Mortgage Option Deltas

Abstract

Mortgage options are European options on TBA contracts that are forwards on securitized pools of agency-backed mortgages. Because of the significant negative convexity of TBAs, calculation of option deltas is a delicate issue. It is common to model TBA options with the S-curve framework. Mortgage option prices, however, may be significantly higher than such a model predicts. There are various ways of dealing with this price discrepancy, including adjusting the TBA DV01 curve, applying a scaling factor to swaption volatilities used in calibration, or adding an extra rate-independent variance to TBA prices. These different modifications of the base S-curve framework may lead to the same option prices but different deltas. In this article, the authors estimate deltas using local price volatility and compare the deltas resulting from different modifications of the base S-curve framework to these “model-free” estimates. The analysis is primarily important for risk management in terms of mark-to-the-market pricing of mortgage options and its implication for the deltas. Although in practice only at-the-money mortgage options are marked to market, the authors also discuss the implications for skew and some valuation implications.