UIC Professor Presents “Cross-Over Options” Research at Federal Reserve Board
A new class of derivatives introduces a model-free approach to volatility trading, with implications for financial markets, risk management, and policy.
CO Options
Oleg Bondarenko, professor of finance at UIC Business and director of the International Center for Futures and Derivatives (ICFD), recently presented his research, Cross-Over Options, at the Federal Reserve Board. The solo-authored paper introduces a new class of derivative securities that could reshape how volatility is measured, priced, and traded.
The research has been presented at leading international conferences, including the World Congress of the Econometric Society — held once every five years — and received the Best Paper Award at the Financial Management Association Conference on Derivatives and Volatility. During his visit, Federal Reserve Board economists noted that they actively use Bondarenko’s prior research in their policy work.
Rethinking Volatility Trading
Volatility products — such as OTC variance swaps, futures on realized variance, and VIX derivatives — represent a rapidly growing segment of global financial markets. Yet the tools used to hedge these products are often imperfect, relying on assumptions that break down when prices jump, markets close overnight, or trading is discrete.
Bondarenko’s research addresses a central question:
Is it possible to measure and replicate volatility risk more precisely, without relying on restrictive modeling assumptions?
A New Framework: Cross-Over Options
A New Framework: Cross-Over Options
To answer this question, the paper introduces a novel type of derivative whose value depends on how asset prices evolve over time. Termed cross-over (CO) options, these instruments track each time a price crosses a specified level and accumulate value from those crossing events.
The framework delivers three core contributions:
- A pricing approach that requires no parametric volatility model
- A replication strategy combining standard options with simple, discrete trading in the underlying asset
- A general method for constructing a wide range of volatility-based contracts, with CO options serving as modular building blocks
At the heart of the framework is the Aggregation Property, which allows complex, path-dependent payoffs to be valued as simpler, path-independent contracts.
Key Findings
Key Findings
The findings offer both theoretical advances and practical tools for financial markets.
A simpler way to price complex risk
One of the paper’s most striking results is that the price of a cross-over option is identical to that of a standard out-of-the-money option with the same strike and maturity — regardless of monitoring frequency. This eliminates a major source of complexity in pricing these derivatives.
Model-free replication
The study shows that volatility exposures can be replicated using:
- A static position in standard options
- Discrete trading in the underlying asset
This approach avoids reliance on specific financial models and remains exact even in markets with jumps, gaps, or irregular trading.
New insights into option value
Option prices can be decomposed into two distinct components: a continuous part driven by smooth price movements and a jump component capturing discontinuities such as overnight gaps and weekend closures. This decomposition provides a clearer understanding of the sources of option value.
A new strategy for long-dated options
The paper introduces a method for replicating long-term options using a rolling sequence of short-term contracts. For example, a 10-year option can be replicated by rolling ten 1-year contracts. This is particularly valuable in markets where long-dated options are illiquid or unavailable.
Implications for Practice and Policy
Implications for Practice and Policy
For traders and market makers
- More accurate hedging of volatility products
- Reduced model risk
- Operational simplicity through static replication
For asset managers and investors
- Improved tools for managing volatility exposure
- Greater transparency in how risk is priced
For financial institutions and policymakers
- Better measurement of systemic risk
- More robust frameworks for pricing complex derivatives
A New Foundation for Volatility Trading
A New Foundation for Volatility Trading
Bondarenko’s “Cross-Over Options” introduces a fundamentally new way to think about volatility. By offering a model-free framework that simplifies pricing and enables exact replication, the research bridges theory and practice — providing tools that could reshape modern financial markets.
The paper’s recognition at leading conferences and its presentation at the Federal Reserve Board highlight both its intellectual depth and its real-world significance.