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 -