Conservative data hedging provides device for passing from nonparametric bounds on cumulative interest rates to hedging strategies for options. The resulting strategies in turn provide intervals for the value of options. Such intervals can often be uncomfortably wide, therefore useless. The purpose of this paper is to show how one can reduce this problem by involving auxiliary securities, in particular, market traded options on zero coupon bonds. As a concise illustration, it is shown how to interpolate call options. This interpolation lowers the upper interval level for vanilla or exotic option. The interpolation algorithm developed in the paper substantially reduces the length of intervals for prices that are generated under uncertainty in the predicted volatility and interest rates.