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

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.

In this paper, a general model is developed to obtain the optimal δ hedge for a portfolio of m‐fixed‐income‐securities (a₁, a₂, a₃,…; 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.

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.

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.

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.