Document Type : Research Article
Authors
Department of Mathematics, Allameh Tabataba'i University, Tehran, Iran
Abstract
In this paper, we first present a nonlinear structural model for pricing mortgage-backed securities. These derivatives are considered to be the primary cause of the 2008 financial crisis that was raised in the United States. We focus our work on pass-through mortgages, which pay both the principal and interest to the investors. We begin our work by introducing the factors that affect the market of mortgage-backed securities. Then, by applying some assumptions and conditions to the parameters of the initial model, and without the loss of generality, we show that this model can be greatly simplified. We focus our attention on how the change in interest rates can affect the value of mortgage-backed securities. Various numerical methods can be used to solve the reduced model that is achieved. We adapt the mesh-less method of radial basis functions to solve the reduced model. The numerical results indicate that the method that we have used can capture the market trends in a specific interval.
Keywords
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[2] F. Black, M. Scholes, The pricing of options and corporate liabilities, World Scienti c Reference on Contingent Claims Analysis in Corporate Finance: Volume 1: Foundations of CCA and Equity Valuation, (2019), pp. 3-21.
[3] L. Bos, S. De Marchi, A. Sommariva, M. Vianello, Computing multi-variate Fekete and Leja points by numerical linear algebra, SIAM Journal on Numerical Analysis, 48 (2010), pp. 19841999.
[4] R. Campagna, S. Cuomo, S. De Marchi, E. Perracchione, G. Severino, A stable meshfree pde solver for source-type ows in porous media, Applied Numerical Mathematics, 149 (2020), pp. 30-42.
[5] S. Cuomo, F. Sica, G. Toraldo, Greeks computation in the option pricing problem by means of RBF-PU methods, Journal of Computational and Applied Mathematics, 376 (2020), pp. 112882.
[6] S. De Marchi, F. DellAccio, M. Mazza, On the constrained mock Chebyshev least-squares, Journal of Computational and Applied Mathematics, 280 (2015), pp. 94-109.
[7] M. del Carmen Calvo-Garrido, C. Vazquez, Effects of jump-diffusion models for the house price dynamics in the pricing of xed-rate mortgages, insurance and coinsurance, Journal of Applied Mathematics and Computation, 271 (2015),
pp. 730-742.
[8] R.L. Hardy, Multiquadric equations of topography and other irregular surfaces, Journal of geophysical research, 76 (1971), pp. 1905-1915.
[9] Y.C. Hon, X.Z. Mao, A radial basis function method for solving options pricing model, Journal of Financial Engineering, 81 (1999), pp.31-50.
[10] J.B. Kau, D.C. Keenan, W.J. Muller, J.F. Epperson, A generalized valuation model for xed-rate residential mortgages, Journal of money, credit and banking, 24 (1992), pp. 279-299.
[11] J.J. McConnell, M. Singh, Valuation and analysis of collateralized mortgage obligations, Management Science, 39 (1993), pp. 692-709.
[12] J.J. McConnell, S.A. Buser, The origins and evolution of the market for mortgage-backed securities, Annu. Rev. Financ. Econ., 3 (2011), pp. 173-192.
[13] A. Neisy, K. Salmani, An inverse nance problem for estimation of the volatility, Computational Mathematics and Mathematical Physics, 53 (2013), pp. 6377.
[14] M. Papi, M. Briani, A PDE-based approach for pricing mortgage-backed securities, Advanced Mathematical Methods for Finance, (2011), pp. 257-291.
[15] R.D. Parshad, A reduced modelling approach to the pricing of mortgage backed securities, Electronic Journal of Differential Equations, 2010 (2010), pp. 114.
(2012), pp. 421-433.
[17] N. Rom-Poulsen, Semi-analytical MBS pricing, The Journal of Real Estate Finance and Economics, 34 (2007), pp. 463-498.
[18] M. Safaei, A. Neisy, N. Nematollahi, New splitting scheme for pricing american options under the heston model, Computational Economics, 52 (2018), pp. 405420.
[19] A. Safdari-Vaighani, A. Heryudono, E. Larsson, A radial basis function partition of unity collocation method for convectiondiffusion equations arising in nancial applications, Journal of Scienti c Computing, 64 (2015), pp. 341367.
[20] E.S. Schwartz, W.N. Torous, Prepayment and the valuation of mortgage- backed securities, Journal of Finance, 44 (1989), pp. 375-392.
[21] M.A. Shahrokhabadi, A. Neisy, E. Perracchione, M. Polato, Learning with subsampled kernel-based methods: Environmental and nancial applications,Dolomites Research Notes on Approximation, 12 (2019).
[22] R. Stanton, Rational prepayment and the valuation of mortgage-backed securities, The Review of nancial studies, 8 (1995), pp. 677-708.
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