Delta hedging a multi‐fixed‐income‐securities portfolio under gamma and vega constraints

Purpose – The purpose of this paper is to present an innovative model that helps create a portfolio of m‐fixed‐income securities, each with the optimal weight, in order for the portfolio to be δ ‐ and γ ‐hedged against small changes in interest rates. Re‐balancing a portfolio on a periodic basis is necessary, but also very costly. The model presented in this paper minimizes the necessity of rebalancing a portfolio, by choosing the optimal δ ‐hedge ratios when constructing the initial portfolio to be hedged against interest rate risk. Design/methodology/approach – In this paper, a general model is developed to obtain the optimal δ hedge for a portfolio of m ‐fixed‐income‐securities ( a 1 , a 2 , a 3 ,…; a i , … , a m ), each, a function of the market interest rate y , such that when the value of each of the individual securities changes up or down, because of changes in market rates y , the total value of the portfolio is unchanged. The delta hedge is developed under the constraint of a zero‐gamma, in order to avoid costs related to the re‐balancing of such portfolio. Findings – An innovative model is developed that helps create a portfolio of m ‐fixed‐income securities, each with the optimal weight, in order for the portfolio to be δ ‐ and γ ‐hedged against small changes in interest rates. Practical implications – The model minimizes the necessity of rebalancing a portfolio, by choosing the optimal δ ‐hedge ratios when constructing the initial portfolio to be hedged against interest rate risk. Originality/value – An innovative model has been developed that helps create a portfolio of m ‐fixed‐income securities, each with the optimal weight, in order for the portfolio to be delta‐ and gamma‐hedged against small changes in interest rates.