Bond Pricing via Parameters Inferred from Options on a Stock

Abstract:     
We study a bond pricing problem for a case when the short term interest rate is a random process with unknown prior distribution and evolution law. We assume that there is a stock and options on this stock with observable prices; the stock volatility can be random. We assume that the option prices are generated by a risk-neutral valuation method and that they are correlated with the short term interest rate that generates the bond price. We suggest to price bonds via volatility and cumulative risk free interest rate inferred from stock and option prices. These parameters can be found unconditionally from a system of two equations. We found that the implied forward risk free rate inferred from system of put and call options does not depend of the option strike price, and, therefore, it can be effectively used for bond pricing.

Keywords: Bond price, diffusion market models, Black-Scholes, stochastic volatility, implied volatility, implied forward risk-free rate

JEL Classifications: G13, C53

Working Paper Series