The following document describes the fundamental bases of the stochastic calculation applied to the valuation of options starting from a historical contextualization of the origins of the financial instruments, going through the mathematical formalization of the Brownian movements, Wiener's method and its relation with the Ito motto, as a source of estimation of the Black & Schole method and new applications through climate options against adverse risks of extreme or moderate weather conditions; for which finally a proposal of coverage for the production of rice in Colombia is presented, identifying through the Cobb-Douglas production model the variable of greater incidence for the estimation of an index from which the Strike of a Call and Put position and its respective valuation taking as reference the index of Extreme Heat Degrees (HDD) of the Mercantile Exchange of Chicago (CME) which defines the respective valuation premiums.