Ensuring the security of a software product in the conditions of large companies, taking into account confidential financial and corporate data, is quite an urgent topic in 2021-2023. Over the past year, the number of leaks of confidential information reached a historic peak, together with cyber attacks, and amounts to 114 identified cases. In modern conditions, software security testing is aimed at identifying security errors and design flaws at all stages of the software development lifecycle. At the same time, at the design stage, this type of work should be provided in order to facilitate the implementation of these characteristics in the final version of the security-related system. Research has shown that there is a wide range of opportunities for developing and using security testing software. These options may differ in implementation technologies, cost and other tactical and technical indicators, characteristics of individual elements, and so on. The main task of developing a software security testing method is to develop, improve and select models, methods and tools that belong to a subset and provide maximum software security indicators. Our approach allows us to prevent any penetration into the information system, while maintaining 100% security of confidential files and the system as a whole. The threat prevention model works with the help of proactive technology, and if you calculate the economic effect of these measures, it can be different, depending on the value of the enterprise’s information itself, and can also be calculated in millions of US dollars. The reliability of the results of mathematical modelling of technologies for creating and implementing «penetration testing» tools is evaluated. The experimental results showed that for all the studied data types, the confidence probability that the value of the statistical value «does not deviate» from the mathematical expectation by more than 1 is 0.94.
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Dissertations / Theses on the topic "Options (Finance) Australia Mathematical models"

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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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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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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.
published_or_final_version
Mathematics
Doctoral
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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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.
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.
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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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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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.
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蕭德權 and Tak-kuen Siu. "Risk measures in finance and insurance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31242297.

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Nhongo, Tawuya D. R. "Pricing exotic options using C++." Thesis, Rhodes University, 2007. http://hdl.handle.net/10962/d1008373.

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This document demonstrates the use of the C++ programming language as a simulation tool in the efficient pricing of exotic European options. Extensions to the basic problem of simulation pricing are undertaken including variance reduction by conditional expectation, control and antithetic variates. Ultimately we were able to produce a modularized, easily extend-able program which effectively makes use of Monte Carlo simulation techniques to price lookback, Asian and barrier exotic options. Theories of variance reduction were validated except in cases where we used control variates in combination with the other variance reduction techniques in which case we observed increased variance. Again, the main aim of this half thesis was to produce a C++ program which would produce stable pricings of exotic options.
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Books on the topic "Options (Finance) Australia Mathematical models"

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Hughston, L. P., and Matheus R. Grasselli. Finance at Fields. Singapore: World Scientific, 2013.

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Eades, Simon. Options, hedging & arbitrage. London: McGraw-Hill, 1992.

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Wilmott, Paul. Option pricing: Mathematical models and computation. Oxford, UK: Oxford Financial Press, 1997.

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Frequently asked questions in quantitative finance. 2nd ed. New York: Wiley, 2009.

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Olivier, Pironneau, ed. Computational methods for option pricing. Philadelphia: Society for Industrial and Applied Mathematics, 2005.

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Shaffer, Sherrill L. Immunizing options against changes in volatility. [Philadelphia]: Federal Reserve Bank of Philadelphia, 1989.

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Matthias, Ehrhardt, ed. Nonlinear models in mathematical finance: New research trends in option pricing. New York: Nova Science Publishers, 2008.

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Bates, David S. Testing option pricing models. Cambridge, MA: National Bureau of Economic Research, 1995.

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1960-, Laroche Pierre, ed. Options et contrats à terme. 2nd ed. [Québec, Québec]: Presses de l'Université Laval, 1995.

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Hecker, Renate. Informationsgehalt von Optionspreisen: Eine empirische Untersuchung der Preisbildung am Markt für Kaufoptionen im Vorfeld abnormaler Kursbewegungen am Aktienmarkt. Heidelberg: Physica, 1993.

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Book chapters on the topic "Options (Finance) Australia 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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"Barrier Options in the BK and Verhulst Models." In Generalized Integral Transforms in Mathematical Finance, 289–308. WORLD SCIENTIFIC, 2021. http://dx.doi.org/10.1142/9789811231742_0014.

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"Barrier Options in the Time-Dependent CEV and CIR Models." In Generalized Integral Transforms in Mathematical Finance, 251–87. WORLD SCIENTIFIC, 2021. http://dx.doi.org/10.1142/9789811231742_0013.

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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.
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