Proposition 1. Suppose that Figure 1: The prices for December 2003 and January 2004, denoted by o and e respectively Given estimated values of 0, v and p from the Table 1 we calculate the plug-in volatility y(t,71,72) from (79) and (48). Figure 2 illustrates the dependence 0 +> y(7 — 0,71, 72) of using the equation (55) and all observed forward prices P;,(T1), Pi;(T2), 7 = 0,...,n. To estimate other parameters, we took the subset J C {to,...,tn} where for each i € J the time to the next observation is tj, — t; = 6 := 1/365 = one day. This leaves us with |J| = 87 observed price pairs giving an estimation of v? and p according to the formulas (66) and (77) respectively. The results are summarized in the Table 1. Now we turn to option valuation. Since the volatilities are deterministic, EURO -prices
