References:
[1] F. Black and M. Scholes, “The pricing of options and corporate
liabilities,” The journal of political economy, pp. 637–654, 1973.
[2] R. C. Merton, “Option pricing when underlying stock returns are
discontinuous,” Journal of financial economics, vol. 3, no. 1-2,
pp. 125–144, 1976.
[3] S. G. Kou, “A jump-diffusion model for option pricing,” Management
science, vol. 48, no. 8, pp. 1086–1101, 2002.
[4] L. Andersen and J. Andreasen, “Jump-diffusion processes: Volatility
smile fitting and numerical methods for option pricing,” Review of
Derivatives Research, vol. 4, no. 3, pp. 231–262, 2000.
[5] K. I. Amin, “Jump diffusion option valuation in discrete time,” The
journal of finance, vol. 48, no. 5, pp. 1833–1863, 1993.
[6] S. Hussain and N. Rehman, “Regularity of the american option value
function in jump-diffusion model.,” Journal of Computational Analysis
and Applications, vol. 22, no. 2, pp. 286–297, 2017.
[7] Y. Chen, W. Wang, and A. Xiao, “An efficient algorithm for
options under merton’s jump-diffusion model on nonuniform grids,”
Computational Economics, vol. 53, no. 4, pp. 1565–1591, 2019.
[8] X. Gan, Y. Yang, and K. Zhang, “A robust numerical method for pricing
american options under kou’s jump-diffusion models based on penalty
method,” Journal of Applied Mathematics and Computing, vol. 62,
no. 1-2, pp. 1–21, 2020.
[9] D. Tangman, A. Gopaul, and M. Bhuruth, “Exponential time integration
and chebychev discretisation schemes for fast pricing of options,”
Applied Numerical Mathematics, vol. 58, no. 9, pp. 1309–1319, 2008.
[10] L. Boen and K. J. in’t Hout, “Operator splitting schemes for american
options under the two-asset merton jump-diffusion model,” Applied
Numerical Mathematics, 2020.
[11] S. Salmi and J. Toivanen, “Imex schemes for pricing options under
jump–diffusion models,” Applied Numerical Mathematics, vol. 84,
pp. 33–45, 2014.
[12] M. K. Kadalbajoo, L. P. Tripathi, and A. Kumar, “Second order accurate
imex methods for option pricing under merton and kou jump-diffusion
models,” Journal of Scientific Computing, vol. 65, no. 3, pp. 979–1024,
2015.
[13] R. Mollapourasl, A. Fereshtian, H. Li, and X. Lu, “Rbf-pu method
for pricing options under the jump–diffusion model with local
volatility,” Journal of Computational and Applied Mathematics, vol. 337,
pp. 98–118, 2018.
[14] K. Kazmi, “An imex predictor–corrector method for pricing options
under regime-switching jump-diffusion models,” International Journal
of Computer Mathematics, vol. 96, no. 6, pp. 1137–1157, 2019.
[15] A. Khaliq, B. Wade, M. Yousuf, and J. Vigo-Aguiar, “High
order smoothing schemes for inhomogeneous parabolic problems
with applications in option pricing,” Numerical Methods for Partial
Differential Equations, vol. 23, no. 5, pp. 1249–1276, 2007.
[16] H. P. Bhatt and A.-Q. M. Khaliq, “Fourth-order compact schemes for the
numerical simulation of coupled burgers’ equation,” Computer Physics
Communications, vol. 200, pp. 117–138, 2016.
[17] H. P. Bhatt and A. Khaliq, “A compact fourth-order l-stable scheme
for reaction–diffusion systems with nonsmooth data,” Journal of
Computational and Applied Mathematics, vol. 299, pp. 176–193, 2016.
[18] R. Zvan, P. Forsyth, and K. Vetzal, “Penalty methods for american
options with stochastic volatility,” Journal of Computational and Applied
Mathematics, vol. 91, no. 2, pp. 199–218, 1998.
[19] Y. dHalluin, P. A. Forsyth, and G. Labahn, “A penalty method
for american options with jump diffusion processes,” Numerische
Mathematik, vol. 97, no. 2, pp. 321–352, 2004.
[20] L. N. Trefethen, Spectral methods in MATLAB, vol. 10. Siam, 2000.
[21] S. Cox and P. Matthews, “Exponential time differencing for stiff
systems,” Journal of Computational Physics, vol. 176, no. 2,
pp. 430–455, 2002.
[22] A.-K. Kassam and L. N. Trefethen, “Fourth-order time-stepping for
stiff pdes,” SIAM Journal on Scientific Computing, vol. 26, no. 4,
pp. 1214–1233, 2005.
[23] A. Khaliq, J. Martin-Vaquero, B. Wade, and M. Yousuf, “Smoothing
schemes for reaction-diffusion systems with nonsmooth data,” Journal of
Computational and Applied Mathematics, vol. 223, no. 1, pp. 374–386,
2009.
[24] V. Thom´ee, Galerkin finite element methods for parabolic problems,
vol. 1054. Springer, 1984.
[25] E. Gallopoulos and Y. Saad, “On the parallel solution of parabolic
equations,” in Proceedings of the 3rd international conference on
Supercomputing, pp. 17–28, ACM, 1989.
[26] A. Khaliq, E. Twizell, and D. Voss, “On parallel algorithms
for semidiscretized parabolic partial differential equations based on
subdiagonal pad´e approximations,” Numerical Methods for Partial
Differential Equations, vol. 9, no. 2, pp. 107–116, 1993.
[27] M. Yousuf, A. Khaliq, and B. Kleefeld, “The numerical approximation
of nonlinear black–scholes model for exotic path-dependent american
options with transaction cost,” International Journal of Computer
Mathematics, vol. 89, no. 9, pp. 1239–1254, 2012.
[28] C. R. Vogel, Computational methods for inverse problems, vol. 23. Siam,
2002.
[29] A. Almendral and C. W. Oosterlee, “Numerical valuation of options
with jumps in the underlying,” Applied Numerical Mathematics, vol. 53,
no. 1, pp. 1–18, 2005.
