The inference of the value of missing or unknown data within the range of existing or known data. In other words, the missing data may be a number intermediate between two numbers. Interpolation is a method used to approximate price or yield based on financial tables that don”;t give the exact yield on every amount invested at every interest rate for every maturity. In so doing, interpolation assumes that a given percentage change in yield will cause an equal percentage change in price. The assumption is not always valid, but the variance is often insignificant and thus can be ignored. For example, suppose the 1-year spot rate is 4% and the 2-year spot rate is 6%. Using linear interpolation, the 18-month rate would be 5% (because it should be half way between the two rates). Likewise, the rate at 15 months would be:

4% × (3/4) + 6% × (1/4) = 5.5%

Another example of interpolation can be found in option pricing, where it is used to estimate the cumulative probability N(x) i.e., the probability that a variable with a standard distribution, φ (0,1), will be less than x. For example, in N(x) tables when a specific probability is not given, it can be figured out using the two probabilities surrounding it. Suppose x is bigger than zero, and we want to know the probability of x= 0.6278. With interpolation:

N(0.6278)= N(0.62) + 0.78 [N(0.63- N(0.62)]

N(0.6278)= 0.7324 + 0.78 (0.7357 – 0.7324)= 0.7350