When setting the parameters for structured products in FX hedging, particularly those with multiple option legs, practitioners face a multitude of challenges:
Strike Price: Where should the strike be set to minimize costs without rendering the option out-of-the-money (OTM)?
Leverage: How should leverage be adjusted to maximize hedging efficiency or “bang for the buck”?
Comparison: How can different parameter sets be effectively measured against each other?
Without assistance, these questions quickly become unmanageable. A simulation engine can provide significant insights, showing the distribution, variance, and mean of specific parameter combinations. However, relying on random experimentation is highly inefficient, and even promising solutions may not be optimal. This is where machine learning in FX hedging becomes indispensable.
Optimization in FX Hedging
It is easy for a program to try many combinations of parameters. The program needs to be able to measure a metric for success, some function that we try to minimize or maximize. Optimization programs work with what are called loss functions. The program then naturally tries to minimize loss. A fictitious loss function can be visualized for just two parameters in a 3D graph such as in fig 1. As you can see, there are various maximums and minimums for this function depending on the value of x and y.
When optimizing hedging parameters, the practitioner generally is trying to do two things:
Maximize the net return, and
Minimize the variance of the outcomes.
We need to combine those two terms into a loss function. We minimize this function by seeking the parameters that produce the lowest point.
An example loss function for combining the maximum mean and minimum standard deviation (volatility) of a simulated distribution given a specific balance between the two is:
Exposure_std_deviation optimization_ratio – exposure_mean (1- optimization_ratio)
While Fig. 1 illustrates a simple case with two parameters, real-world problems often involve 4–6 parameters, making visualization impossible. Such problems must be solved using mathematical optimization techniques.
Solving a Loss Function with Multiple Parameters
There are many different types of optimization algorithms, each with its unique advantages and disadvantages. For this problem, we have a particular challenge. Just like in Fig 1, our loss function may have several ‘local’ minimums, only one of which will be the lowest, the global minimum. Many algorithms can get ‘trapped’ into a local minimum, and not escape, producing a non-optimal result. One approach to avoiding this is a two-stage optimization.
The first stage is to use an algorithm which is guaranteed to find the general vicinity of the global minima. One such algorithm is called a Random Forest.
Once we have found the neighborhood of the global minima, we can confidently enter the second stage.
The second stage uses robust optimization algos to find the precise bottom within that subspace. One of the most powerful is stochastic gradient descent, shown in Fig 3.
Constrained Optimization
Many times, the practitioner will have various constraints on the final derivative structure. For example, they may have a maximum cost. Or, they may have a sensitivity to tail risk (expressed as a limit to the value of the 25th quartile). They may also require the strike of the long (bought) leg to provide an at-the-money (ATM) protection of a budget rate.
These constraints can be embedded into the optimization algorithm, automatically restricting the solutions to those that both satisfy the minimization and obey the constraints. Fig. 4 demonstrates how optimization respects these constraints, ensuring practical, usable solutions for hedging structured products.
Conclusion
There is a large set of parameters and values that appear in a structured option product. Setting those purely manually is essentially impossible without programming help. You can neither measure performance of some particular set of parameters, nor find the best set of parameters. Utilizing machine learning libraries with various constrained optimization and visualization capabilities, you can:
Performance Comparison: Simulations to evaluate the relative performance of multiple structures.
Goal-Oriented Loss Functions: Tailored loss functions to reflect specific optimization objectives.
Robust Parameter Optimization: Algorithms that efficiently minimize loss functions for optimal hedging performance.
Constraint Compliance: Integration of cost, tail risk, budget rates, and other constraints directly into the optimization process.
Machine learning in FX hedging not only streamlines the process but also ensures superior outcomes, making it a critical tool for currency risk management.
Not leveraging machine learning algorithms for parameter optimization is no longer an option - it’s a necessity in today’s data-driven financial landscape.
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