Delta hedging of mortgage‐servicing portfolios under gamma constraints

Purpose – Interest only strips are created by stripping the interest portion of cash flows generated in mortgage‐backed securities or simply by servicing portfolios of mortgages. A number of financial institutions have significant amounts of mortgage‐servicing rights (MSR) which need to be delta (dynamic) hedged. Because MSR have a positive duration when prepayment effect is stronger than discount effect, it is possible to delta hedge a portfolio of MSR with other fixed income securities such that the value of the portfolio is not affected by increases or decreases in market rates. The purpose of this paper is to address this issue. Design/methodology/approach – The paper develops the delta‐hedge‐ratio of MSR within a dynamic approach, using three different securities. To lower the cost of the delta hedge, the authors compare three hedge ratios dynamically, in order to obtain the portfolio that needs the least delta hedge. Findings – The model enables the reduction of the amount of portfolio rebalancing and therefore reduces the cost of MSR portfolio hedging. Practical implications – The paper develops the gamma‐hedge‐ratio function for each of the three securities. The lowest gamma corresponds to the hedged portfolio that needs the least re‐balancing. Originality/value – This paper is innovative with the introduction of a delta‐hedge‐ratio function of interest and prepayment rates.