A New Set of Financial Instruments

TL;DR

This paper introduces perpetual derivatives as a new set of financial instruments tailored for hedging in complex market models, providing novel pricing equations and a potential early warning system for market crashes.

Contribution

It proposes perpetual derivatives specifically designed for hedging in jump-diffusion and stochastic volatility markets, along with new pricing equations and a risk measure for market crash prediction.

Findings

Perpetual derivatives are effective for hedging complex market models.

New pricing equations are derived for these instruments.

The tail-loss ratio measure can serve as an early market crash indicator.

Abstract

In complete markets, there are risky assets and a riskless asset. It is assumed that the riskless asset and the risky asset are traded continuously in time and that the market is frictionless. In this paper, we propose a new method for hedging derivatives assuming that a hedger should not always rely on trading existing assets that are used to form a linear portfolio comprised of the risky asset, the riskless asset, and standard derivatives, but rather should design a set of specific, most-suited financial instruments for the hedging problem. We introduce a sequence of new financial instruments best suited for hedging jump-diffusion and stochastic volatility market models. The new instruments we introduce are perpetual derivatives. More specifically, they are options with perpetual maturities. In a financial market where perpetual derivatives are introduced, there is a new set of partial and partial-integro differential equations for pricing derivatives. Our analysis demonstrates that the set of new financial instruments together with a risk measure called the tail-loss ratio measure defined by the new instrument's return series can be potentially used as an early warning system for a market crash.