Analytical solution of the Dupire-like equation in calibration to the generalized stochastic volatility jump-diffusion model for option pricing

被引：0
作者：
Jraifi, Abdelilah [1 ]
Darouichi, Aziz [2 ]
Elmouki, Ilias [1 ]
机构：
[1] Natl Sch Appl Sci Safi ENSA S, Lab Math Comp Sci & Commun Syst MISCOM, Safi, Morocco
[2] Cadi Ayyad Univ, Dept Comp Sci, FST, Marrakech, Morocco
来源：
RICERCHE DI MATEMATICA | 2024年
关键词：
Dupire equation; Calibration problem; Stochastic volatility model; Stochastic jump-diffusion model; Optimal control;
D O I：
10.1007/s11587-024-00890-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we succeed to solve the open problem that was about finding the analytical solution of the Dupire-like equation and that we have considered as a result of our Corollary 4.1 (Jraifi et al. in J Adv Math Stud 11(2):282-294, 2018) and which was defined by, partial derivative(T omega )+& sum;F-n(i=1)i(T, K)partial derivative(Ki)omega + (r + & sum;F-n (i=1)i ')omega = 1/2 & sum;(n)(i,j = 1)(integral R-d(GG(T))(ij )Psi (T,K, (y) over bar )d (y) over bar)+I(Psi)(T, K, (y) over bar) with taking as example F-i = alpha K-i(i), K is an element of R+n, T>t(& lowast;) , and in the presence of the initial condition omega|(T = t & lowast;) = h(x(& lowast;)). Since we are taking a generalized form of stochastic volatility jump-diffusion models for option pricing, such new results also represent an important step of contribution to the theory of stochastic control problems of jump diffusions as more precised in our conclusion.
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页数：12
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