房貸基礎證券評價運用風險中立方法之適當性

Abstract

傳統上提到衍生性金融商品評價時，風險中立評價方法是最被廣泛使用的方式，但應用於房貸基礎證券評價時，則因房貸基礎證券內隱含的提前還本買權與違約賣權本身並無交易市場，使得這二種風險因子無法藉由連續交易來規避，造成房貸基礎證券運用風險中立方法評價時，可能會產生誤差。本研究以此為出發點，利用Chen, Liao, and Yang (2004)所提出之Equilibrium Mortgage Pricing Model之架構下進行不同風險測度下之評價分析，以探討風險中立評價方法於房貸基礎證券評價之適當性，與利用風險值(Value at Risk, VaR)來評估房貸基礎證券之市場風險時，是否也會因風險中立評價方法而造成影響。在透過一連串的數值分析之下，證明當房貸基礎證券之標的資產無法連續交易時，風險中立方法將產生相當的評價誤差，此外，房貸基礎證券之風險值的評估也將受到影響。

Traditionally, when it comes to derivative pricing, risk neutral pricing is the widely-used methodology. However, when it applies to mortgage-backed security valuation, the risk neutral methodology may result in pricing biases. It is due to that there is no trading market for both the prepayment call option and default put option embedded in the mortgage-backed security. Therefore, the two risk factors can not be hedged away via continuous trading. This research will proceed on basis of this issue and make use of the Equilibrium Mortgage Pricing Model proposed by Chen, Liao, and Yang (2004) to implement mortgage-backed security pricing under different probability measure to investigate if the risk neutral methodology is appropriate for mortgage-backed security pricing. At the same time, the research will also study if the risk neutral methodology will affect Value at Risk measuring the market risk of the mortgage-backed security. Via a number of numerical examples, it demonstrates that large pricing biases are introduced by the risk neutral methodology when the underlying asset, the mortgage pool backing the mortgage-backed security, is not continuously traded. In addition, the risk neutral methodology also results in the measurement biases in the Value at Risk of the mortgage-backed security.