最佳預測成本法危機預警模型及複合式障礙選擇權評價

Abstract

本文提出新式危機預警模型，並稱之為最佳預測成本法（簡稱成本法）危機預警模型。此新模型以平均預測成本作為預測好壞之比較標準，由此建構出最佳預警方案。相較知名的 KLR (Kaminsky, Lizondo and Reinhart, 1998) 雜信比法危機預警模型，成本法模型在理論上有幾個不同特點： 一、基本概念不同：成本是會計概念，雜信比為機率概念。對比較預警方案、制定預警政策的政策決定者而言，成本法模型更直覺好用。 二、錯誤預測時權重不同：雜信比機率概念將型一錯誤預測和型二錯誤預測視作相同，但成本法可設定不同的權重給不同類型之錯誤預測，政策決定者實務上也確有此種權重設定需求。 三、預警方案範圍不同：成本法預警模型的最佳預警方案可能不存在雜信比，換言之，成本法最佳方案範圍比雜信比法最佳方案範圍更大。 四、預警方案特性不同：雜信比法最佳預警方案有可能為了預警到唯一的危機卻發出過多的預警，造成預警成效低落。成本法在危機很少且錯誤預測成本時，最佳預警方案為不發出任何預警。 五、篩選指標方法不同：成本法當某指標變數的成本法最佳預警方案不包含任何預警信號時，在模型中可剔除該指標變數而不減少預警成效。雜信比法普遍用雜信比大於1時剔除指標變數。 成本法模型和雜信比法模型的不同之處源自於預測哲學的不同：成本法模型可能不去預測任何危機，而雜信比法要求一定要預測到某些危機。乍看之下很難理解，成本法模型的預測哲學反而會有較好的平均預測成效。深思過後可以理解，正因為放棄了必須有正確預測紀錄的這種負擔，成本法反而能得到更好的平均預測成效。

This paper proposes a new kind of early warning system (EWS) based on the optimal forecast cost and we call it “the cost-based EWS” for short. Our new EWS adopts the average forecast cost of error as the forecast performance measure to find the optimal forecast policy. Compared to the famous KLR’s (Kaminsky, Lizondo and Reinhart, 1998) NSR-based EWS, our model has several different features: 1. Different fundamental concepts: The concept of cost is an accounting one, and that of the noise-to-signal ratio (NSR) is a probability one. It is more intuitive for policymakers to compare and decide forecast policies in the optimal cost model. 2. Different weights of forecast errors: The type-I forecast error and type-II forecast error are regarded as equal important in the calculation of NSR, while these errors can be specified with different weights to different types. The flexible weight settings can satisfy the practical needs of policymakers. 3. Different scopes of forecast policies: The optimal cost-based forecast policy may have no NSR, i.e., the scope of the optimal cost-based forecast policy is wider than that of the optimal NSR-based forecast policy. 4. Different forecast characteristics: the optimal NSR-based forecast policy needs at least one correct forecast and it may issue too many warnings to satisfy this requirement. This may make the optimal NSR-based forecast policy inefficient. The optimal cost-based forecast policy may issue no warning signal when there are few crises and the cost without warning a crisis is relatively low. 5. Different criteria for index selection: In the cost-based EWS, an indicator can be excluded if its optimal cost-based forecast policy contains no warning signal. The exclusion of this indicator does not reduce forecast efficiency. On the other hand, it is usual to exclude an indicator when the optimal NSR-based forecast policy is greater than one in the NSR-based EWS. The different features in the NSR-based EWS and in the cost-based EWS root in their fundamental differences in forecast philosophies: The cost-based EWS may fail to warn any crises while the NSR-based EWS must warn some crises correctly. It seems unreasonable at first that the forecast philosophy in the cost-based EWS may benefit the forecast performance in average. However, on reflection one would admit that the cost-based EWS obtains better average performance by giving up the load of the must-warn property that is not a must in forecast. Thesis 2: Formulas for Brick Options of Two Bricks This paper presents closed-form formulas for a broad class of barrier-type options which we call brick options. The building blocks, called bricks for short, may contain continuous and discrete barriers. A brick option is serially built from 7 types of bricks, and its barrier structure may have plentiful mixtures. Trigger events can be classified according to barrier types and the brick's time period, and three commonly used rebate schemes are considered. We survey the brick options of two bricks, and present the closed-form formulas for 27 scenarios. These formulas also unify previous results on the barrier-type options of various barrier structures. Just as the barrier option framework beneficial to corporate securities valuation, Our brick option framework, including the barrier option framework as a special case, will benefit future research.