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1

Guo, Zhi Jun Mathematics &amp Statistics Faculty of Science UNSW. "Small time asymptotics of implied volatility under local volatility models." Publisher:University of New South Wales. Mathematics & Statistics, 2009. http://handle.unsw.edu.au/1959.4/43746.

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Under a class of one dimensional local volatility models, this thesis establishes closed form small time asymptotic formulae for the gradient of the implied volatility, whether or not the options are at the money, and for the at the money Hessian of the implied volatility. Along the way it also partially verifies the statement by Berestycki, Busca and Florent (2004) that the implied volatility admits higher order Taylor series expansions in time near expiry. Both as a prelude to the presentation of these main results and as a highlight of the importance of the no arbitrage condition, this thes
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2

Nogueira, Leonardo Martins. "Hedging options with local and stochastic volatility models." Thesis, University of Reading, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.435713.

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3

Tomassini, Monia. "Pricing in stochastic-local volatility models with default." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7043/.

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In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a cons
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4

Todeschi, Tiziano. "Calibration of local-stochastic volatility models with neural networks." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23052/.

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During the last twenty years several models have been proposed to improve the classic Black-Scholes framework for equity derivatives pricing. Recently a new model has been proposed: Local-Stochastic Volatility Model (LSV). This model considers volatility as the product between a deterministic and a stochastic term. So far, the model choice was not only driven by the capacity of capturing empirically observed market features well, but also by the computational tractability of the calibration process. This is now undergoing a big change since machine learning technologies offer new perspectives
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5

Martini, Paolo. "Forward implied volatility expansions in LSV models." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amslaurea.unibo.it/6343/.

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In this work we address the problem of finding formulas for efficient and reliable analytical approximation for the calculation of forward implied volatility in LSV models, a problem which is reduced to the calculation of option prices as an expansion of the price of the same financial asset in a Black-Scholes dynamic. Our approach involves an expansion of the differential operator, whose solution represents the price in local stochastic volatility dynamics. Further calculations then allow to obtain an expansion of the implied volatility without the aid of any special function or expensive fro
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6

Merino, Fernández Raúl. "Option Price Decomposition for Local and Stochastic Volatility Jump Diffusion Models." Doctoral thesis, Universitat de Barcelona, 2021. http://hdl.handle.net/10803/671682.

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In this thesis, an option price decomposition for local and stochastic volatility jump diffusion models is studied. On the one hand, we generalise and extend the Alòs decomposition to be used in a wide variety of models such as a general stochastic volatility model, a stochastic volatility jump dffusion model with finite activity or a rough volatility model. Furthermore, we note that in the case of local volatility models, speci_cally, spot-dependent models, a new decomposition formula must be used to obtain good numerical results. In particular, we study the CEV model. On the other hand, we
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7

Rossi, Lucia. "Dupire's formula for exponential Lévy models." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amslaurea.unibo.it/6301/.

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Questa tesi è incentrata sull'analisi della formula di Dupire, che permette di ottenere un'espressione della volatilità locale, nei modelli di Lévy esponenziali. Vengono studiati i modelli di mercato Merton, Kou e Variance Gamma dimostrando che quando si è off the money la volatilità locale tende ad infinito per il tempo di maturità delle opzioni che tende a zero. In particolare viene proposta una procedura di regolarizzazione tale per cui il processo di volatilità locale di Dupire ricrea i corretti prezzi delle opzioni anche quando si ha la presenza di salti. Infine tale risultato viene prova
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8

Cozma, Andrei. "Numerical methods for foreign exchange option pricing under hybrid stochastic and local volatility models." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:44a27fbc-1b7a-4f1a-bd2d-abeb38bf1ff7.

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In this thesis, we study the FX option pricing problem and put forward a 4-factor hybrid stochastic-local volatility model. The model, which describes the dynamics of an exchange rate, its volatility and the domestic and foreign short rates, allows for a perfect calibration to European options and has a good hedging performance. Due to the high-dimensionality of the problem, we propose a Monte Carlo simulation scheme that combines the full truncation Euler scheme for the stochastic volatility component and the stochastic short rates with the log-Euler scheme for the exchange rate. We analyze e
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9

Eriksson, Bjorn. "On the valuation of barrier and American options in local volatility models with jumps." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/28104.

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In this thesis two novel approaches to pricing of barrier and American options are developed in the setting of local volatility models with jumps: the moments method and the Markov chain method. The moments method is a valuation approach for barrier options that is based on a characterisation of the exit location measure and the expected occupation measure of the price process of the underlying in terms of the corresponding moments. It is shown how the value of barrier-type derivatives can be expressed using these moments, which are in turn shown to be characterised by an infinite-dimensional
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10

Zetoun, Mirella. "Pricing With Uncertainty : The impact of uncertainty in the valuation models ofDupire and Black&Scholes." Thesis, KTH, Matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-122416.

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Theaim of this master-thesis is to study the impact of uncertainty in the local-and implied volatility surfaces when pricing certain structured products suchas capital protected notes and autocalls. Due to their long maturities, limitedavailability of data and liquidity issue, the uncertainty may have a crucialimpact on the choice of valuation model. The degree of sensitivity andreliability of two different valuation models are studied. The valuation models chosen for this thesis are the local volatility model of Dupire and the implied volatility model of Black&Scholes. The two models are
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11

Chiurchiu, Pier Paolo. "Approximations in Credit Risk Models." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12385/.

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In this thesis we present the intensity-based approach to consider default in a general local-stochastic volatility model with stochastic interest rate. In this setting we describe, as in [18], a technique to find approximate solutions of the corresponding partial differential equations and we provide numerical examples in the particular case of JDCEV and Vasicek model, respectively, for the dynamics of the asset and the short rate. Finally, we introduce a formula for the par CDS spreads and applying the approximation method we calibrate our intensity model to credit data finding the model par
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12

Santos, Douglas Gomes dos. "Estimação de volatilidade em séries financeiras : modelos aditivos semi-paramétricos e GARCH." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2008. http://hdl.handle.net/10183/14892.

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A estimação e previsão da volatilidade de ativos são de suma importância para os mercados financeiros. Temas como risco e incerteza na teoria econômica moderna incentivaram a procura por métodos capazes de modelar uma variância condicional que evolui ao longo do tempo. O objetivo principal desta dissertação é comparar alguns métodos de regressão global e local quanto à extração da volatilidade dos índices Ibovespa e Standard and Poor´s 500. Para isto, são realizadas estimações e previsões com os modelos GARCH paramétricos e com os modelos aditivos semi-paramétricos. Os primeiros, tradicionalme
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13

Rayée, Grégory. "Essays on pricing derivatives by taking into account volatility and interest rates risks." Doctoral thesis, Universite Libre de Bruxelles, 2012. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209649.

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Dans le Chapitre 1, nous présentons une nouvelle approche pour évaluer des options dites à barrières basée sur une méthode connue sous le nom de méthode Vanna-Volga. Cette nouvelle méthode nous permet une calibration simple et rapide sur le marché des options à barrières directement ce qui permet d'évaluer ces options avec un outil en accord avec le marché. Nous comparons également nos résultats avec ceux provenant d’autres modèles célèbres et nous étudions la sensibilité de cette méthode par rapport aux données du marché. Nous donnons une nouvelle justification théorique associée à la méthode
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14

Livieri, Giulia. "Stochastic models for financial time series: modelling, estimation and option pricing." Doctoral thesis, Scuola Normale Superiore, 2017. http://hdl.handle.net/11384/85728.

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15

Acosta, Argueta Lesly María. "Particle filtering estimation for linear and nonlinear state-space models." Doctoral thesis, Universitat Politècnica de Catalunya, 2013. http://hdl.handle.net/10803/134356.

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The sequential estimation of the states (filtering) and the corresponding simultaneous estimation of the states and fixed parameters of a dynamic state-space model, being linear or not, is an important probleminmany fields of research, such as in the area of finance. The main objective of this research is to estimate sequ entially and efficiently –from a Bayesian perspective via the particle filtering methodology– the states and/or the fixed parameters of a nonstandard dynamic state-spacemodel: one that is possibly nonlinear, non-stationary or non-Gaussian. The present thesis consists of sev
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16

Cowen, Nicholas. "Local Stochastic Volatility—The Hyp-Hyp Model." Master's thesis, Faculty of Commerce, 2021. http://hdl.handle.net/11427/32556.

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Volatility modelling is used predominantly in order to explain the volatility smile observed in the market. Stochastic volatility models are mainly used to capture the curvature of a volatility smile while local volatility models generally model the skew. Jackel and Kahl ¨ (2008) present a hyperbolic-local hyperbolic-stochastic volatility (Hyp-Hyp) model which aims to improve upon existing local and stochastic volatility models such as the stochastic alpha, beta, rho (SABR) and constant elasticity of variance (CEV) models. The advantageous features of the Hyp-Hyp model are corroborated by impl
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17

Zanchini, Giulia. "Stochastic local volatility model for fx markets." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7685/.

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Questa tesi verte sullo studio di un modello a volatilità stocastica e locale, utilizzato per valutare opzioni esotiche nei mercati dei cambio. La difficoltà nell'implementare un modello di tal tipo risiede nella calibrazione della leverage surface e uno degli scopi principali di questo lavoro è quello di mostrarne la procedura.
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18

Benmakhlouf, Andaloussi Mohammed. "The Swap Market Model with Local Stochastic Volatility." Thesis, KTH, Matematisk statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-249561.

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Modeling volatility is an intricate part of all financial models and the pricing of derivative contracts. And while local volatility has gained popularity in equity and FX models, it remained neglected in interest rates models. In this thesis, using spot starting swaps, the goal is to build a swap market model with non-parametric local volatility functions and stochastic volatility scaling factors. The local stochastic volatility formula is calibrated through a particle algorithm to match the market’s swaption volatility smile. Numerical experiments are conducted for different currencies to co
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19

Mertlík, Jakub. "Valuation and Hedging of Foreign Exchange Barrier Options." Doctoral thesis, Vysoká škola ekonomická v Praze, 2004. http://www.nusl.cz/ntk/nusl-77859.

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The main aim of this thesis is in analyzing and empirically testing the various valuation models and hedging schemes of foreign exchange barrier options and their robustness with respect to changing of market conditions. The purpose of the main empirical section is to get a detailed understanding of the static and dynamic performance of the analyzed models for the barrier options payoff mainly in the extreme market conditions, where we performed a benchmarking of the various hedging schemes. As a by-product, we analyzed the accomplishment of some of the model assumptions in real world setting,
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20

CAMPOS, EDUARDO LIMA. "LOCAL SCALE MODEL: AN MULTIPLICATIVE ALTERNATIVE SPECIFICATION TO VOLATILITY ESTIMATION AND FORECASTING FOR FINANCIAL RETIVEN SERIES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1998. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=7771@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>Este trabalho apresenta um modelo de volatilidade estocástica com especificação multiplicativa, chamado modelo de escala local. O modelo trabalha com a precisão (recíproca da variância) de uma série temporal. A precisão é tratada como componente não observável, caracterizando o modelo como estrutural, e é suposta evoluir segundo um filtro Gama, com um ruído multiplicativo que segue distribuição Beta. A função de previsão para a variância é uma média móvel com amortecimento exponencial (EWMA) no quadrado das observaçõe
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21

Santos, Julio Cesar Grimalt dos. "Cálculo do Value at Risk (VaR) para o Ibovespa, pós crise de 2008, por meio dos modelos de heterocedasticidade condicional (GARCH) e de volatilidade estocástica (Local Scale Model - LSM)." reponame:Repositório Institucional do FGV, 2015. http://hdl.handle.net/10438/13521.

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Submitted by JULIO CESAR GRIMALT DOS SANTOS (grimbil@hotmail.com) on 2015-02-23T21:08:49Z No. of bitstreams: 1 Dissertação Final.pdf: 1416129 bytes, checksum: fcbac3f948355bac6f5b59569bf2610a (MD5)<br>Approved for entry into archive by Janete de Oliveira Feitosa (janete.feitosa@fgv.br) on 2015-03-04T16:04:21Z (GMT) No. of bitstreams: 1 Dissertação Final.pdf: 1416129 bytes, checksum: fcbac3f948355bac6f5b59569bf2610a (MD5)<br>Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2015-03-12T19:06:25Z (GMT) No. of bitstreams: 1 Dissertação Final.pdf: 1416129 bytes, checksum
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Feldkircher, Martin, Florian Huber, and Gregor Kastner. "Sophisticated and small versus simple and sizeable: When does it pay off to introduce drifting coefficients in Bayesian VARs?" WU Vienna University of Economics and Business, 2018. http://epub.wu.ac.at/6021/1/wp260.pdf.

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We assess the relationship between model size and complexity in the time-varying parameter VAR framework via thorough predictive exercises for the Euro Area, the United Kingdom and the United States. It turns out that sophisticated dynamics through drifting coefficients are important in small data sets while simpler models tend to perform better in sizeable data sets. To combine best of both worlds, novel shrinkage priors help to mitigate the curse of dimensionality, resulting in competitive forecasts for all scenarios considered. Furthermore, we discuss dynamic model selection to improve upon
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23

Henrik, Hasseltoft. "Essays on the term structure of interest rates and long-run risks." Doctoral thesis, Handelshögskolan i Stockholm, Finansiell Ekonomi (FI), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:hhs:diva-925.

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Stocks, Bonds, and Long-Run Consumption Risks. Bansal and Yaron (2004) show that long-run consumption risks and time-varying economic uncertainty in conjunction with recursive preferences can account for important features of equity markets. I bring the model to the term structure of interest rates and show that a calibrated version of the model can simultaneously explain properties of bonds and equities. Specifically, the model accounts for deviations from the expectations hypothesis, the upward sloping nominal yield curve, and the predictive power of the nominal yield spread. However, an est
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24

Lok, U. Hou, and 陸裕豪. "On the Construction of Trees for Local-Volatility Models." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/nf5rcn.

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博士<br>國立臺灣大學<br>資訊工程學研究所<br>105<br>The local-volatility (LV) model for option pricing assumes the instantaneous volatility is a function of the stock price and time. This model is popular because it captures the volatility smile observed in practice as well as retains the preference freedom of the Black-Scholes model. A tree for the LV model is called an LV tree. It is the basis for option pricing and model calibration under the LV model. Most LV trees are recombining, i.e., they are binomial or trinomial trees. Past attempts to construct a smile-consistent LV tree all resort heuristics to dea
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Tseng, Chia-Ching, and 曾家慶. "A Comparison of the 1-FSV and GARCH Models in Local Volatility Forecasts." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/80679723264266482679.

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碩士<br>國立成功大學<br>財務金融研究所<br>94<br>This paper compares the accuracy of different measures for forecasting the volatility of S&P 500 (SPX) index options prices. Using daily data reported daily by the CBOE from September 2003 through June 2004, we examine the predictive performance of volatilities of the 1-FSV and GARCH models and then contrast them with the realized volatilities obtained from S&P 500 index. The results of our study suggest that the GARCH (1,1) model outperforms the 1-FSV model in terms of ex ante forecasting power of volatility. Besides, we plot the volatility surface to exhibit
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26

Majmin, Lisa. "Local and Stochastic Volatility Models: An Investigation into the Pricing of Exotic Equity Options." Thesis, 2006. http://hdl.handle.net/10539/1495.

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Faculty of Science; School of Computational and Applied Maths; MSC Thesis<br>The assumption of constant volatility as an input parameter into the Black-Scholes option pricing formula is deemed primitive and highly erroneous when one considers the terminal distribution of the log-returns of the underlying process. To account for the `fat tails' of the distribution, we consider both local and stochastic volatility option pricing models. Each class of models, the former being a special case of the latter, gives rise to a parametrization of the skew, which may or may not re°ect the correct dyna
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27

Hu, Li-Ren, and 胡力仁. "The Use of Local Volatility Model for Solving Volatility Smile Phenomenon." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/84423832537221614190.

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碩士<br>國立臺灣大學<br>財務金融學研究所<br>89<br>We try to utilize the theory that was developed by Dupire in 1994,then use the price information of European equity call options with different strikes and maturities to evaluate other type of options. The crux for implementing this theory is to find out the local volatilities generated by options prices in the market. Therefore, we propose a new idea to achieve it. By the practical study of Natenberg in 1994, he uncovered that there is one specific variable can perfectly describe the volatility smile pattern even in different maturities.
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28

WEI, HUANG-LING, and 魏凰鈴. "Calibration and Verification of the Local Volatility Model." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/5kgx37.

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碩士<br>東吳大學<br>財務工程與精算數學系<br>103<br>Foreign exchange option implied volatility of market information is quoted. Implied volatility have volatility smile. Dupire (1994) propose local volatility model explain volatility smile. Local volatility was the volatility of the underlying asset. It was a function of time and the underlying assets. Dupire (1994) has also been a function of local volatility and European option price. Andersen and Ratcliffe (1998) and Gatheral (2006) were two further local volatility functions, as a function of the local volatility function and the implied volatility of the
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LIN, JENG-YA, and 林正亞. "The Study of Stochastic Local Volatility Model of Target Redemption Forward." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/uqrkcb.

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碩士<br>東吳大學<br>財務工程與精算數學系<br>104<br>This article refers to Ren et al. (2007) the stochastic local volatility model to describe the dynamic model of the foreign exchange. We used foreign exchange option implied volatility from market data with loss function approach to calibration parameter of stochastic volatility model. We used foreign exchange option implied volatility from market data with Andersen and Brotherton -Ratcliffe (1998), which refers relationship between implied volatility and local volatility function, with the cubic spline interpolation to calibration local volatility model. We
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30

CHENG, YA FANG, and 鄭雅方. "Credit Valuation Adjustment for Interest Rate Swap with Counterparty Credit Risk in the Local Volatility LM Model." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/xdgb22.

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碩士<br>東吳大學<br>財務工程與精算數學系<br>102<br>The Basel III Accord will counterparty credit risk (CCR) to adjust the value called credit valuation adjustment (CVA). Recent literatures suggest that investor and counterparty may default, and therefore the bilateral counterparty credit risk (BCCR) is proposed. Under the base of BCCR, the adjustment to the net present value is called bilateral credit valuation adjustment (BCVA). This article consider a constant elasticity of variance (CEV) of the LM model which is proposed by Andersen and Andreasen (2000), and is called CEV-LM model. In this article, the val
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