Valuation of Residential Mortgage-Backed Securities with Proportional Hazard Model: Cumulant Expansion Approach to Pricing RMBS

Abstract

Notes: We regard the prices computed by Monte Carlo with 10 7 sample paths as the exact prices denoted by EP. CEP1 and CEP2 denote the prices by the first and second order cumulant expansion respectively. CEP2* is the prices by the second order cumulant expansion with the spline interpolation. Here we define error := EP -CEP and error ratio := 100 × error/EP. E X H I B I T 3 RMBS, IO and PO Prices in the Case of w = 3, 5, 10Notes: Exhibit 4 shows RMBS, IO and PO prices, errors, and error ratios in the case of w = 20, 30, 50. E X H I B I T 4 RMBS, IO and PO Prices in the Case of w = 20, 30, 50 Notes: The solid line denotes the effective convexity of IO by CEP2*. The dashed line denotes the effective convexity of IO by MCI. The dotted line denotes the effective convexity of IO by MCF. The definition of IO effective convexity is the same as that of RMBS. E X H I B I T 1 7 Effective Convexity of IONotes: The solid line denotes the effective convexity of PO by CEP2*. The dashed line denotes the effective convexity of PO by MCI. The dotted line denotes the effective convexity of PO by MCF. The definition of PO effective convexity is the same as that of RMBS.

Mortgage contract design and systemic risk immunization

“…Do specific US mortgage contract features combine in a systemically perverse fashion with 'originate-to-distribute' underwriting procedures used in the creation of collateralised mortgage obligations and related financing vehicles, e.g., Wilmarth (2009)? 7 Will improvement in pricing models permit accurate enough pricing of the interest rate and default options inherent in collateralized mortgage products to prevent future mortgage funding system failures, e.g., Kau, Keenan, Muller, and Epperson (1995), Deng and Gabriel (2006), Longstaff and Rajan (2007), and Ozeki, Umezawa, Yamazaki, and Yoshikawa (2009)? Or, alternatively, is a substantive change in mortgage contract design required?…”