A New Set of Financial Instruments

dc.creatorShirvani, Abootaleb (TTU)
dc.creatorStoyanov, Stoyan V.
dc.creatorRachev, Svetlozar T. (TTU)
dc.creatorFabozzi, Frank J.
dc.description© Copyright © 2020 Shirvani, Stoyanov, Rachev and Fabozzi. cc-by
dc.description.abstractIn 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.
dc.identifier.citationShirvani, A., Stoyanov, S.V., Rachev, S.T., & Fabozzi, F.J.. 2020. A New Set of Financial Instruments. Frontiers in Applied Mathematics and Statistics, 6. https://doi.org/10.3389/fams.2020.606812
dc.subjectMerton’s jump diffusion model
dc.subjectoption pricing
dc.subjectstochastic volatility model
dc.subjecttail-loss ratio risk measure
dc.titleA New Set of Financial Instruments


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