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Journal articles on the topic 'Double Exponential Jump-Diffusion'

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Published: 4 June 2021

Last updated: 18 February 2022

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1

Kou, S. G., and Hui Wang. "First passage times of a jump diffusion process." Advances in Applied Probability 35, no. 02 (June 2003): 504–31. http://dx.doi.org/10.1017/s0001867800012350.

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This paper studies the first passage times to flat boundaries for a double exponential jump diffusion process, which consists of a continuous part driven by a Brownian motion and a jump part with jump sizes having a double exponential distribution. Explicit solutions of the Laplace transforms, of both the distribution of the first passage times and the joint distribution of the process and its running maxima, are obtained. Because of the overshoot problems associated with general jump diffusion processes, the double exponential jump diffusion process offers a rare case in which analytical solutions for the first passage times are feasible. In addition, it leads to several interesting probabilistic results. Numerical examples are also given. The finance applications include pricing barrier and lookback options.

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2

Kou, S. G., and Hui Wang. "First passage times of a jump diffusion process." Advances in Applied Probability 35, no. 2 (June 2003): 504–31. http://dx.doi.org/10.1239/aap/1051201658.

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This paper studies the first passage times to flat boundaries for a double exponential jump diffusion process, which consists of a continuous part driven by a Brownian motion and a jump part with jump sizes having a double exponential distribution. Explicit solutions of the Laplace transforms, of both the distribution of the first passage times and the joint distribution of the process and its running maxima, are obtained. Because of the overshoot problems associated with general jump diffusion processes, the double exponential jump diffusion process offers a rare case in which analytical solutions for the first passage times are feasible. In addition, it leads to several interesting probabilistic results. Numerical examples are also given. The finance applications include pricing barrier and lookback options.

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3

Suzuki, Atsuo, and Katsushige Sawaki. "Game Russian Options for Double Exponential Jump Diffusion Processes." Journal of Mathematical Finance 04, no. 01 (2014): 47–54. http://dx.doi.org/10.4236/jmf.2014.41005.

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4

Zhou, Jiang, and Lan Wu. "Occupation times of refracted double exponential jump diffusion processes." Statistics & Probability Letters 106 (November 2015): 218–27. http://dx.doi.org/10.1016/j.spl.2015.07.023.

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5

Kou, S. G., and Hui Wang. "Option Pricing Under a Double Exponential Jump Diffusion Model." Management Science 50, no. 9 (September 2004): 1178–92. http://dx.doi.org/10.1287/mnsc.1030.0163.

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6

KUDRYAVTSEV, OLEG, and SERGEI LEVENDORSKIǏ. "PRICING OF FIRST TOUCH DIGITALS UNDER NORMAL INVERSE GAUSSIAN PROCESSES." International Journal of Theoretical and Applied Finance 09, no. 06 (September 2006): 915–49. http://dx.doi.org/10.1142/s0219024906003834.

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We calculate prices of first touch digitals under normal inverse Gaussian (NIG) processes, and compare them to prices in the Brownian model and double exponential jump-diffusion model. Numerical results are produced to show that for typical parameters values, the relative error of the Brownian motion approximation to NIG price can be 2–3 dozen percent if the spot price is at the distance 0.05–0.2 from the barrier (normalized to one). A similar effect is observed for approximations by the double exponential jump-diffusion model, if the jump component of the approximation is significant. We show that two jump-diffusion processes can give approximately the same results for European options but essentially different results for first touch digitals and barrier options. A fast approximate pricing formula under NIG is derived.

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7

Wong, Hoi Ying, and Ka Yung Lau. "Analytical Valuation of Turbo Warrants under Double Exponential Jump Diffusion." Journal of Derivatives 15, no. 4 (May 31, 2008): 61–73. http://dx.doi.org/10.3905/jod.2008.707211.

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8

Liu, Yu-hong, I.-Ming Jiang, and Wei-tze Hsu. "Compound option pricing under a double exponential Jump-diffusion model." North American Journal of Economics and Finance 43 (January 2018): 30–53. http://dx.doi.org/10.1016/j.najef.2017.10.002.

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9

Ramezani, Cyrus A., and Yong Zeng. "Maximum likelihood estimation of the double exponential jump-diffusion process." Annals of Finance 3, no. 4 (November 3, 2006): 487–507. http://dx.doi.org/10.1007/s10436-006-0062-y.

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10

BOYARCHENKO, MITYA, and SVETLANA BOYARCHENKO. "DOUBLE BARRIER OPTIONS IN REGIME-SWITCHING HYPER-EXPONENTIAL JUMP-DIFFUSION MODELS." International Journal of Theoretical and Applied Finance 14, no. 07 (November 2011): 1005–43. http://dx.doi.org/10.1142/s0219024911006620.

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We present a very fast and accurate algorithm for calculating prices of finite lived double barrier options with arbitrary terminal payoff functions under regime-switching hyper-exponential jump-diffusion (HEJD) models, which generalize the double-exponential jump-diffusion model pioneered by Kou and Lipton. Numerical tests demonstrate an excellent agreement of our results with those obtained using other methods, as well as a significant increase in computation speed (sometimes by a factor of 5). The first step of our approach is Carr's randomization, whose convergence we prove for barrier and double barrier options under strong Markov processes of a wide class. The resulting sequence of perpetual option pricing problems is solved using an efficient iteration algorithm and the Wiener-Hopf factorization.

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11

Karnaukh, Ie V. "Two-sided boundary problem for Kou's process." Researches in Mathematics 21 (August 11, 2013): 92. http://dx.doi.org/10.15421/241313.

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12

SUZUKI, ATSUO, and KATSUSHIGE SAWAKI. "THE VALUATION OF RUSSIAN OPTIONS FOR DOUBLE EXPONENTIAL JUMP DIFFUSION PROCESSES." Asia-Pacific Journal of Operational Research 27, no. 02 (April 2010): 227–42. http://dx.doi.org/10.1142/s021759591000265x.

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In this paper, we derive closed form solution for Russian option with jumps. First, we discuss the pricing of Russian options when the stock pays dividends continuously. Secondly, we derive the value function of Russian options by solving the ordinary differential equation with some conditions (the value function is continuous and differentiable at the optimal boundary for the buyer). And we investigate properties of optimal boundaries of the buyer. Finally, some numerical results are presented to demonstrate analytical properties of the value function.

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13

Yang, Rui-cheng, Mao-xiu Pang, and Zhuang Jin. "Valuing Credit Default Swap under a double exponential jump diffusion model." Applied Mathematics-A Journal of Chinese Universities 29, no. 1 (March 2014): 36–43. http://dx.doi.org/10.1007/s11766-014-3074-9.

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14

KUNITA, HIROSHI, and TAKUYA YAMADA. "AVERAGE OPTIONS FOR JUMP DIFFUSION MODELS." Asia-Pacific Journal of Operational Research 27, no. 02 (April 2010): 143–66. http://dx.doi.org/10.1142/s0217595910002612.

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In this paper, we study the problem of pricing average strike options in the case where the price processes are jump diffusion processes. As to the striking value we take the geometric average of the price process. Two cases are studied in details: One is the case where the jumping law of the price process is subject to a Gaussian distribution called Merton model, and the other is the case where the jumping law is subject to a double exponential distribution called Kou model. In both cases the price of the average strike option is represented as a time average of a suitable European put option.

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15

Zhang, Su-mei, and Li-he Wang. "A Fast Fourier Transform Technique for Pricing European Options with Stochastic Volatility and Jump Risk." Mathematical Problems in Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/761637.

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We consider European options pricing with double jumps and stochastic volatility. We derived closed-form solutions for European call options in a double exponential jump-diffusion model with stochastic volatility (SVDEJD). We developed fast and accurate numerical solutions by using fast Fourier transform (FFT) technique. We compared the density of our model with those of other models, including the Black-Scholes model and the double exponential jump-diffusion model. At last, we analyzed several effects on option prices under the proposed model. Simulations show that the SVDEJD model is suitable for modelling the long-time real-market changes and stock returns are negatively correlated with volatility. The model and the proposed option pricing method are useful for empirical analysis of asset returns and managing the corporate credit risks.

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16

Sato, Kimitoshi, and Atsuo Suzuki. "Optimal Impulse Control for Cash Management with Double Exponential Jump Diffusion Processes." International Journal of Real Options and Strategy 6 (2018): 45–63. http://dx.doi.org/10.12949/ijros.6.45.

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17

Ahlip, Rehez, Laurence A. F. Park, and Ante Prodan. "Pricing currency options in the Heston/CIR double exponential jump-diffusion model." International Journal of Financial Engineering 04, no. 01 (March 2017): 1750013. http://dx.doi.org/10.1142/s242478631750013x.

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We examine currency options in the double exponential jump-diffusion version of the Heston stochastic volatility model for the exchange rate. We assume, in addition, that the domestic and foreign stochastic interest rates are governed by the CIR dynamics. The instantaneous volatility is correlated with the dynamics of the exchange rate return, whereas the domestic and foreign short-term rates are assumed to be independent of the dynamics of the exchange rate and its volatility. The main result furnishes a semi-analytical formula for the price of the European currency call option in the hybrid foreign exchange/interest rates model.

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18

Fuh, Cheng-Der, Sheng-Feng Luo, and Ju-Fang Yen. "Pricing discrete path-dependent options under a double exponential jump–diffusion model." Journal of Banking & Finance 37, no. 8 (August 2013): 2702–13. http://dx.doi.org/10.1016/j.jbankfin.2013.03.023.

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19

Cai, Ning. "Pricing and Hedging of Quantile Options in a Flexible Jump Diffusion Model." Journal of Applied Probability 48, no. 03 (September 2011): 637–56. http://dx.doi.org/10.1017/s0021900200008214.

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This paper proposes a Laplace-transform-based approach to price the fixed-strike quantile options as well as to calculate the associated hedging parameters (delta and gamma) under a hyperexponential jump diffusion model, which can be viewed as a generalization of the well-known Black-Scholes model and Kou's double exponential jump diffusion model. By establishing a relationship between floating- and fixed-strike quantile option prices, we can also apply this pricing and hedging method to floating-strike quantile options. Numerical experiments demonstrate that our pricing and hedging method is fast, stable, and accurate.

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20

Cai, Ning. "Pricing and Hedging of Quantile Options in a Flexible Jump Diffusion Model." Journal of Applied Probability 48, no. 3 (September 2011): 637–56. http://dx.doi.org/10.1239/jap/1316796904.

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This paper proposes a Laplace-transform-based approach to price the fixed-strike quantile options as well as to calculate the associated hedging parameters (delta and gamma) under a hyperexponential jump diffusion model, which can be viewed as a generalization of the well-known Black-Scholes model and Kou's double exponential jump diffusion model. By establishing a relationship between floating- and fixed-strike quantile option prices, we can also apply this pricing and hedging method to floating-strike quantile options. Numerical experiments demonstrate that our pricing and hedging method is fast, stable, and accurate.

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21

Zhang, Li-Hua, Wei-Guo Zhang, Wei-Jun Xu, and Wei-Lin Xiao. "The double exponential jump diffusion model for pricing European options under fuzzy environments." Economic Modelling 29, no. 3 (May 2012): 780–86. http://dx.doi.org/10.1016/j.econmod.2012.02.005.

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22

Sene, Ndeye Fatou, Mamadou Abdoulaye Konte, and Jane Aduda. "Pricing Bitcoin under Double Exponential Jump-Diffusion Model with Asymmetric Jumps Stochastic Volatility." Journal of Mathematical Finance 11, no. 02 (2021): 313–30. http://dx.doi.org/10.4236/jmf.2021.112018.

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23

LI, T. RAY, and MARIANITO R. RODRIGO. "Alternative results for option pricing and implied volatility in jump-diffusion models using Mellin transforms." European Journal of Applied Mathematics 28, no. 5 (December 6, 2016): 789–826. http://dx.doi.org/10.1017/s0956792516000516.

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In this article, we use Mellin transforms to derive alternative results for option pricing and implied volatility estimation when the underlying asset price is governed by jump-diffusion dynamics. The current well known results are restrictive since the jump is assumed to follow a predetermined distribution (e.g., lognormal or double exponential). However, the results we present are general since we do not specify a particular jump-diffusion model within the derivations. In particular, we construct and derive an exact solution to the option pricing problem in a general jump-diffusion framework via Mellin transforms. This approach of Mellin transforms is further extended to derive a Dupire-like partial integro-differential equation, which ultimately yields an implied volatility estimator for assets subjected to instantaneous jumps in the price. Numerical simulations are provided to show the accuracy of the estimator.

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24

Chiang, Mi-Hsiu, Chang-Yi Li, and Son-Nan Chen. "Pricing currency options under double exponential jump diffusion in a Markov-modulated HJM economy." Review of Quantitative Finance and Accounting 46, no. 3 (September 10, 2014): 459–82. http://dx.doi.org/10.1007/s11156-014-0478-9.

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25

SEPP, ARTUR. "ANALYTICAL PRICING OF DOUBLE-BARRIER OPTIONS UNDER A DOUBLE-EXPONENTIAL JUMP DIFFUSION PROCESS: APPLICATIONS OF LAPLACE TRANSFORM." International Journal of Theoretical and Applied Finance 07, no. 02 (March 2004): 151–75. http://dx.doi.org/10.1142/s0219024904002402.

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We derive explicit formulas for pricing double (single) barrier and touch options with time-dependent rebates assuming that the asset price follows a double-exponential jump diffusion process. We also consider incorporating time-dependent volatility. Assuming risk-neutrality, the value of a barrier option satisfies the generalized Black–Scholes equation with the appropriate boundary conditions. We take the Laplace transform of this equation in time and solve it explicitly. Option price and risk parameters are computed via the numerical inversion of the corresponding solution. Numerical examples reveal that the pricing formulas are easy to implement and they result in accurate prices and risk parameters. Proposed formulas allow fast computing of smile-consistent prices of barrier and touch options.

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26

Mijatović, Aleksandar, Martijn R. Pistorius, and Johannes Stolte. "Randomisation and recursion methods for mixed-exponential Lévy models, with financial applications." Journal of Applied Probability 52, no. 04 (December 2015): 1076–96. http://dx.doi.org/10.1017/s0021900200113099.

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We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of the first-passage time probability and expected occupation time of sets of a Lévy bridge process that relies in part on a randomisation of the time parameter. We establish this recursion for general Lévy processes and derive its explicit form for mixed-exponential jump-diffusions, a dense subclass (in the sense of weak approximation) of Lévy processes, which includes Brownian motion with drift, Kou's double-exponential model, and hyperexponential jump-diffusion models. We present a highly accurate numerical realisation and derive error estimates. By way of illustration the method is applied to the valuation of range accruals and barrier options under exponential Lévy models and Bates-type stochastic volatility models with exponential jumps. Compared with standard Monte Carlo methods, we find that the method is significantly more efficient.

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27

Mijatović, Aleksandar, Martijn R. Pistorius, and Johannes Stolte. "Randomisation and recursion methods for mixed-exponential Lévy models, with financial applications." Journal of Applied Probability 52, no. 4 (December 2015): 1076–96. http://dx.doi.org/10.1239/jap/1450802754.

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We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of the first-passage time probability and expected occupation time of sets of a Lévy bridge process that relies in part on a randomisation of the time parameter. We establish this recursion for general Lévy processes and derive its explicit form for mixed-exponential jump-diffusions, a dense subclass (in the sense of weak approximation) of Lévy processes, which includes Brownian motion with drift, Kou's double-exponential model, and hyperexponential jump-diffusion models. We present a highly accurate numerical realisation and derive error estimates. By way of illustration the method is applied to the valuation of range accruals and barrier options under exponential Lévy models and Bates-type stochastic volatility models with exponential jumps. Compared with standard Monte Carlo methods, we find that the method is significantly more efficient.

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28

LEVENDORSKIĬ, SERGEI. "METHOD OF PAIRED CONTOURS AND PRICING BARRIER OPTIONS AND CDSs OF LONG MATURITIES." International Journal of Theoretical and Applied Finance 17, no. 05 (July 28, 2014): 1450033. http://dx.doi.org/10.1142/s0219024914500332.

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For prices of options with barrier and lookback features, defaultable bonds and credit default swaps (CDSs), and probability distribution functions in Lévy models, as well as for joint probability distributions of a Lévy process and its supremum or/and infimum, one can derive explicit analytical formulas in terms of inverse Laplace/Fourier transforms and the Wiener–Hopf factorization. Unless the characteristic exponent is rational, the main examples being Brownian motion, double exponential jump-diffusion and hyper-exponential jump-diffusion models, accurate numerical realization of these formulas is difficult or very time consuming, especially for options of very long and very short maturities. In this paper, a systematic approach to contour deformations in pricing formulas is developed, which greatly increases the accuracy and speed of calculations; the efficiency of the method is demonstrated with numerical examples. For options and CDSs of moderate and long maturities, much faster asymptotic formulas of comparable level of accuracy are developed.

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29

AitSahlia, Farid, and Andreas Runnemo. "A canonical optimal stopping problem for American options under a double exponential jump-diffusion model." Journal of Risk 10, no. 1 (September 2007): 85–100. http://dx.doi.org/10.21314/jor.2007.154.

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30

Chen, Rongda, Zexi Li, Liyuan Zeng, Lean Yu, Qi Lin, and Jia Liu. "Option Pricing under the Double Exponential Jump-Diffusion Model with Stochastic Volatility and Interest Rate." Journal of Management Science and Engineering 2, no. 4 (December 2017): 252–89. http://dx.doi.org/10.3724/sp.j.1383.204012.

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31

Cai, Ning, Nan Chen, and Xiangwei Wan. "Occupation Times of Jump-Diffusion Processes with Double Exponential Jumps and the Pricing of Options." Mathematics of Operations Research 35, no. 2 (May 2010): 412–37. http://dx.doi.org/10.1287/moor.1100.0447.

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32

Luo, Pengfei, Jie Xiong, Jinqiang Yang, and Zhaojun Yang. "Real options under a double exponential jump-diffusion model with regime switching and partial information." Quantitative Finance 19, no. 6 (July 20, 2017): 1061–73. http://dx.doi.org/10.1080/14697688.2017.1328560.

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33

Chen, Son-Nan, and Pao-Peng Hsu. "Pricing and hedging barrier options under a Markov-modulated double exponential jump diffusion-CIR model." International Review of Economics & Finance 56 (July 2018): 330–46. http://dx.doi.org/10.1016/j.iref.2017.11.003.

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34

Kostrzewski, Maciej, and Jadwiga Kostrzewska. "The Impact of Forecasting Jumps on Forecasting Electricity Prices." Energies 14, no. 2 (January 9, 2021): 336. http://dx.doi.org/10.3390/en14020336.

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The paper is devoted to forecasting hourly day-ahead electricity prices from the perspective of the existence of jumps. We compare the results of different jump detection techniques and identify common features of electricity price jumps. We apply the jump-diffusion model with a double exponential distribution of jump sizes and explanatory variables. In order to improve the accuracy of electricity price forecasts, we take into account the time-varying intensity of price jump occurrences. We forecast moments of jump occurrences depending on several factors, including seasonality and weather conditions, by means of the generalised ordered logit model. The study is conducted on the basis of data from the Nord Pool power market. The empirical results indicate that the model with the time-varying intensity of jumps and a mechanism of jump prediction is useful in forecasting electricity prices for peak hours, i.e., including the probabilities of downward, no or upward jump occurrences into the model improves the forecasts of electricity prices.

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35

Kostrzewski, Maciej, and Jadwiga Kostrzewska. "The Impact of Forecasting Jumps on Forecasting Electricity Prices." Energies 14, no. 2 (January 9, 2021): 336. http://dx.doi.org/10.3390/en14020336.

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The paper is devoted to forecasting hourly day-ahead electricity prices from the perspective of the existence of jumps. We compare the results of different jump detection techniques and identify common features of electricity price jumps. We apply the jump-diffusion model with a double exponential distribution of jump sizes and explanatory variables. In order to improve the accuracy of electricity price forecasts, we take into account the time-varying intensity of price jump occurrences. We forecast moments of jump occurrences depending on several factors, including seasonality and weather conditions, by means of the generalised ordered logit model. The study is conducted on the basis of data from the Nord Pool power market. The empirical results indicate that the model with the time-varying intensity of jumps and a mechanism of jump prediction is useful in forecasting electricity prices for peak hours, i.e., including the probabilities of downward, no or upward jump occurrences into the model improves the forecasts of electricity prices.

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36

Li, Xiaoping, and Chunyang Zhou. "Dynamic asset allocation with asymmetric jump distribution." China Finance Review International 8, no. 4 (November 19, 2018): 387–98. http://dx.doi.org/10.1108/cfri-08-2017-0180.

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Purpose The purpose of this paper is to solve the optimal dynamic portfolio problem under the double-exponential jump diffusion (DEJD) distribution, which can allow the asset returns to jump asymmetrically. Design/methodology/approach The authors solve the problem by solving the HJB equation. Meanwhile, in the presence of jump component in the asset returns, the investor may suffer a large loss due to high leveraged position, so the authors impose the short-sale and borrowing constraints when solving the optimization problem. Findings The authors provide sufficient conditions such that the optimal solution exists and show theoretically that the optimal risky asset weight is an increasing function of jump-up probability and average jump-up size and a decreasing function of average jump-down size. Research limitations/implications In this study, the authors assume that the jump-up and jump-down intensities are constant. In the future, the authors will relax the assumption and allows the jump intensities to be time varying. Practical implications Empirical studies based on Chinese Shanghai stock index data show that the jump distribution of Shanghai index returns is asymmetric, and the DEJD model can fit the data better than the log-normal jump-diffusion model. The numerical results are consistent with the theoretical prediction, and the authors find that the less risk-averse investor will suffer more economic cost if ignoring asymmetric jump distribution. Originality/value This study first examines how asymmetric jumps affect the investor’s portfolio allocation.

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37

Wu, Liang, Jun-tao Wang, Jie-fang Liu, and Ya-ming Zhuang. "The Total Return Swap Pricing Model under Fuzzy Random Environments." Discrete Dynamics in Nature and Society 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/9762841.

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This paper models the jump amplitude and frequency of random parameters of asset value as a triangular fuzzy interval. In other words, we put forward a new double exponential jump diffusion model with fuzziness, express the parameters in terms of total return swap pricing, and derive a fuzzy form pricing formula for the total return swap. Following simulation, we find that the more the fuzziness in financial markets, the more the possibility of fuzzy credit spreads enlarging. On the other hand, when investors exhibit stronger subjective beliefs, fuzzy credit spreads diminish. Using fuzzy information and random analysis, one can consider more uncertain sources to explain how the asset price jump process works and the subjective judgment of investors in financial markets under a variety of fuzzy conditions. An appropriate price range will give investors more flexibility in making a choice.

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38

Han, Gyu-Sik. "Valuation of American Option Prices Under the Double Exponential Jump Diffusion Model with a Markov Chain Approximation." Journal of Korean Institute of Industrial Engineers 38, no. 4 (December 1, 2012): 249–53. http://dx.doi.org/10.7232/jkiie.2012.38.4.249.

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39

Dao, Binh, and Monique Jeanblanc. "Double-exponential jump-diffusion processes: a structural model of an endogenous default barrier with a rollover debt structure." Journal of Credit Risk 8, no. 2 (June 2012): 21–43. http://dx.doi.org/10.21314/jcr.2012.140.

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40

Deng, Guohe. "Pricing European option in a double exponential jump-diffusion model with two market structure risks and its comparisons." Applied Mathematics-A Journal of Chinese Universities 22, no. 2 (June 2007): 127–37. http://dx.doi.org/10.1007/s11766-007-0201-x.

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41

Forsyth, Peter A., and Kenneth R. Vetzal. "Defined Contribution Pension Plans: Who Has Seen the Risk?" Journal of Risk and Financial Management 12, no. 2 (April 24, 2019): 70. http://dx.doi.org/10.3390/jrfm12020070.

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The trend towards eliminating defined benefit (DB) pension plans in favour of defined contribution (DC) plans implies that increasing numbers of pension plan participants will bear the risk that final realized portfolio values may be insufficient to fund desired retirement cash flows. We compare the outcomes of various asset allocation strategies for a typical DC plan investor. The strategies considered include constant proportion, linear glide path, and optimal dynamic (multi-period) time consistent quadratic shortfall approaches. The last of these is based on a double exponential jump diffusion model. We determine the parameters of the model using monthly US data over a 90-year sample period. We carry out tests in a synthetic market which is based on the same jump diffusion model and also using bootstrap resampling of historical data. The probability that portfolio values at retirement will be insufficient to provide adequate retirement incomes is relatively high, unless DC investors adopt optimal allocation strategies and raise typical contribution rates. This suggests there is a looming crisis in DC plans, which requires educating DC plan holders in terms of realistic expectations, required contributions, and optimal asset allocation strategies.

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42

Černá, Dana. "Cubic spline wavelets with four vanishing moments on the interval and their applications to option pricing under Kou model." International Journal of Wavelets, Multiresolution and Information Processing 17, no. 01 (January 2019): 1850061. http://dx.doi.org/10.1142/s0219691318500613.

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The paper is concerned with the construction of a cubic spline wavelet basis on the unit interval and an adaptation of this basis to the first-order homogeneous Dirichlet boundary conditions. The wavelets have four vanishing moments and they have the shortest possible support among all cubic spline wavelets with four vanishing moments corresponding to B-spline scaling functions. We provide a rigorous proof of the stability of the basis in the space [Formula: see text] or its subspace incorporating boundary conditions. To illustrate the applicability of the constructed bases, we apply the wavelet-Galerkin method to option pricing under the double exponential jump-diffusion model and we compare the results with other cubic spline wavelet bases and with other methods.

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43

Su, Xiaoshan, and Manying Bai. "First-Passage Time Model Driven by Lévy Process for Pricing CoCos." Mathematical Problems in Engineering 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/5171470.

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Contingent convertible bonds (CoCos) are typical form of contingent capital that converts into equity of issuing firm or writes down if a prespecified trigger occurs. This paper proposes a general Lévy framework for pricing CoCos. The Lévy framework indicates that the difficulty in giving closed-form expression for CoCos price is the possible introduction of the Lévy process whose first-passage time problem has not been solved. According to characteristics of new Lévy measure after the measure transform, three specific Lévy models driven by drifted Brownian motion, spectrally negative Lévy process, and double exponential jump diffusion process are proposed to give the solution keeping the form of the driving process unchanged under the measure transform. These three Lévy models provide closed-form expressions for CoCos price while the latter two possess them up to Laplace transform, whose pricing results are given by combining with numerical Fourier inversion and Laplace inversion. Numerical results show that negative jumps have large influence on CoCos pricing and the Black-Scholes model would overestimate CoCos price by simply compressing jumps information into volatility while the other two models would give more accurate CoCos price by taking jump risk into consideration.

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Wu, Liang, Jian-guo Sun, and Xian-bin Mei. "Introducing Fuzziness in CDS Pricing under a Structural Model." Mathematical Problems in Engineering 2018 (May 31, 2018): 1–7. http://dx.doi.org/10.1155/2018/6363474.

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OTC credit derivatives are nonstandardized financial derivatives which have the following characteristics. (1) Information on trades is not public. (2) There is no performance guarantee from the stock exchange. (3) The bigger the risk in performance, the bigger the price floating. These result in an asymmetry of market information flow and this asymmetry acts as a decisive factor in the credit risk pricing of financial instruments. The asymmetry of market information flows will lead to obvious fuzziness in how counterparty risks are characterized, as in the process of valuing assets when discontinuous jumping takes place. Accurately measuring the amplitude and frequency of asset values when influenced by information asymmetry cannot be arrived at just by analyzing the random values of historical data. With this in mind, this paper hypothesizes both asset value jump amplitude and frequency of random parameters as a triangular fuzzy interval, i.e., a new double exponential jump diffusion model with fuzzy analysis. It then gives a credit default swap pricing formula in the form of fuzziness. Through the introduction of fuzzy information, this model has the advantage of being able to arrive at results in the form of triangular fuzziness and, consequently, being able to solve some inherent problems in a world characterized by asymmetry in the flow of market information and, to a certain extent, the inadequate disclosure of information.

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Alijean, Marie Angèle Cathleen, and Jason Narsoo. "Evaluation of the Kou-Modified Lee-Carter Model in Mortality Forecasting: Evidence from French Male Mortality Data." Risks 6, no. 4 (October 20, 2018): 123. http://dx.doi.org/10.3390/risks6040123.

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Mortality forecasting has always been a target of study by academics and practitioners. Since the introduction and rising significance of securitization of risk in mortality and longevity, more in-depth studies regarding mortality have been carried out to enable the fair pricing of such derivatives. In this article, a comparative analysis is performed on the mortality forecasting accuracy of four mortality models. The methodology employs the Age-Period-Cohort model, the Cairns-Blake-Dowd model, the classical Lee-Carter model and the Kou-Modified Lee-Carter model. The Kou-Modified Lee-Carter model combines the classical Lee-Carter with the Double Exponential Jump Diffusion model. This paper is the first study to employ the Kou model to forecast French mortality data. The dataset comprises death data of French males from age 0 to age 90, available for the years 1900–2015. The paper differentiates between two periods: the 1900–1960 period where extreme mortality events occurred for French males and the 1961–2015 period where no significant jump is observed. The Kou-modified Lee-Carter model turns out to give the best mortality forecasts based on the RMSE, MAE, MPE and MAPE metrics for the period 1900–1960 during which the two World Wars occurred. This confirms that the consideration of jumps and leptokurtic features conveys important information for mortality forecasting.

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CROSBY, JOHN, NOLWENN LE SAUX, and ALEKSANDAR MIJATOVIĆ. "APPROXIMATING LÉVY PROCESSES WITH A VIEW TO OPTION PRICING." International Journal of Theoretical and Applied Finance 13, no. 01 (February 2010): 63–91. http://dx.doi.org/10.1142/s0219024910005681.

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We examine how to approximate a Lévy process by a hyperexponential jump-diffusion (HEJD) process, composed of Brownian motion and of an arbitrary number of sums of compound Poisson processes with double exponentially distributed jumps. This approximation will facilitate the pricing of exotic options since HEJD processes have a degree of tractability that other Lévy processes do not have. The idea behind this approximation has been applied to option pricing by Asmussen et al. (2007) and Jeannin and Pistorius (2008). In this paper we introduce a more systematic methodology for constructing this approximation which allow us to compute the intensity rates, the mean jump sizes and the volatility of the approximating HEJD process (almost) analytically. Our methodology is very easy to implement. We compute vanilla option prices and barrier option prices using the approximating HEJD process and we compare our results to those obtained from other methodologies in the literature. We demonstrate that our methodology gives very accurate option prices and that these prices are more accurate than those obtained from existing methodologies for approximating Lévy processes by HEJD processes.

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Esunge, Julius, Kalev Pärna, and Dean Teneng. "The Double Barrier Problem With Double Exponential Jump Diffusion." Communications on Stochastic Analysis 11, no. 4 (January 1, 2017). http://dx.doi.org/10.31390/cosa.11.4.08.

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Bhar, Ramaprasad, and Nedim Handzic. "CDS Option Valuation under Double-Exponential Jump-Diffusion (DEJD)." SSRN Electronic Journal, 2012. http://dx.doi.org/10.2139/ssrn.2204409.

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Kou, Steven G., and Hui NMI1 Wang. "Option Pricing Under A Double Exponential Jump Diffusion Model." SSRN Electronic Journal, 2001. http://dx.doi.org/10.2139/ssrn.284202.

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Wong, Hoi Ying, and Ka Yung Lau. "Analytical Valuation of Turbo Warrants Under Double Exponential Jump Diffusion." SSRN Electronic Journal, 2006. http://dx.doi.org/10.2139/ssrn.943373.

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