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Journal articles on the topic 'Affine Jump Diffusion'

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Author: Grafiati

Published: 4 June 2021

Last updated: 30 January 2023

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1

Glasserman, Paul, and Kyoung-Kuk Kim. "Saddlepoint approximations for affine jump-diffusion models." Journal of Economic Dynamics and Control 33, no. 1 (January 2009): 15–36. http://dx.doi.org/10.1016/j.jedc.2008.04.007.

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2

Li, Lingfei, Rafael Mendoza-Arriaga, and Daniel Mitchell. "Analytical representations for the basic affine jump diffusion." Operations Research Letters 44, no. 1 (January 2016): 121–28. http://dx.doi.org/10.1016/j.orl.2015.12.003.

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3

Filipović, Damir, Eberhard Mayerhofer, and Paul Schneider. "Density approximations for multivariate affine jump-diffusion processes." Journal of Econometrics 176, no. 2 (October 2013): 93–111. http://dx.doi.org/10.1016/j.jeconom.2012.12.003.

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4

Chung, Tsz Kin, and Yue Kuen Kwok. "Equity-credit modeling under affine jump-diffusion models with jump-to-default." Journal of Financial Engineering 01, no. 02 (June 2014): 1450017. http://dx.doi.org/10.1142/s2345768614500172.

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This paper considers the stochastic models for pricing credit-sensitive financial derivatives using the joint equity-credit modeling approach. The modeling of credit risk is embedded into a stochastic asset dynamics model by adding the jump-to-default (JtD) feature. We discuss the class of stochastic affine jump-diffusion (AJD) models with JtD and apply the models to price defaultable European options and credit default swaps. Numerical studies of the equity-credit models are also considered. The impact on the pricing behavior of derivative products with the added JtD feature is examined.

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5

Gapeev, Pavel V., and Yavor I. Stoev. "On the construction of non-affine jump-diffusion models." Stochastic Analysis and Applications 35, no. 5 (June 30, 2017): 900–918. http://dx.doi.org/10.1080/07362994.2017.1333008.

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6

Da Fonseca, José, and Katja Ignatieva. "Jump activity analysis for affine jump-diffusion models: Evidence from the commodity market." Journal of Banking & Finance 99 (February 2019): 45–62. http://dx.doi.org/10.1016/j.jbankfin.2018.11.014.

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7

FRAME, SAMUEL J., and CYRUS A. RAMEZANI. "BAYESIAN ESTIMATION OF ASYMMETRIC JUMP-DIFFUSION PROCESSES." Annals of Financial Economics 09, no. 03 (December 2014): 1450008. http://dx.doi.org/10.1142/s2010495214500080.

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The hypothesis that asset returns are normally distributed has been widely rejected. The literature has shown that empirical asset returns are highly skewed and leptokurtic. The affine jump-diffusion (AJD) model improves upon the normal specification by adding a jump component to the price process. Two important extensions proposed by Ramezani and Zeng (1998) and Kou (2002) further improve the AJD specification by having two jump components in the price process, resulting in the asymmetric affine jump-diffusion (AAJD) specification. The AAJD specification allows the probability distribution of the returns to be asymmetrical. That is, the tails of the distribution are allowed to have different shapes and densities. The empirical literature on the "leverage effect" shows that the impact of innovations in prices on volatility is asymmetric: declines in stock prices are accompanied by larger increases in volatility than the reverse. The asymmetry in AAJD specification indirectly accounts for the leverage effect and is therefore more consistent with the empirical distributions of asset returns. As a result, the AAJD specification has been widely adopted in the portfolio choice, option pricing, and other branches of the literature. However, because of their complexity, empirical estimation of the AAJD models has received little attention to date. The primary objective of this paper is to contribute to the econometric methods for estimating the parameters of the AAJD models. Specifically, we develop a Bayesian estimation technique. We provide a comparison of the estimated parameters under the Bayesian and maximum likelihood estimation (MLE) methodologies using the S&P 500, the NASDAQ, and selected individual stocks. Focusing on the most recent spectacular market bust (2007–2009) and boom (2009–2010) periods, we examine how the parameter estimates differ under distinctly different economic conditions.

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8

Ignatieva, Katja, and Patrick Wong. "Modelling high frequency crude oil dynamics using affine and non-affine jump–diffusion models." Energy Economics 108 (April 2022): 105873. http://dx.doi.org/10.1016/j.eneco.2022.105873.

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9

Nunes, João Pedro Vidal, and Tiago Ramalho Viegas Alcaria. "Valuation of forward start options under affine jump-diffusion models." Quantitative Finance 16, no. 5 (July 31, 2015): 727–47. http://dx.doi.org/10.1080/14697688.2015.1049200.

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10

Yun, Jaeho. "Out-of-sample density forecasts with affine jump diffusion models." Journal of Banking & Finance 47 (October 2014): 74–87. http://dx.doi.org/10.1016/j.jbankfin.2014.06.024.

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11

Friesen, Martin, Peng Jin, Jonas Kremer, and Barbara Rüdiger. "Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices." Advances in Applied Probability 52, no. 3 (September 2020): 825–54. http://dx.doi.org/10.1017/apr.2020.21.

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AbstractThis article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite $d\times d$ matrices. In particular, for conservative and subcritical affine processes we show that a finite $\log$ -moment of the state-independent jump measure is sufficient for the existence of a unique limit distribution. Moreover, we study the convergence rate of the underlying transition kernel to the limit distribution: first, in a specific metric induced by the Laplace transform, and second, in the Wasserstein distance under a first moment assumption imposed on the state-independent jump measure and an additional condition on the diffusion parameter.

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12

CHIARELLA, CARL, CHRISTINA NIKITOPOULOS SKLIBOSIOS, and ERIK SCHLÖGL. "A MARKOVIAN DEFAULTABLE TERM STRUCTURE MODEL WITH STATE DEPENDENT VOLATILITIES." International Journal of Theoretical and Applied Finance 10, no. 01 (February 2007): 155–202. http://dx.doi.org/10.1142/s0219024907004147.

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The defaultable forward rate is modelled as a jump diffusion process within the Schönbucher [26,27] general Heath, Jarrow and Morton [20] framework where jumps in the defaultable term structure fd(t,T) cause jumps and defaults to the defaultable bond prices Pd(t,T). Within this framework, we investigate an appropriate forward rate volatility structure that results in Markovian defaultable spot rate dynamics. In particular, we consider state dependent Wiener volatility functions and time dependent Poisson volatility functions. The corresponding term structures of interest rates are expressed as finite dimensional affine realizations in terms of benchmark defaultable forward rates. In addition, we extend this model to incorporate stochastic spreads by allowing jump intensities to follow a square-root diffusion process. In that case the dynamics become non-Markovian and to restore path independence we propose either an approximate Markovian scheme or, alternatively, constant Poisson volatility functions. We also conduct some numerical simulations to gauge the effect of the stochastic intensity and the distributional implications of various volatility specifications.

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13

Broadie, Mark, and Özgür Kaya. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes." Operations Research 54, no. 2 (April 2006): 217–31. http://dx.doi.org/10.1287/opre.1050.0247.

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14

Nomikos, N. K., and O. Soldatos. "Using Affine Jump Diffusion Models for Modelling and Pricing Electricity Derivatives." Applied Mathematical Finance 15, no. 1 (February 2008): 41–71. http://dx.doi.org/10.1080/13504860701427362.

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15

Avram, Florin, and Miguel Usabel. "The Gerber-shiu Expected Discounted Penalty-reward Function under an Affine Jump-diffusion Model." ASTIN Bulletin 38, no. 2 (November 2004): 461–81. http://dx.doi.org/10.1017/s0515036100015257.

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We provide a unified analytical treatment of first passage problems under an affine state-dependent jump-diffusion model (with drift and volatility depending linearly on the state). Our proposed model, that generalizes several previously studied cases, may be used for example for obtaining probabilities of ruin in the presence of interest rates under the rational investement strategies proposed by Berk & Green (2004).

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16

Jin, Peng, Barbara Rüdiger, and Chiraz Trabelsi. "Positive Harris recurrence and exponential ergodicity of the basic affine jump-diffusion." Stochastic Analysis and Applications 34, no. 1 (December 23, 2015): 75–95. http://dx.doi.org/10.1080/07362994.2015.1105752.

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17

Minenna, Marcello, and Paolo Verzella. "A revisited and stable Fourier transform method for affine jump diffusion models." Journal of Banking & Finance 32, no. 10 (October 2008): 2064–75. http://dx.doi.org/10.1016/j.jbankfin.2007.05.019.

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18

Yun, Jaeho. "Density Forecast Evaluations via a Simulation-Based Dynamic Probability Integral Transformation*." Journal of Financial Econometrics 18, no. 1 (November 28, 2018): 24–58. http://dx.doi.org/10.1093/jjfinec/nby030.

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Abstract This paper presents simulation-based density forecast evaluation methods using particle filters. The simulation-based dynamic probability integral transformation or log-likelihood evaluation method is combined with the existing density forecast evaluation methods. This methodology is applicable to various density forecast models, such as log stochastic volatility models and affine jump diffusion (AJD) models, for which the probability integral transform or likelihood computation is difficult due to the presence of latent stochastic volatilities. This methodology is applied to the daily S&P 500 stock index. The empirical results show that the AJD models with jumps perform the best for out-of-sample evaluations.

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19

Schneider, Paul, Leopold Sögner, and Tanja Veža. "The Economic Role of Jumps and Recovery Rates in the Market for Corporate Default Risk." Journal of Financial and Quantitative Analysis 45, no. 6 (September 17, 2010): 1517–47. http://dx.doi.org/10.1017/s0022109010000554.

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AbstractUsing an extensive cross section of U.S. corporate credit default swaps (CDSs), this paper offers an economic understanding of implied loss given default (LGD) and jumps in default risk. We formulate and underpin empirical stylized facts about CDS spreads, which are then reproduced in our affine intensity-based jump-diffusion model. Implied LGD is well identified, with obligors possessing substantial tangible assets expected to recover more. Sudden increases in the default risk of investment-grade obligors are higher relative to speculative grade. The probability of structural migration to default is low for investment-grade and heavily regulated obligors because investors fear distress rather through rare but devastating events.

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20

Avram, Florin, and Miguel Usabel. "The Gerber-shiu Expected Discounted Penalty-reward Function under an Affine Jump-diffusion Model." ASTIN Bulletin 38, no. 02 (November 2008): 461–81. http://dx.doi.org/10.2143/ast.38.2.2033350.

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We provide a unified analytical treatment of first passage problems under an affine state-dependent jump-diffusion model (with drift and volatility depending linearly on the state). Our proposed model, that generalizes several previously studied cases, may be used for example for obtaining probabilities of ruin in the presence of interest rates under the rational investement strategies proposed by Berk & Green (2004).

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21

Ahlip, Rehez, Laurence A. F. Park, Ante Prodan, and Stephen Weissenhofer. "Forward start options under Heston affine jump-diffusions and stochastic interest rate." International Journal of Financial Engineering 08, no. 01 (March 2021): 2150005. http://dx.doi.org/10.1142/s2424786321500055.

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This paper presents a generalization of forward start options under jump diffusion framework of Duffie et al. [Duffie, D, J Pan and K Singleton (2000). Transform analysis and asset pricing for affine jump-diffusions, Econometrica 68, 1343–1376.]. We assume, in addition, the short-term rate is governed by the CIR dynamics introduced in Cox et al. [Cox, JC, JE Ingersoll and SA Ross (1985). A theory of term structure of interest rates, Econometrica 53, 385–408.]. The instantaneous volatilities are correlated with the dynamics of the stock price process, whereas the short-term rate is assumed to be independent of the dynamics of the price process and its volatility. The main result furnishes a semi-analytical formula for the price of the Forward Start European call option. It is derived using probabilistic approach combined with the Fourier inversion technique, as developed in Ahlip and Rutkowski [Ahlip, R and M Rutkowski (2014). Forward start foreign exchange options under Heston’s volatility and CIR interest rates, Inspired By Finance Springer, pp. 1–27], Carr and Madan [Carr, P and D Madan (1999). Option valuation using the fast Fourier transform, Journal of Computational Finance 2, 61–73, Carr, P and D Madan (2009). Saddle point methods for option pricing, Journal of Computational Finance 13, 49–61] as well as Levendorskiĩ [Levendorskiĩ, S (2012). Efficient pricing and reliable calibration in the Heston model, International Journal of Applied Finance 15, 1250050].

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22

Yang, Seungho, and Jaewook Lee. "Do affine jump-diffusion models require global calibration? Empirical studies from option markets." Quantitative Finance 14, no. 1 (September 11, 2013): 111–23. http://dx.doi.org/10.1080/14697688.2013.825048.

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23

Wu, Jiang-Lun, and Wei Yang. "Valuation of synthetic CDOs with affine jump-diffusion processes involving Lévy stable distributions." Mathematical and Computer Modelling 57, no. 3-4 (February 2013): 570–83. http://dx.doi.org/10.1016/j.mcm.2012.06.038.

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24

Aschakulporn, Pakorn, and Jin E. Zhang. "Bakshi, Kapadia, and Madan (2003) risk‐neutral moment estimators: An affine jump‐diffusion approach." Journal of Futures Markets 42, no. 3 (October 14, 2021): 365–88. http://dx.doi.org/10.1002/fut.22280.

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25

Moutsinga, Claude Rodrigue Bambe, Edson Pindza, and Eben Maré. "A time multidomain spectral method for valuing affine stochastic volatility and jump diffusion models." Communications in Nonlinear Science and Numerical Simulation 84 (May 2020): 105159. http://dx.doi.org/10.1016/j.cnsns.2019.105159.

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26

Ignatieva, Katja, Paulo Rodrigues, and Norman Seeger. "Empirical Analysis of Affine Versus Nonaffine Variance Specifications in Jump-Diffusion Models for Equity Indices." Journal of Business & Economic Statistics 33, no. 1 (January 2, 2015): 68–75. http://dx.doi.org/10.1080/07350015.2014.922471.

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27

CHANG, JOW-RAN, and HSU-HSIEN CHU. "ELUCIDATING EQUITY PREMIUM USING CORPORATE DIVIDENDS AND HABIT FORMATION." Annals of Financial Economics 10, no. 02 (December 2015): 1550014. http://dx.doi.org/10.1142/s2010495215500141.

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This paper extends Longstaff and Piazzesi (2004, Journal of Financial Economics, 74, 401–421.) to a habit formation model. By combining corporate fraction ratio, and surplus consumption ratio, we derive closed-form solutions for stock values when dividends, habit ratio and consumption follow exponential affine jump-diffusion processes. We can prove that Longstaff and Piazzesi (2004) is only a special case of our model. In addition, calibrated results show that the corporate fraction and habit ratio to shocks significantly increases the equity premium and decreases the risk-free rate. The model determines realistic values for the equity premium and the risk-free rate.

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28

Durham, J. B. "Jump-Diffusion Processes and Affine Term Structure Models : Additional Closed-Form Approximate Solutions, Distributional Assumptions for Jumps, and Parameter Estimates." Finance and Economics Discussion Series 2005, no. 53 (November 2005): 1–57. http://dx.doi.org/10.17016/feds.2005.53.

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29

Gapeev, Pavel V., and Yavor I. Stoev. "On the Laplace transforms of the first exit times in one-dimensional non-affine jump–diffusion models." Statistics & Probability Letters 121 (February 2017): 152–62. http://dx.doi.org/10.1016/j.spl.2016.10.011.

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30

Soleymani, Fazlollah, and Ali Akgül. "Asset pricing for an affine jump-diffusion model using an FD method of lines on nonuniform meshes." Mathematical Methods in the Applied Sciences 42, no. 2 (November 11, 2018): 578–91. http://dx.doi.org/10.1002/mma.5363.

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31

FAMILY, FEREYDOON, and JACQUES G. AMAR. "THE MORPHOLOGY AND EVOLUTION OF THE SURFACE IN EPITAXIAL AND THIN FILM GROWTH: A CONTINUUM MODEL WITH SURFACE DIFFUSION." Fractals 01, no. 04 (December 1993): 753–66. http://dx.doi.org/10.1142/s0218348x93000794.

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A number of discrete models as well as continuum equations have been proposed for describing epitaxial and thin film growth. We have shown that there exists a macroscopic groove instability in many of these models. This unphysical feature in the continuum equations arises from the truncation or linearization of the diffusion operator along the surface. A similar artifact occurs in the discrete models, because in these models adatoms only diffuse horizontally and must take an unphysical vertical jump at step edges. We have proposed and studied a continuum equation for epitaxial and thin-film growth in which the full diffusion along the surface is taken into account. The results of the solutions of this continuum equation, for the growth and the morphology of the surface, are in excellent agreement with recent low temperature molecular-beam epitaxy and ion-sputtering experiments. In particular, we find that at late times dynamic scaling breaks down and the surface is no longer a self-affine fractal. The surface develops a characteristic morphology whose dependence on deposition rate and surface diffusion is similar to that found in experiments.

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32

TAKAHASHI, AKIHIKO, and KOHTA TAKEHARA. "A HYBRID ASYMPTOTIC EXPANSION SCHEME: AN APPLICATION TO LONG-TERM CURRENCY OPTIONS." International Journal of Theoretical and Applied Finance 13, no. 08 (December 2010): 1179–221. http://dx.doi.org/10.1142/s0219024910006169.

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This paper develops a general approximation scheme, henceforth called a hybrid asymptotic expansion scheme for valuation of multi-factor European path-independent derivatives. Specifically, we apply it to pricing long-term currency options under a market model of interest rates and a general diffusion stochastic volatility model with jumps of spot exchange rates. Our scheme is very effective for a type of models in which there exist correlations among all the factors whose dynamics are not necessarily affine nor even Markovian so long as the randomness is generated by Brownian motions. It can also handle models that include jump components under an assumption of their independence of the other random variables when the characteristic functions for the jump parts can be analytically obtained. An asymptotic expansion approach provides a closed-form approximation formula for their values, which can be calculated in a moment and thus can be used for calibration or for an explicit approximation of Greeks of options. Moreover, this scheme develops Fourier transform method with an asymptotic expansion as well as with closed-form characteristic functions obtainable in parts of a model, extending the method proposed by Takehara and Takahashi (2008) to be applicable to a general class of models. It also introduces a characteristic-function-based Monte Carlo simulation method with the asymptotic expansion as a control variable in order to make full use of analytical approximations by the asymptotic expansion and of the closed-form characteristic functions. Finally, a series of numerical examples shows the effectiveness of our scheme.

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33

KOURITZIN, MICHAEL A. "EXPLICIT HESTON SOLUTIONS AND STOCHASTIC APPROXIMATION FOR PATH-DEPENDENT OPTION PRICING." International Journal of Theoretical and Applied Finance 21, no. 01 (February 2018): 1850006. http://dx.doi.org/10.1142/s0219024918500061.

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New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: (1) stochastic approximation replaces regression in the LSM algorithm; (2) explicit weak solutions to stochastic differential equations are developed and applied to Heston model simulation; and (3) importance sampling expands these explicit solutions. The approach complements Heston [(1993) A closed-form solutions for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies 6, 327–343] and Broadie & Kaya [(2006) Exact simulation of stochastic volatility and other affine jump diffusion processes, Operations Research 54 (2), 217–231] by handling the case of path-dependence in the option’s execution strategy. Numeric comparison against standard Monte Carlo methods demonstrates up to two orders of magnitude speed improvement. The general ideas will extend beyond the important Heston setting.

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34

PERISSINOTTO, LUDOVICO, and CLAUDIO TEBALDI. "A "COHERENT STATE TRANSFORM" APPROACH TO DERIVATIVE PRICING." International Journal of Theoretical and Applied Finance 12, no. 02 (March 2009): 125–51. http://dx.doi.org/10.1142/s0219024909005221.

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We propose an extension of the transform approach to option pricing introduced in Duffie, Pan and Singleton (Econometrica68(6) (2000) 1343–1376) and in Carr and Madan (Journal of Computational Finance2(4) (1999) 61–73). We term this extension the "coherent state transform" approach, it applies when the Markov generator of the factor process can be decomposed as a linear combination of generators of a Lie symmetry group. Then the family of group invariant coherent states determine the transform to price derivatives. We exemplify this procedure deriving a coherent state transform for affine jump-diffusion processes with positive state space. It improves the traditional FFT because inversion of the latter requires integration over an unbounded domain, while inversion of the coherent state transform requires integration over unit ball. We explicitly perform the pricing exercise for some contracts like the plain vanilla options on (credit) risky bonds and on the spread option.

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35

Ma, Changfu, Wei Xu, and Yue Kuen Kwok. "Willow tree algorithms for pricing VIX derivatives under stochastic volatility models." International Journal of Financial Engineering 07, no. 01 (March 2020): 2050003. http://dx.doi.org/10.1142/s2424786320500036.

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VIX futures and options are the most popular contracts traded in the Chicago Board Options Exchange. The bid-ask spreads of traded VIX derivatives remain to be wide, possibly due to the lack of reliable pricing models. In this paper, we consider pricing VIX derivatives under the consistent model approach, which considers joint modeling of the dynamics of the S&P index and its instantaneous variance. Under the affine jump-diffusion formulation with stochastic volatility, analytic integral formulas can be derived to price VIX futures and options. However, these integral formulas invariably involve Fourier inversion integrals with cumbersome hyper-geometric functions, thus posing various challenges in numerical evaluation. We propose a unified numerical approach based on the willow tree algorithms to price VIX derivatives under various common types of joint process of the S&P index and its instantaneous variance. Given the analytic form of the characteristic function of the instantaneous variance of the S&P index process in the Fourier domain, we apply the fast Fourier transform algorithm to obtain the transition density function numerically in the real domain. We then construct the willow tree that approximates the dynamics of the instantaneous variance process up to the fourth order moment. Our comprehensive numerical tests performed on the willow tree algorithms demonstrate high level of numerical accuracy, runtime efficiency and reliability for pricing VIX futures and both European and American options under the affine model and 3/2-model. We also examine the implied volatility smirks and the term structures of the implied skewness of VIX options.

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36

BANERJEE, TAMAL, MRINAL K. GHOSH, and SRIKANTH K. IYER. "PRICING CREDIT DERIVATIVES IN A MARKOV-MODULATED REDUCED-FORM MODEL." International Journal of Theoretical and Applied Finance 16, no. 04 (June 2013): 1350018. http://dx.doi.org/10.1142/s0219024913500180.

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Numerous incidents in the financial world have exposed the need for the design and analysis of models for correlated default timings. Some models have been studied in this regard which can capture the feedback in case of a major credit event. We extend the research in the same direction by proposing a new family of models having the feedback phenomena and capturing the effects of regime switching economy on the market. The regime switching economy is modeled by a continuous time Markov chain. The Markov chain may also be interpreted to represent the credit rating of the firm whose bond we seek to price. We model the default intensity in a pool of firms using the Markov chain and a risk factor process. We price some single-name and multi-name credit derivatives in terms of certain transforms of the default and loss processes. These transforms can be calculated explicitly in case the default intensity is modeled as a linear function of a conditionally affine jump diffusion process. In such a case, under suitable technical conditions, the price of credit derivatives are obtained as solutions to a system of ODEs with weak coupling, subject to appropriate terminal conditions. Solving the system of ODEs numerically, we analyze the credit derivative spreads and compare their behavior with the nonswitching counterparts. We show that our model can easily incorporate the effects of business cycle. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low floating interest rate, high default intensity rate, and high volatility. We also model the effects of firm restructuring on the credit spread, in case of a default.

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37

Duffie, Darrell, Jun Pan, and Kenneth Singleton. "Transform Analysis and Asset Pricing for Affine Jump-diffusions." Econometrica 68, no. 6 (November 2000): 1343–76. http://dx.doi.org/10.1111/1468-0262.00164.

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38

Barletta, Andrea, and Elisa Nicolato. "Orthogonal expansions for VIX options under affine jump diffusions." Quantitative Finance 18, no. 6 (October 5, 2017): 951–67. http://dx.doi.org/10.1080/14697688.2017.1371322.

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39

Tappe, Stefan. "Existence of affine realizations for Lévy term structure models." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2147 (June 27, 2012): 3685–704. http://dx.doi.org/10.1098/rspa.2012.0089.

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We investigate the existence of affine realizations for term structure models driven by Lévy processes. It turns out that we obtain more severe restrictions on the volatility than in the classical diffusion case without jumps. As special cases, we study constant direction volatilities and the existence of short-rate realizations.

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40

Lu, Shan. "Monte Carlo analysis of methods for extracting risk‐neutral densities with affine jump diffusions." Journal of Futures Markets 39, no. 12 (September 8, 2019): 1587–612. http://dx.doi.org/10.1002/fut.22049.

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41

Song, Jiao, Jiang-Lun Wu, and Fangzhou Huang. "First jump time in simulation of sampling trajectories of affine jump-diffusions driven by \begin{document}$ \alpha $\end{document}-stable white noise." Communications on Pure & Applied Analysis 19, no. 8 (2020): 4127–42. http://dx.doi.org/10.3934/cpaa.2020184.

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42

Kaeck, Andreas, and Carol Alexander. "Volatility dynamics for the S&P 500: Further evidence from non-affine, multi-factor jump diffusions." Journal of Banking & Finance 36, no. 11 (November 2012): 3110–21. http://dx.doi.org/10.1016/j.jbankfin.2012.07.012.

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43

Zhen, Fang, and Jin E. Zhang. "Dissecting skewness under affine jump-diffusions." Studies in Nonlinear Dynamics & Econometrics 24, no. 4 (November 8, 2019). http://dx.doi.org/10.1515/snde-2018-0086.

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AbstractThis paper derives the theoretical skewness in a five-factor affine jump-diffusion model with stochastic variance and jump intensity, and jumps in prices and variances. Numerical analysis shows that all of the uncertainties in this model affect skewness. The information regarding jumps in prices is mainly reflected in the short-term skewness. The skewness for other maturities carries the information that is highly correlated with variance. Furthermore, the theoretical VIX and skewness under a simplified five-factor model are used to fit the market risk-neutral volatility and skewness sequentially. The fitting performances are better than traditional double-jump models.

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44

Jiang, George J., and Shu Yan. "Affine-Quadratic Jump-Diffusion Term Structure Models." SSRN Electronic Journal, 2005. http://dx.doi.org/10.2139/ssrn.687423.

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45

Li, Lingfei, Rafael Mendoza-Arriaga, and Daniel Mitchell. "Analytical Representations for the Basic Affine Jump Diffusion." SSRN Electronic Journal, 2015. http://dx.doi.org/10.2139/ssrn.2618864.

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46

Filipovic, Damir, Eberhard Mayerhofer, and Paul Georg Schneider. "Density Approximations for Multivariate Affine Jump-Diffusion Processes." SSRN Electronic Journal, 2011. http://dx.doi.org/10.2139/ssrn.1851511.

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47

Da Fonseca, Joss, and Katja Ignatieva. "Jump Activity Analysis for Affine Jump-Diffusion Models: Evidences from the Commodity Market." SSRN Electronic Journal, 2016. http://dx.doi.org/10.2139/ssrn.2773076.

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48

Ruan, Xinfeng, and Jin E. Zhang. "Equilibrium Asset Pricing under Affine Jump-Diffusion with Recursive Preferences." SSRN Electronic Journal, 2018. http://dx.doi.org/10.2139/ssrn.3168248.

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49

Ignatieva, Katja, Paulo Rodrigues, and Norman Seeger. "Empirical Analysis of Affine vs. Non-Affine Variance Specifications in Jump-Diffusion Models for Equity Indices." SSRN Electronic Journal, 2012. http://dx.doi.org/10.2139/ssrn.1344226.

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50

Orłowski, Piotr. "Informative Option Portfolios in Unscented Kalman Filter Design for Affine Jump Diffusion Models." SSRN Electronic Journal, 2019. http://dx.doi.org/10.2139/ssrn.3527094.

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