A New Set of Financial Instruments

20 Pages Posted: 26 Nov 2019

See all articles by Abootaleb Shirvani

Abootaleb Shirvani

Texas Tech University - Department of Mathematics and Statistics

Stoyan V. Stoyanov

Charles Schwab

Svetlozar T. Rachev

Texas Tech University

Frank J. Fabozzi

EDHEC Business School

Date Written: November 14, 2019

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.

Keywords: option pricing, hedging, Merton's jump diffusion model, stochastic volatility model, tail-loss ratio risk measure

JEL Classification: G10, G12, G13

Suggested Citation

Shirvani, Abootaleb and Stoyanov, Stoyan Veselinov and Rachev, Svetlozar T. and Fabozzi, Frank J., A New Set of Financial Instruments (November 14, 2019). Available at SSRN: https://ssrn.com/abstract=3486655 or http://dx.doi.org/10.2139/ssrn.3486655

Abootaleb Shirvani (Contact Author)

Texas Tech University - Department of Mathematics and Statistics ( email )

Lubbock, TX 79409-1042
United States

Stoyan Veselinov Stoyanov

Charles Schwab ( email )

101 Montgomery Street (120K-15)
San Francisco, CA 94104
United States

Svetlozar T. Rachev

Texas Tech University ( email )

2500 Broadway
Lubbock, TX 79409
United States

Frank J. Fabozzi

EDHEC Business School ( email )

France
215 598-8924 (Phone)

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