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For quantitative trading risk management purposes, we present a novel idea: the realized local volatility surface. Concisely, it stands for the conditional expected volatility when sudden market behaviors of the underlying occur. One is able to explore risk management usages by following the orthotical Delta-Gamma dynamic hedging framework. The realized local volatility surface is, mathematically, a generalized Wiene…
We undertake a systematic comparison between implied volatility, as represented by VIX (new methodology) and VXO (old methodology), and realized volatility. We compare visually and statistically distributions of realized and implied variance (volatility squared) and study the distribution of their ratio. We find that the ratio is best fitted by heavy-tailed -- lognormal and fat-tailed (power-law) -- distributions, de…
We analyze realized volatilities constructed using high-frequency stock data on the Tokyo Stock Exchange. In order to avoid non-trading hours issue in volatility calculations we define two realized volatilities calculated separately in the two trading sessions of the Tokyo Stock Exchange, i.e. morning and afternoon sessions. After calculating the realized volatilities at various sampling frequencies we evaluate the b…
We study market microstructure noise in high-frequency data and analyze its implications for the realized variance (RV) under a general specification for the noise. We show that kernel-based estimators can unearth important characteristics of market microstructure noise and that a simple kernel-based estimator dominates the RV for the estimation of integrated variance (IV). An empirical analysis of the Dow Jones Indu…
We present a new class of Bayesian dynamic models for bivariate price-realized volatility time series in financial forecasting. A novel dynamic gamma process model adopted for realized volatility is integrated with traditional Bayesian dynamic linear models (DLMs) for asset price series. This represents reduced-form volatility leverage and feedback effects through use of realized volatility proxies in conditional DLM…
We show that the Realized GARCH model yields close-form expression for both the Volatility Index (VIX) and the volatility risk premium (VRP). The Realized GARCH model is driven by two shocks, a return shock and a volatility shock, and these are natural state variables in the stochastic discount factor (SDF). The volatility shock endows the exponentially affine SDF with a compensation for volatility risk. This leads t…
An automated market maker (AMM) provides a method for creating a decentralized exchange on the blockchain. For this purpose, individual investors lend liquidity to the AMM pool in exchange for a stream of fees earned from its operations as a market maker. Within this work, we reinterpret the loss-versus-rebalancing as the implied fee stream generated by an AMM so that a risk-neutral investor is indifferent in the dec…
The composition of natural liquidity has been changing over time. An analysis of intraday volumes for the S&P500 constituent stocks illustrates that (i) volume surprises, i.e., deviations from their respective forecasts, are correlated across stocks, and (ii) this correlation increases during the last few hours of the trading session. These observations could be attributed, in part, to the prevalence of portfolio tra…
This study investigates whether regime-dependent volatility forecasting and machine-learning-based return prediction can be jointly integrated to improve both statistical forecasting performance and economic strategy outcomes in equity markets. Using high-frequency CSI 300 Index data from 2005 to 2023, a sequential twostage framework is developed. In the first stage, realized volatility is modeled using regime-augmen…
A credit rating of AAA asserts near-certainty of repayment. This paper asks whether the pre-crisis information environment could have supported that assertion for structured products. Bayes' theorem implies that any reliability target requires a minimum level of statistical discrimination between instruments that will repay and those that will not. At structured-finance base rates, a four-nines reliability target dem…
Accurate volatility forecasts are vital in modern finance for risk management, portfolio allocation, and strategic decision-making. However, existing methods face key limitations. Fully multivariate models, while comprehensive, are computationally infeasible for realistic portfolios. Factor models, though efficient, primarily use static factor loadings, failing to capture evolving volatility co-movements when they ar…
This paper introduces a global stock market volatility forecasting model that enhances forecasting accuracy and practical utility in real-world financial decision-making by integrating dynamic graph structures and encompassing all active trading days of different stock markets. The model employs a spatial-temporal graph neural network architecture to capture the volatility spillover effect, where shocks in one market…
Automated Market Makers based on concentrated liquidity, such as Uniswap v3, significantly improve capital efficiency but expose Liquidity Providers (LPs) to adverse selection costs, formalized as Loss-Versus-Rebalancing (LVR). While theoretical literature quantifies these costs, the interplay between realistic blockchain microstructure and endogenous pricing mechanisms remains under-explored. This paper develops a g…
The basic financial purpose of an enterprise is maximization of its value. Trade credit management should also contribute to realization of this fundamental aim. Many of the current asset management models that are found in financial management literature assume book profit maximization as the basic financial purpose. These book profitbased models could be lacking in what relates to another aim (i.e., maximization of…
We provide a large-scale empirical audit of DEX routing using 2.98 million WETH-USDC swaps on Ethereum. Comparing realized routes with optimized benchmarks, we measure an average shortfall of 2.02 bps per trade or \$24 million. To attribute losses, we introduce three reproducible optimal benchmarks: a Support-Constrained Optimum (SCO) that evaluates split quality conditional on the pools actually used; a Full-Venue O…
We study a one period limit order market with informed traders, noise traders, and competitive liquidity suppliers, in which the number of informed traders is random. Liquidity suppliers know the distribution of the informed trader count, but not its realization, and therefore face uncertainty about both the presence and the intensity of informed trading. We characterize equilibrium by a fixed point integral equation…
As cryptocurrency evolved, new financial instruments, such as lending and borrowing protocols, currency exchanges, fungible and non-fungible tokens (NFT), staking and mining protocols have emerged. A financial ecosystem built on top of a blockchain is supposed to be fair and transparent for each participating actor. Yet, there are sophisticated actors who turn their domain knowledge and market inefficiencies to their…
Regarding the intraday sequence of high frequency returns of the S&P index as daily realizations of a given stochastic process, we first demonstrate that the scaling properties of the aggregated return distribution can be employed to define a martingale stochastic model which consistently replicates conditioned expectations of the S&P 500 high frequency data in the morning of each trading day. Then, a more general fo…
Variance Risk Premium — Gap between implied and realized volatility that systematic vol sellers harvest.
Realized Volatility — Historical return variation that determines PnL for delta-hedged option positions.
Volatility Arbitrage — Trading discrepancies between implied, realized, and cross-asset volatility.
Variance Swap — Contract paying realized variance versus strike, core institutional vol transfer instrument.
Gamma Scalping — Trading realized vol against a long gamma book via delta hedging.
Historical Volatility — Realized return dispersion used as a benchmark versus implied.
Implied Realized Spread — Gap between implied and realized vol that defines carry for short-vol books.
Volatility Risk Premium — Average excess of implied over subsequent realized volatility.
Correlation Trading — Trading implied versus realized correlation in index members.
Vol Targeting Overlay — Scaling exposure to hold portfolio realized vol near a budget.
Ex Post Risk (Systems).
Unrealized Losses Banks — Mark losses on securities books in rising-rate regimes.
Realized Kernel (Quant).
Crypto Realized Vol Regime — Shifts in realized volatility that redefine sizing and carry.
AOCI Capital Filter — Treatment of unrealized AFS gains/losses in regulatory capital.
Realized Vol 1M — Options and volatility market structure concept used in hedging books.
Realized Vol 3M — Options and volatility market structure concept used in hedging books.
Realized Vol 6M — Options and volatility market structure concept used in hedging books.
Realized Vol 1Y — Options and volatility market structure concept used in hedging books.
Realized Vol 2Y — Options and volatility market structure concept used in hedging books.
Realized Vol 5Y — Options and volatility market structure concept used in hedging books.
Realized Vol 7Y — Options and volatility market structure concept used in hedging books.
Realized Vol 10Y — Options and volatility market structure concept used in hedging books.
Realized Vol 20Y — Options and volatility market structure concept used in hedging books.
Realized Vol 30Y — Options and volatility market structure concept used in hedging books.
Realized Vol front — Options and volatility market structure concept used in hedging books.
Realized Vol belly — Options and volatility market structure concept used in hedging books.
Realized Vol long-end — Options and volatility market structure concept used in hedging books.
Realized Vol ultra-long — Options and volatility market structure concept used in hedging books.
Realized Vol SPX — Options and volatility market structure concept used in hedging books.
Realized Vol NDX — Options and volatility market structure concept used in hedging books.
Realized Vol RUT — Options and volatility market structure concept used in hedging books.
Realized Vol SX5E — Options and volatility market structure concept used in hedging books.
Realized Vol NKY — Options and volatility market structure concept used in hedging books.
Realized Vol single-name — Options and volatility market structure concept used in hedging books.
Realized Vol index — Options and volatility market structure concept used in hedging books.
AOCI Capital Filter — Treatment of unrealized AFS gains/losses in regulatory capital.
Correlation Trading — Trading implied versus realized correlation in index members.
Crypto Realized Vol Regime — Shifts in realized volatility that redefine sizing and carry.
The risk that your trade logic is right but your realized fill, slippage, timing, or spread destroys the expected edge.
Gamma Scalping — Trading realized vol against a long gamma book via delta hedging.
Historical Volatility — Realized return dispersion used as a benchmark versus implied.
Implied Realized Spread — Gap between implied and realized vol that defines carry for short-vol books.
Realized Kernel (Quant).
Realized Vol 10Y — Options and volatility market structure concept used in hedging books.
Realized Vol 1M — Options and volatility market structure concept used in hedging books.
Realized Vol 1Y — Options and volatility market structure concept used in hedging books.
Realized Vol 20Y — Options and volatility market structure concept used in hedging books.
Realized Vol 2Y — Options and volatility market structure concept used in hedging books.
Realized Vol 30Y — Options and volatility market structure concept used in hedging books.
Realized Vol 3M — Options and volatility market structure concept used in hedging books.
Realized Vol 5Y — Options and volatility market structure concept used in hedging books.
Realized Vol 6M — Options and volatility market structure concept used in hedging books.
Realized Vol 7Y — Options and volatility market structure concept used in hedging books.
Realized Vol ATM — Options and volatility market structure concept used in hedging books.
Realized Vol belly — Options and volatility market structure concept used in hedging books.
Realized Vol front — Options and volatility market structure concept used in hedging books.
Realized Vol index — Options and volatility market structure concept used in hedging books.
Realized Vol long-end — Options and volatility market structure concept used in hedging books.
Realized Vol NDX — Options and volatility market structure concept used in hedging books.