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. •Paper derives an exact price for a corporate coupon bond.•The price of the bond is defined as an option on the issuing firm’s valuation.•The coupons are stochastic, depending on the valuation of the company.•The value of the coupon are based on the principle of risk-sharing.•The coupons increase or decrease with the valuation of the firm.•Negative coupons are generated by the model.•These can be a pre-cursor to the default of a conventional fixed-coupon bond and could be useful for of risk management.