122 Valuation and Risk Management of Weather Derivatives: The Application of CME Rainfall Index Binary Contracts measured as the product of the occurrence model Xt and the magnitude model Mt. Rt = Xt × Mt . (2.1) 2.1 Occurrence Model The occurrence model is defined as a zero-one process, in which “0” means no rain and “1” means rain: 0, day t it does not rain, Xt = ⎧ ⎨ ⎩ (2.2) 1, day t it rains. As shown in Figure 1, Xt is a first-order, two-state Markov chain. The Markovian property implies that the transition probability of whether it rains or not on day t only depends on the rainfall situation on day t-1, as listed from (2.3) to (2.5). P{Xt | Xt-1, Xt-2, …, X2 } = P{Xt | Xt-1 }, (2.3) p00 = P{Xt = 0 | Xt-1 = 0 } p01 = P{Xt = 1 | Xt-1 = 0 } = 1 - p00, (2.4) p10 = P{Xt = 0 | Xt-1 = 1 } p11 = P{Xt = 1 | Xt-1 = 1 } = 1 - p10. (2.5) Figure 1 First-order, Two-state Markov Chain State 0 (no rain) State 1 (rain) p00 p11 p01 p10
RkJQdWJsaXNoZXIy ODg3MDU=