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Journal articles on the topic 'Options (Finance) – Prices – Mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 January 2023

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1

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 supersed

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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 t

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Kumar Jaiswal, Jitendra, and Raja Das. "Artificial Neural Network Algorithms based Nonlinear Data Analysis for Forecasting in the Finance Sector." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 169. http://dx.doi.org/10.14419/ijet.v7i4.10.20829.

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The involvement of big populace in the quantitative trading has been increased remarkably since the wired and wireless systems have become quite ubiquitous in the fields of finance and economics. Statistical, mathematical and technical analysis in parallel with machine learning and artificial intelligence are frequently being applied to perceive prices moving pattern and forecasting. However stock price do not follow any deterministic regulatory function, factor or circumstances rather than many considerations such as economy and finance, political environments, demand and supply, buying and s

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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 evaluati

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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

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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 nitro

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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

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Nguyen, Ngoc Quynh Anh, and Thi Ngoc Trang Nguyen. "Risk measures computation by Fourier inversion." Journal of Risk Finance 18, no. 1 (January 16, 2017): 76–87. http://dx.doi.org/10.1108/jrf-03-2016-0034.

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Purpose The purpose of this paper is to present the method for efficient computation of risk measures using Fourier transform technique. Another objective is to demonstrate that this technique enables an efficient computation of risk measures beyond value-at-risk and expected shortfall. Finally, this paper highlights the importance of validating assumptions behind the risk model and describes its application in the affine model framework. Design/methodology/approach The method proposed is based on Fourier transform methods for computing risk measures. The authors obtain the loss distribution b

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9

Madan, Dilip B., and King Wang. "Risk Neutral Jump Arrival Rates Implied in Option Prices and Their Models." Applied Mathematical Finance 28, no. 3 (May 4, 2021): 201–35. http://dx.doi.org/10.1080/1350486x.2021.2007145.

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10

SKIADOPOULOS, GEORGE. "VOLATILITY SMILE CONSISTENT OPTION MODELS: A SURVEY." International Journal of Theoretical and Applied Finance 04, no. 03 (June 2001): 403–37. http://dx.doi.org/10.1142/s021902490100105x.

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The developing literature on "smile consistent" no-arbitrage models has emerged from the need to price and hedge exotic options consistently with the prices of standard European options. This survey paper describes the steps through which this literature has evolved by providing a taxonomy of the various models. It highlights the main ideas behind the different models, and it outlines their advantages and limitations. Practical issues in implementing the models are also discussed.

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Ekström, Erik, and Johan Tysk. "PROPERTIES OF OPTION PRICES IN MODELS WITH JUMPS." Mathematical Finance 17, no. 3 (July 2007): 381–97. http://dx.doi.org/10.1111/j.1467-9965.2007.00308.x.

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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

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MERINO, R., J. POSPÍŠIL, T. SOBOTKA, and J. VIVES. "DECOMPOSITION FORMULA FOR JUMP DIFFUSION MODELS." International Journal of Theoretical and Applied Finance 21, no. 08 (December 2018): 1850052. http://dx.doi.org/10.1142/s0219024918500528.

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In this paper, we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alòs [(2012) A decomposition formula for option prices in the Heston model and applications to option pricing approximation, Finance and Stochastics 16 (3), 403–422, doi: https://doi.org/10.1007/s00780-012-0177-0 ] for Heston [(1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options, The Review of Financial Studies 6 (2),

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ERIKSSON, JONATAN. "MONOTONICITY IN THE VOLATILITY OF SINGLE-BARRIER OPTION PRICES." International Journal of Theoretical and Applied Finance 09, no. 06 (September 2006): 987–96. http://dx.doi.org/10.1142/s0219024906003822.

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We generalize earlier results on barrier options for puts and calls and log-normal stock processes to general local volatility models and convex contracts. We show that Γ ≥ 0, that Δ has a unique sign and that the option price is increasing with the volatility for convex contracts in the following cases: • If the risk-free rate of return dominates the dividend rate, then it holds for up-and-out options if the contract function is zero at the barrier and for down-and-in options in general. • If the risk-free rate of return is dominated by the dividend rate, then it holds for down-and-out option

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Henderson, Vicky. "ANALYTICAL COMPARISONS OF OPTION PRICES IN STOCHASTIC VOLATILITY MODELS." Mathematical Finance 15, no. 1 (January 2005): 49–59. http://dx.doi.org/10.1111/j.0960-1627.2005.00210.x.

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SCHOUTENS, WIM, and STIJN SYMENS. "THE PRICING OF EXOTIC OPTIONS BY MONTE–CARLO SIMULATIONS IN A LÉVY MARKET WITH STOCHASTIC VOLATILITY." International Journal of Theoretical and Applied Finance 06, no. 08 (December 2003): 839–64. http://dx.doi.org/10.1142/s0219024903002249.

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Recently, stock price models based on Lévy processes with stochastic volatility were introduced. The resulting vanilla option prices can be calibrated almost perfectly to empirical prices. Under this model, we will price exotic options, like barrier, lookback and cliquet options, by Monte–Carlo simulation. The sampling of paths is based on a compound Poisson approximation of the Lévy process involved. The precise choice of the terms in the approximation is crucial and investigated in detail. In order to reduce the standard error of the Monte–Carlo simulation, we make use of the technique of co

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TAKAHASHI, AKIHIKO, and KOHTA TAKEHARA. "FOURIER TRANSFORM METHOD WITH AN ASYMPTOTIC EXPANSION APPROACH: AN APPLICATION TO CURRENCY OPTIONS." International Journal of Theoretical and Applied Finance 11, no. 04 (June 2008): 381–401. http://dx.doi.org/10.1142/s0219024908004853.

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This paper develops a Fourier transform method with an asymptotic expansion approach for option pricing. The method is applied to European currency options with a libor market model of interest rates and jump-diffusion stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas of the characteristic functions of log-prices of the underlying assets and the prices of currency options based on a third order asymptotic expansion scheme; we use a jump-diffusion model with a mean-reverting stochastic variance process such as in Heston [7]/Bates [1

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BENTH, FRED ESPEN, and RODWELL KUFAKUNESU. "PRICING OF EXOTIC ENERGY DERIVATIVES BASED ON ARITHMETIC SPOT MODELS." International Journal of Theoretical and Applied Finance 12, no. 04 (June 2009): 491–506. http://dx.doi.org/10.1142/s0219024909005324.

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Based on a non-Gaussian Ornstein–Uhlenbeck model for energy spot, we derive prices for Asian and spread options using Fourier techniques. The option prices are expressed in terms of the Fourier transform of the payoff function and the characteristic functions of the driving noises, being independent increment processes. In many relevant situations, these functions are explicitly available, and fast Fourier transform can be used for efficient numerical valuation. The arithmetic nature of our model implies that only a one-dimensional Fourier transform is required in the computation of the price,

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EKSTRÖM, ERIK, and JOHAN TYSK. "OPTIONS WRITTEN ON STOCKS WITH KNOWN DIVIDENDS." International Journal of Theoretical and Applied Finance 07, no. 07 (November 2004): 901–7. http://dx.doi.org/10.1142/s0219024904002694.

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There are two common methods for pricing European call options on a stock with known dividends. The market practice is to use the Black–Scholes formula with the stock price reduced by the present value of the dividends. An alternative approach is to increase the strike price with the dividends compounded to expiry at the risk-free rate. These methods correspond to different stock price models and thus in general give different option prices. In the present paper we generalize these methods to time- and level-dependent volatilities and to arbitrary contract functions. We show, for convex contra

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20

BIELECKI, TOMASZ R., IGOR CIALENCO, ISMAIL IYIGUNLER, and RODRIGO RODRIGUEZ. "DYNAMIC CONIC FINANCE: PRICING AND HEDGING IN MARKET MODELS WITH TRANSACTION COSTS VIA DYNAMIC COHERENT ACCEPTABILITY INDICES." International Journal of Theoretical and Applied Finance 16, no. 01 (February 2013): 1350002. http://dx.doi.org/10.1142/s0219024913500027.

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In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures. We introduce the dynamic ask and bid prices of a derivative contract in markets with transaction costs. Based on these results, we derive a representation theorem for the dynamic bid and ask prices in terms of dynamically consistent sequence of sets of probability measures and risk-neutral measures. To i

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21

GAPEEV, PAVEL V., and MONIQUE JEANBLANC. "FIRST-TO-DEFAULT AND SECOND-TO-DEFAULT OPTIONS IN MODELS WITH VARIOUS INFORMATION FLOWS." International Journal of Theoretical and Applied Finance 24, no. 04 (June 2021): 2150022. http://dx.doi.org/10.1142/s0219024921500229.

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We continue to study a credit risk model of a financial market introduced recently by the authors, in which the dynamics of intensity rates of two default times are described by linear combinations of three independent geometric Brownian motions. The dynamics of two default-free risky asset prices are modeled by two geometric Brownian motions that are not independent of the ones describing the default intensity rates. We obtain closed form expressions for the no-arbitrage prices of some first-to-default and second-to-default European style contingent claims given the reference filtration initi

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22

TENG, LONG, MATTHIAS EHRHARDT, and MICHAEL GÜNTHER. "QUANTO PRICING IN STOCHASTIC CORRELATION MODELS." International Journal of Theoretical and Applied Finance 21, no. 05 (August 2018): 1850038. http://dx.doi.org/10.1142/s0219024918500383.

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Correlation plays an important role in pricing multi-asset options. In this work we incorporate stochastic correlation into pricing quanto options which is one special and important type of multi-asset option. Motivated by the market observations that the correlations between financial quantities behave like a stochastic process, instead of using a constant correlation, we allow the asset price process and the exchange rate process to be stochastically correlated with a parameter which is driven either by an Ornstein–Uhlenbeck process or a bounded Jacobi process. We derive an exact quanto opti

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LI, MINQIANG, and FABIO MERCURIO. "CLOSED-FORM APPROXIMATION OF PERPETUAL TIMER OPTION PRICES." International Journal of Theoretical and Applied Finance 17, no. 04 (June 2014): 1450026. http://dx.doi.org/10.1142/s0219024914500265.

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We develop an asymptotic expansion technique for pricing timer options in stochastic volatility models when the effect of volatility of variance is small. Based on the pricing PDE, closed-form approximation formulas have been obtained. The approximation has an easy-to-understand Black–Scholes-like form and many other attractive properties. Numerical analysis shows that the approximation formulas are very fast and accurate, especially when the volatility of variance is not large.

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MARABEL, JACINTO. "PRICING DIGITAL OUTPERFORMANCE OPTIONS WITH UNCERTAIN CORRELATION." International Journal of Theoretical and Applied Finance 14, no. 05 (August 2011): 709–22. http://dx.doi.org/10.1142/s0219024911006425.

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Multi-asset options exhibit sensitivity to the correlations between the underlying assets and these correlations are notoriously unstable. Moreover, some of these options such as the digital outperformance options, have a cross-gamma that changes sign depending on the relative evolution of the underlying assets. In this paper, I present a model to price digital outperformance options when there is uncertainty about correlation, but it is assumed to lie within a certain range. Under the assumption that assets prices follow a Geometric Brownian motion with constant instantaneous volatilities I p

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ALÒS, E., F. ANTONELLI, A. RAMPONI, and S. SCARLATTI. "CVA AND VULNERABLE OPTIONS IN STOCHASTIC VOLATILITY MODELS." International Journal of Theoretical and Applied Finance 24, no. 02 (March 2021): 2150010. http://dx.doi.org/10.1142/s0219024921500102.

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This work aims to provide an efficient method to evaluate the Credit Value Adjustment (CVA) for a vulnerable European option, which is an option subject to some default event concerning the issuer solvability. Financial options traded in OTC markets are of this type. In particular, we compute the CVA in some popular stochastic volatility models such as SABR, Hull et al., which have proven to fit quite well market derivatives prices, admitting correlation with the default event. This choice covers the relevant case of Wrong Way Risk (WWR) when a credit deterioration determines an increase in th

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BOSSENS, FRÉDÉRIC, GRÉGORY RAYÉE, NIKOS S. SKANTZOS, and GRISELDA DEELSTRA. "VANNA-VOLGA METHODS APPLIED TO FX DERIVATIVES: FROM THEORY TO MARKET PRACTICE." International Journal of Theoretical and Applied Finance 13, no. 08 (December 2010): 1293–324. http://dx.doi.org/10.1142/s0219024910006212.

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We study Vanna-Volga methods which are used to price first generation exotic options in the Foreign Exchange market. They are based on a rescaling of the correction to the Black–Scholes price through the so-called "probability of survival" and the "expected first exit time". Since the methods rely heavily on the appropriate treatment of market data we also provide a summary of the relevant conventions. We offer a justification of the core technique for the case of vanilla options and show how to adapt it to the pricing of exotic options. Our results are compared to a large collection of indica

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

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

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Maller, Ross A., David H. Solomon, and Alex Szimayer. "A MULTINOMIAL APPROXIMATION FOR AMERICAN OPTION PRICES IN LÉVY PROCESS MODELS." Mathematical Finance 16, no. 4 (September 1, 2006): 613–33. http://dx.doi.org/10.1111/j.1467-9965.2006.00286.x.

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Yu, Cindy L., Haitao Li, and Martin T. Wells. "MCMC ESTIMATION OF LÉVY JUMP MODELS USING STOCK AND OPTION PRICES." Mathematical Finance 21, no. 3 (October 19, 2010): 383–422. http://dx.doi.org/10.1111/j.1467-9965.2010.00439.x.

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VON HAMMERSTEIN, ERNST AUGUST, EVA LÜTKEBOHMERT, LUDGER RÜSCHENDORF, and VIKTOR WOLF. "OPTIMALITY OF PAYOFFS IN LÉVY MODELS." International Journal of Theoretical and Applied Finance 17, no. 06 (September 2014): 1450041. http://dx.doi.org/10.1142/s0219024914500411.

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In this paper, we determine the lowest cost strategy for a given payoff in Lévy markets where the pricing is based on the Esscher martingale measure. In particular, we consider Lévy models where prices are driven by a normal inverse Gaussian (NIG)- or a variance Gamma (VG)-process. Explicit solutions for cost-efficient strategies are derived for a variety of vanilla options, spreads, and forwards. Applications to real financial market data show that the cost savings associated with these strategies can be quite substantial. The empirical findings are supplemented by a result that relates the m

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ERIKSSON, BJORN, and MARTIJN PISTORIUS. "METHOD OF MOMENTS APPROACH TO PRICING DOUBLE BARRIER CONTRACTS IN POLYNOMIAL JUMP-DIFFUSION MODELS." International Journal of Theoretical and Applied Finance 14, no. 07 (November 2011): 1139–58. http://dx.doi.org/10.1142/s0219024911006644.

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We present a method of moments approach to pricing double barrier contracts when the underlying is modelled by a polynomial jump-diffusion. By general principles the price is linked to certain infinite dimensional linear programming problems. Subsequently approximating these by finite dimensional linear programming problems, upper and lower bounds for the prices of such options are found. We derive theoretical convergence results for this algorithm, and provide numerical illustrations by applying the method to the valuation of several double barrier-type contracts (double barrier knock-out cal

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BELOMESTNY, DENIS, ANASTASIA KOLODKO, and JOHN SCHOENMAKERS. "PRICING CMS SPREAD OPTIONS IN A LIBOR MARKET MODEL." International Journal of Theoretical and Applied Finance 13, no. 01 (February 2010): 45–62. http://dx.doi.org/10.1142/s021902491000567x.

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We present two approximation methods for the pricing of CMS spread options in Libor market models. Both approaches are based on approximating the underlying swap rates with lognormal processes under suitable measures. The first method is derived straightforwardly from the Libor market model. The second one uses a convexity adjustment technique under a linear swap model assumption. A numerical study demonstrates that both methods provide satisfactory approximations of spread option prices and can be used for calibration of a Libor market model to the CMS spread option market.

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Lindström, Erik. "Implications of Parameter Uncertainty on Option Prices." Advances in Decision Sciences 2010 (May 5, 2010): 1–15. http://dx.doi.org/10.1155/2010/598103.

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Financial markets are complex processes where investors interact to set prices. We present a framework for option valuation under imperfect information, taking risk neutral parameter uncertainty into account. The framework is a direct generalization of the existing valuation methodology. Many investors base their decisions on mathematical models that have been calibrated to market prices. We argue that the calibration process introduces a source of uncertainty that needs to be taken into account. The models and parameters used may differ to such extent that one investor may find an option unde

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PELLEGRINO, TOMMASO. "SECOND-ORDER STOCHASTIC VOLATILITY ASYMPTOTICS AND THE PRICING OF FOREIGN EXCHANGE DERIVATIVES." International Journal of Theoretical and Applied Finance 23, no. 03 (May 2020): 2050021. http://dx.doi.org/10.1142/s0219024920500211.

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We consider models for the pricing of foreign exchange derivatives, where the underlying asset volatility as well as the one for the foreign exchange rate are stochastic. Under this framework, singular perturbation methods have been used to derive first-order approximations for European option prices. In this paper, based on a previous result for the calibration and pricing of single underlying options, we derive the second-order approximation pricing formula in the two-dimensional case and we apply it to the pricing of foreign exchange options.

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Li, Yu. "A mean bound financial model and options pricing." International Journal of Financial Engineering 04, no. 04 (December 2017): 1750047. http://dx.doi.org/10.1142/s2424786317500475.

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Most of financial models, including the famous Black–Scholes–Merton options pricing model, rely upon the assumption that asset returns follow a normal distribution. However, this assumption is not justified by empirical data. To be more concrete, the empirical observations exhibit fat tails or heavy tails and implied volatilities against the strike prices demonstrate U-shaped curve resembling a smile, which is the famous volatility smile. In this paper we present a mean bound financial model and show that asset returns per time unit are Pareto distributed and assets are log Gamma distributed u

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Derman, Emanuel, and Iraj Kani. "Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility." International Journal of Theoretical and Applied Finance 01, no. 01 (January 1998): 61–110. http://dx.doi.org/10.1142/s0219024998000059.

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In this paper we present an arbitrage pricing framework for valuing and hedging contingent equity index claims in the presence of a stochastic term and strike structure of volatility. Our approach to stochastic volatility is similar to the Heath-Jarrow-Morton (HJM) approach to stochastic interest rates. Starting from an initial set of index options prices and their associated local volatility surface, we show how to construct a family of continuous time stochastic processes which define the arbitrage-free evolution of this local volatility surface through time. The no-arbitrage conditions are

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FUNAHASHI, HIDEHARU. "REPLICATION SCHEME FOR THE PRICING OF EUROPEAN OPTIONS." International Journal of Theoretical and Applied Finance 24, no. 03 (May 2021): 2150014. http://dx.doi.org/10.1142/s021902492150014x.

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This paper proposes an efficient method for calculating European option prices under local, stochastic, and fractional volatility models. Instead of directly calculating the density function of a target underlying asset, we replicate it from a simpler diffusion process with a known analytical solution for the European option. For this purpose, we derive six functions that characterize the density function of a diffusion process, for both the original and simpler processes and match these functions so that the latter mimics the former. Using the analytical formula, we then approximate the optio

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Liu, David, and An Wei. "Regulated LSTM Artificial Neural Networks for Option Risks." FinTech 1, no. 2 (June 2, 2022): 180–90. http://dx.doi.org/10.3390/fintech1020014.

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This research aims to study the pricing risks of options by using improved LSTM artificial neural network models and make direct comparisons with the Black–Scholes option pricing model based upon the option prices of 50 ETFs of the Shanghai Securities Exchange from 1 January 2018 to 31 December 2019. We study an LSTM model, a mathematical option pricing model (BS model), and an improved artificial neural network model—the regulated LSTM model. The method we adopted is first to price the options using the mathematical model—i.e., the BS model—and then to construct the LSTM neural network for tr

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CHANG, CHIA-LIN, SHING-YANG HU, and SHIH-TI YU. "RECENT DEVELOPMENTS IN QUANTITATIVE FINANCE: AN OVERVIEW." Annals of Financial Economics 09, no. 02 (September 2014): 1402002. http://dx.doi.org/10.1142/s2010495214020023.

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Quantitative finance combines mathematical finance, financial statistics, financial econometrics and empirical finance to provide a solid quantitative foundation for the analysis of financial issues. The purpose of this special issue on "Recent developments in quantitative finance" is to highlight some areas of research in which novel methods in quantitative finance have contributed significantly to the analysis of financial issues, specifically fast methods for large-scale non-elliptical portfolio optimization, the impact of acquisitions on new technology stocks: the Google–Motorola case, the

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PAGLIARANI, STEFANO, and ANDREA PASCUCCI. "LOCAL STOCHASTIC VOLATILITY WITH JUMPS: ANALYTICAL APPROXIMATIONS." International Journal of Theoretical and Applied Finance 16, no. 08 (December 2013): 1350050. http://dx.doi.org/10.1142/s0219024913500507.

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We present new approximation formulas for local stochastic volatility models, possibly including Lévy jumps. Our main result is an expansion of the characteristic function, which is worked out in the Fourier space. Combined with standard Fourier methods, our result provides efficient and accurate formulas for the prices and the Greeks of plain vanilla options. We finally provide numerical results to illustrate the accuracy with real market data.

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MERINO, RAÚL, JAN POSPÍŠIL, TOMÁŠ SOBOTKA, TOMMI SOTTINEN, and JOSEP VIVES. "DECOMPOSITION FORMULA FOR ROUGH VOLTERRA STOCHASTIC VOLATILITY MODELS." International Journal of Theoretical and Applied Finance 24, no. 02 (March 2021): 2150008. http://dx.doi.org/10.1142/s0219024921500084.

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The research presented in this paper provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their surprising consistency with financial markets. However, they bring several challenges alongside. Most noticeably, even simple nonlinear financial derivatives as vanilla European options are typically priced by means of Monte–Carlo (MC) simulations which are more computationally demanding than similar MC schemes for standard stochastic volatility models. In this pa

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Wang, Xingchun. "Valuation of options on the maximum of two prices with default risk under GARCH models." North American Journal of Economics and Finance 57 (July 2021): 101422. http://dx.doi.org/10.1016/j.najef.2021.101422.

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Carr, Peter, Andrey Itkin, and Dmitry Muravey. "Semi-Closed Form Prices of Barrier Options in the Time-Dependent CEV and CIR Models." Journal of Derivatives 28, no. 1 (July 10, 2020): 26–50. http://dx.doi.org/10.3905/jod.2020.1.113.

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Singh, Vipul Kumar. "Pricing competitiveness of jump-diffusion option pricing models: evidence from recent financial upheavals." Studies in Economics and Finance 32, no. 3 (August 3, 2015): 357–78. http://dx.doi.org/10.1108/sef-08-2012-0099.

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Purpose – The purpose of this paper is to investigate empirically the forecasting performance of jump-diffusion option pricing models of (Merton and Bates) with the benchmark Black–Scholes (BS) model relative to market, for pricing Nifty index options of India. The specific period chosen for this study canvasses the extreme up and down limits (jumps) of the Indian capital market. In addition, equity markets keep on facing high and low tides of financial flux amid new economic and financial considerations. With this backdrop, the paper focuses on finding an impeccable option-pricing model which

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SIDENIUS, JAKOB, VLADIMIR PITERBARG, and LEIF ANDERSEN. "A NEW FRAMEWORK FOR DYNAMIC CREDIT PORTFOLIO LOSS MODELLING." International Journal of Theoretical and Applied Finance 11, no. 02 (March 2008): 163–97. http://dx.doi.org/10.1142/s0219024908004762.

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We present the SPA framework, a novel approach to the modeling of the dynamics of portfolio default losses. In this framework, models are specified by a two-layer process. The first layer models the dynamics of portfolio loss distributions in the absence of information about default times. This background process can be explicitly calibrated to the full grid of marginal loss distributions as implied by initial CDO tranche values indexed on maturity, as well as to the prices of suitable options. We give sufficient conditions for consistent dynamics. The second layer models the loss process itse

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CUTHBERTSON, CHARLES, GRIGORIOS PAVLIOTIS, AVRAAM RAFAILIDIS, and PETTER WIBERG. "ASYMPTOTIC ANALYSIS FOR FOREIGN EXCHANGE DERIVATIVES WITH STOCHASTIC VOLATILITY." International Journal of Theoretical and Applied Finance 13, no. 07 (November 2010): 1131–47. http://dx.doi.org/10.1142/s0219024910006145.

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We consider models for the valuation of derivative securities that depend on foreign exchange rates. We derive partial differential equations for option prices in an arbitrage-free market with stochastic volatility. By use of standard techniques, and under the assumption of fast mean reversion for the volatility, these equations can be solved asymptotically. The analysis goes further to consider specific examples for a number of options, and to a considerable degree of complexity.

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Vedran Uran. "THE PRINCIPLE OF EXERCISING OPTIONS ON THE ELECTRICITY MARKET." Journal of Energy - Energija 56, no. 1 (November 14, 2022): 114–33. http://dx.doi.org/10.37798/2007561349.

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Continual price fluctuations are possible to hedge by using various financial instruments, including options. An option buyer buys the right to the settlement price of an underlying asset such as electricity. Due to the volatility of the asset price, the buyer is not obliged to exercise the option. In such a case, the buyer’s only loss is the purchased right or the option premium, which is equal to the option price. Mathematical models for option pricing have been developed in the last hundred years. These models were very popular during the 1970s, owing to the application of the Black-Scholes

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LO, HARRY, and ALEKSANDAR MIJATOVIĆ. "VOLATILITY DERIVATIVES IN MARKET MODELS WITH JUMPS." International Journal of Theoretical and Applied Finance 14, no. 07 (November 2011): 1159–93. http://dx.doi.org/10.1142/s0219024911006656.

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It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset price process S is Markov with càdlàg paths and propose a scheme for computing the law of the realized variance of the log returns accrued while the asset was trading in a prespecified corridor. We thus obtain an algorithm for pricing and hedging volatility derivatives and derivatives on the corridor-realized variance in such a market. The class of models un

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MADAN, DILIP B., and KING WANG. "OPTION IMPLIED VIX, SKEW AND KURTOSIS TERM STRUCTURES." International Journal of Theoretical and Applied Finance 24, no. 05 (August 2021): 2150030. http://dx.doi.org/10.1142/s0219024921500308.

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Comparisons are made of the Chicago Board of Options Exchange (CBOE) skew index with those derived from parametric skews of bilateral gamma models and from the differentiation of option implied characteristic exponents. Discrepancies can be due to strike discretization in evaluating prices of powered returns. The remedy suggested employs a finer and wider set of strikes obtaining additional option prices by interpolation and extrapolation of implied volatilities. Procedures of replicating powered return claims are applied to the fourth power and the derivation of kurtosis term structures. Regr

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Lee, C. F., Ta-Peng Wu, and Ren-Raw Chen. "The Constant Elasticity of Variance Models: New Evidence from S&P 500 Index Options." Review of Pacific Basin Financial Markets and Policies 07, no. 02 (June 2004): 173–90. http://dx.doi.org/10.1142/s021909150400010x.

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The seminal work by Cox (1975, 1996), MacBeth and Merville (1979, 1980) and Emanuel and Macbeth (1982) show that, both theoretically and empirically, the constant elasticity of variance option model (CEV) is superior to the Black–Scholes model in explaining market prices. In this paper, we extend the MacBeth and Merville (1979, 1980) research by using a European contract (S&P 500 index options). We find supportive evidence to the MacBeth and Merville results although our sample is not subject to American premium biases. Furthermore, we reduce the approximation errors by using the non-centr

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