Bond pricing and two unconditionally implied parameters inferred from option prices

We study stock option and bond pricing problems for a case when the short-term interest rate and the volatility of the stock are random processes. The option prices are generated by a risk-neutral valuation method and they are correlated with the short-term interest rate generating the bond price. We suggest, to use, for calculation of bond prices, the implied 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.