TY - JOUR

T1 - A New Set of Financial Instruments

AU - Shirvani, Abootaleb

AU - Stoyanov, Stoyan V.

AU - Rachev, Svetlozar T.

AU - Fabozzi, Frank J.

N1 - Publisher Copyright:
© Copyright © 2020 Shirvani, Stoyanov, Rachev and Fabozzi.

PY - 2020/11/26

Y1 - 2020/11/26

N2 - 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.

AB - 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.

KW - Merton’s jump diffusion model

KW - hedging

KW - option pricing

KW - stochastic volatility model

KW - tail-loss ratio risk measure

UR - http://www.scopus.com/inward/record.url?scp=85097489009&partnerID=8YFLogxK

U2 - 10.3389/fams.2020.606812

DO - 10.3389/fams.2020.606812

M3 - Article

AN - SCOPUS:85097489009

SN - 2297-4687

VL - 6

JO - Frontiers in Applied Mathematics and Statistics

JF - Frontiers in Applied Mathematics and Statistics

M1 - 606812

ER -