# Closed-End Formula for options linked to Target Volatility Strategies

## TL;DR

This paper develops closed-form formulas for pricing and hedging options linked to target volatility strategies within a Black-Scholes framework, addressing a gap in the existing literature on structured financial products.

## Contribution

It introduces the first closed-end formulas for VolTarget options, enabling more efficient pricing and hedging in target volatility linked derivatives.

## Key findings

- Closed-form formulas for VolTarget option prices.
- Analytical expressions for key hedging parameters.
- Application within a Black-Scholes setting.

## Abstract

Recent years have seen an emerging class of structured financial products based on options linked to dynamic asset allocation strategies. One of the most chosen approach is the so-called target volatility mechanism. It shifts between risky and riskless assets to control the volatility of the overall portfolio. Even if a series of articles have been already devoted to the analysis of options linked to the target volatility mechanism, this paper is the first, to the best of our knowledge, that tries to develop closed-end formulas for VolTarget options. In particular, we develop closed-end formulas for option prices and some key hedging parameters within a Black and Scholes setting, assuming the underlying follows a target volatility mechanism.