Hedging Strategies for Net Interest Income and Economic Values of Equity

A class of mesh-free algorithms for mathematical finance, machine learning and fluid dynamics

“…We now describe two particular applications of our method for finance problems, and we present first a static hedging strategy, which can be interpreted as a way to get portfolio "protection" agains "negative" events. Our setup will be slightly simplified and we refer to [25] for more general business cases. We thus consider a process X t governed by the stochastic equation (4.1) corresponding, for definiteness, to a D-dimensional martingale log-normal process modeling forward rate swaps.…”

“…These values are computed by the discretization scheme (4.15). In [25] Fair values and their sensitivities are themselves two stochastic processes of interest in the applications, and we now present some of their numerical simulation. In Figure 4.2, the left-hand figure represents the expectation of the EVE process as a function of time, while the right-hand figure shows the sensitivities (at time t = 1) with respect to a particular underlying, called LIB1Y in our model.…”

The Transport‐based Mesh‐free Method: A Short Review

“…is called the forward value of the instrument at time s. Solving the Kolmogorov equations for a given instrument allows one to compute not only its price-which is P(0, y) = P(0, y)| (t,x)=(0,y) in the above setting-but also all of the fair value surface (t, x)  → P(t, x) (for all t ≥ 0 and x ∈ ℝ D ). This latter observation is important in an operational context, since all standard risk measures can be determined from the knowledge of this surface, such as risk measures of internal or regulatory nature, or optimal investment strategies: for instance, American exercising, or sophisticated hedging strategies based on sensitivities [11].…”

“…We point out that we can also treat a broad set of partial derivative operators and, for instance, forward sensitivities: ∇P(s) approximates ∇ y P(t, y n (t)) 1≤n≤N . (5.5) This allows us to compute, for instance, hedging strategies [11]. We can also treat more complex operators such as the Hessian operator or the Helmholtz-Hodge decomposition, which are important in (for instance) fluid dynamics.…”

“…The proposed method was tested extensively [7][8][9] in several academic tests. A business case in asset and liability management using the so-called Libor market model [2] was then treated in [11]. It consists of a decision support tool for determining interest rate hedging strategies based on sensitivity reduction of the net interest margin (NII), as well as the economic value (EVE), to interest rates, under various operational constraints.…”