Merton's equation and the quantum oscillator: pricing risky corporate coupon bonds
Merton has proposed a model of the contingent claims on a firm as an option on the firms value, and the model is based on a generalization of the Black-Scholes stochastic equation. Merton's model can be used to price any contingent claim on the firm. A risk-sharing oscillator model for the pricing of corporate coupon bonds is proposed that leads to stochastic coupons, with the dynamics of the contingent claims being determined by the quantum oscillator. The oscillator model allows for the exact derivation of many results using quantum mathematics. The price of the risk-sharing coupon bonds and the stochastic coupons is derived exactly using the Feynman path integral.
Merton's equation , Corporate coupon bonds , Sukuk , Stochastic coupons , Oscillator potential , Path integral
Baaquie, Belal E. (2020). Merton's equation and the quantum oscillator: pricing risky corporate coupon bonds. Physica A: Statistical Mechanics and its Applications, 541. https://doi.org/10.1016/j.physa.2019.123367