Distributional Replication

Area of Science:

• Financial Mathematics
• Probability Theory
• Optimization

Background:

• Replicating functions transform random variables to a specified distribution.
• Functions can be assigned prices, leading to optimization problems.
• Hedge fund replication is a relevant financial application.

Purpose of the Study:

• To find the cheapest approximation to a replicating function.
• To analyze the proximity of the optimal approximation to distributional replication and minimum cost.
• To explore the financial implications for hedge fund replication.

Main Methods:

• Optimization under regularity conditions.
• Entropy bounds on candidate approximations.
• Analysis of function pricing and approximation costs.

Main Results:

• The optimal approximation closely achieves distributional replication.
• The optimal approximation closely achieves minimum cost among replicating functions.
• Identified the cheapest portfolio of market index options for hedge fund return replication.

Conclusions:

• The developed method provides an optimal and cost-effective approach to distributional replication.
• The findings offer practical insights for financial markets, particularly in replicating complex financial instruments.
• The study bridges theoretical concepts in probability with applied financial optimization.