以基礎期望損失評價非標準批次證券

Abstract

由市場報價帶入標準模型後可以反推得compound correlation，然而有compound correlation smile 的現象發生。於是市場引進了基礎相關係數的概念且使得評價非標準化批次證券變得可能，但是直接對標準批次證券得到的基礎相關係數進行插值時，會造成非標準化批次證券產生不合理的合理價差。 本研究探討對標準化批次證券的基礎相關係數施以不同的插值法時，產生不合理之合理價差的原因，進而引用基礎期望損失的概念以及基礎期望損失所需遵守的性質，並由此建構基礎期望損失的上下界；由不同插值法所得之基礎期望損失曲線隱含的基礎相關係數會發現存在有基礎相關係數微笑的現象。接著以Parcell & Wood 所提出的方法可以建構出一條單調遞增且凹向下的基礎期望損失曲線，而以之對任意的非標準化批次證券評價時，一定可以得到合理的合理價差。

The compound correlations can be inferred from markets quotes with a standard model; however, there exists the behavior of compound correlation smile. The concept of base correlation which makes evaluation of bespoke tranche possible was introduced by the market, but interpolating base correlation for standard tranches directly will generate unreasonable fair spread for bespoke tranches. This paper discusses the reasons generating unreasonable fair spread for bespoke tranches when performing different interpolations, introduces the idea of base expected loss, and constructs the upper and lower bounds using the properties that the base expected loss must obey; the base correlation implied from base expected loss curve with different interpolation exists the behavior of base correlation smile. Then constructing the base expected loss curve that is monotonic increase and concave down proposed by Parcell & Wood can used to price any bespoke tranches in the absence of arbitrage.