A Numerical solution for the new model of time-fractional bond pricing: Using a multi- quadric approximation method

The bond market is an important part of the financial markets. The coupon bonds are issued by companies or banks for increasing capital, and the interest is paid by banks or companies, periodically. In terms of maturities, bonds are divided into three categories as follows: short term, medium term, and long term In this paper, we model the fractional bond pricing under fractional stochastic diferential equation. We implement the multiquadric approximation for solving the fractional bond pricing equation. The equation is discretized in the time direction base on mod- ified Riemann-Liouville derivative and finite diference methods and is approximated by using the multiquadric approximation method in the space direction which achives the semi-discrete solution. We investigate the unconditional stability and convergence of the proposed method. The method presented in the article has been implemented on two examples with different values, which confirm the results of the effectiveness of the method and show that appropriate results can be obtained with the MQ method. it should be noted that all calculations were done with the help of matlab software. Numerical results demonstrate the efficiency and ability of the presented method.