#2244. Robust replication of volatility and hybrid derivatives on jump diffusions

August 2026publication date
Proposal available till 30-05-2025
4 total number of authors per manuscript3000 $

The title of the journal is available only for the authors who have already paid for
Journal’s subject area:
Applied Mathematics;
Economics and Econometrics;
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4 place - free (for sale)

Abstract:
We price and replicate a variety of claims written on the log price (Formula presented.) and quadratic variation (Formula presented.) of a risky asset, modeled as a positive semimartingale, subject to stochastic volatility and jumps. The pricing and hedging formulas do not depend on the dynamics of volatility process, aside from integrability and independence assumptions; in particular, the volatility process may be non-Markovian and exhibit jumps of unknown distribution. The jump risk may be driven by any finite activity Poisson random measure with bounded jump sizes. As hedging instruments, we use the underlying risky asset, a zero-coupon bond, and European calls and puts with the same maturity as the claim to be hedged. Examples of contracts that we price include variance swaps, volatility swaps, a claim that pays the realized Sharpe ratio, and a call on a leveraged exchange traded fund.
Keywords:
jumps; LETF; path-dependent claims; quadratic variation; realized Sharpe ratio; variance swap; volatility swap

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