Papers, wiki, Option Blackboard, encyclopedia, and cards.
We revisit the problem of pricing options with historical volatility estimators. We do this in the context of a generalized GARCH model with multiple time scales and asymmetry. It is argued that the reason for the observed volatility risk premium is tail risk aversion. We parametrize such risk aversion in terms of three coefficients: convexity, skew and kurtosis risk premium. We propose that option prices under the r…
We investigate whether the volatility risk premium is negative by examining the statistical properties of delta-hedged option portfolios (buy the option and hedge with stock). Within a stochastic volatility framework, we demonstrate a correspondence between the sign and magnitude of the volatility risk premium and the mean delta-hedged portfolio returns. Using a sample of S&P 500 index options, we provide emp…
The accumulation of trading experience and empirical evidence since the original Black-Scholes (BS) model was developed, have made it increasingly evident that volatility is not a constant parameter, as BS assumed, but stochastic. With a second random factor associated with volatility affecting security returns, it would not be surprising if investors cared about bearing risk related to that factor. And there is cons…
Recent evidence suggests that the parameters characterizing the implied volatility surface (IVS) in option prices are unstable. We study whether the resulting predictability patterns may be exploited. In a first stage we model the surface along cross-sectional moneyness and maturity dimensions. In a second stage we model the dynamics of the first-stage coefficients. We find that the movements of the S&P 500 IVS a…
Abstract This study employs a non-parametric approach to investigate the volatility risk premium in the over-the-counter currency option market. Using a large database of daily delta-neutral straddle quotes in four major currencies—the British pound, the euro, the Japanese yen, and the Swiss franc—we find that volatility risk is priced in all four currencies across different option maturities. We find that the volati…
In this study, we constructed daily high-frequency sentiment data and used the VAR method to attempt to predict the next day's implied volatility surface. We utilized 630,000 text data entries from the East Money Stock Forum from 2014 to 2023 and employed deep learning methods such as BERT and LSTM to build daily market sentiment indicators. By applying FFT and EMD methods for sentiment decomposition, we found that h…
We propose a new model for the forecasting of both the implied volatility surfaces and the underlying asset price. In the spirit of Guyon and Lekeufack (2023) who are interested in the dependence of volatility indices (e.g. the VIX) on the paths of the associated equity indices (e.g. the S\&P 500), we first study how vanilla options implied volatility can be predicted using the past trajectory of the underlying asset…
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…
This paper examines how shocks to currency volatilities predict exchange rates. Using option-implied volatilities, we construct a dynamic, directed network of volatility connections. Currencies that transmit more volatility shocks, which control for common correlation, earn lower excess returns. Buying the weakest and selling the strongest transmitters delivers high risk-adjusted performance, driven by spot exchange …
We test various volatility models using the Bitcoin spot price series. Our models include HIST, EMA ARCH, GARCH, and EGARCH, models. Both of our in-sample-fit and out-of-sample-forecast results suggest that GARCH and EGARCH models perform much better than other models. Moreover, the EGARCH model's asymmetric term is positive and insignificant, which suggests that Bitcoin prices lack the asymmetric volatility response…
We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets. Both the asset value and the volatility processes are correlated through systemic Brownian motions, with default determined by the asset value reaching a lower boundary. We prove that if our volatility models are picked from a class of mean-reverting diffusions, the system converges as the portfolio become…
Low-frequency historical data, high-frequency historical data and option data are three major sources, which can be used to forecast the underlying security's volatility. In this paper, we propose two econometric models, which integrate three information sources. In GARCH-Itô-OI model, we assume that the option-implied volatility can influence the security's future volatility, and the option-implied volatility is tre…
We derive representations of local risk-minimization of call and put options for Barndorff-Nielsen and Shephard models: jump type stochastic volatility models whose squared volatility process is given by a non-Gaussian rnstein-Uhlenbeck process. The general form of Barndorff-Nielsen and Shephard models includes two parameters: volatility risk premium $β$ and leverage effect $ρ$. Arai and Suzuki (2015, arxiv:1503.0858…
This paper attempts to explain the credit default swap (CDS) premium, using a novel approach to identify the volatility and jump risks of individual firms from high-frequency equity prices. Our empirical results suggest that the volatility risk alone predicts 48% of the variation in CDS spread levels, whereas the jump risk alone forecasts 19%. After controlling for credit ratings, macroeconomic conditions, and firms'…
In this paper, we develop an open-economy macroeconomic model of a Proof-of-Stake network to analyze nominal token-price dynamics and the systemic effects of speculative capital. We first consider a network populated solely by active utility users, who finance network activity through a steady exogenous inflow of fiat currency. We prove the existence of a unique, globally asymptotically stable steady-state equilibriu…
This paper characterizes all continuous price processes that are consistent with current option prices. This extends Derman and Kani (1994) , Dupire (1994 , 1997 ), and Rubinstein (1994) , who only consider processes with deterministic volatility. Our characterization implies a volatility forecast that does not require a specific model, only current option prices. We show how arbitrary volatility processes can be adj…
Abstract Our objective in this paper is to examine whether one can use option-implied information to improve the selection of mean-variance portfolios with a large number of stocks, and to document which aspects of option-implied information are most useful to improve their out-of-sample performance. Portfolio performance is measured in terms of volatility, Sharpe ratio, and turnover. Our empirical evidence shows tha…
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…
VIX term structure tracks the shape of volatility futures across maturities and helps identify whether the market is pricing stable conditions or near-term stress.
Skew measures the relative richness of downside versus upside implied volatility, helping track hedging demand and asymmetry in market risk pricing.
The 2s10s Treasury curve measures the spread between 10-year and 2-year Treasury yields and is a key indicator of growth expectations, policy path, and term structure dynamics.
VIX Index measures implied volatility in S&P 500 options and is widely used as a shorthand for equity market fear and risk aversion.
Volatility Regime (Quant).
The MOVE Index tracks implied volatility in the U.S. Treasury market and serves as a benchmark for rates uncertainty and macro stress.
Nonfarm Payrolls — The headline US jobs report that routinely moves rates, FX, and equity index volatility.
Core PCE Inflation — The Fed's preferred inflation gauge, stripping volatile food and energy components.
Implied Volatility Surface — Strike and tenor structure of implied vol, the core object for vol trading and risk.
Variance Risk Premium — Gap between implied and realized volatility that systematic vol sellers harvest.
Vega Exposure — Sensitivity to implied volatility changes — core risk for vol books and structured products.
Theta Decay — Time decay of option premium, the carry engine for systematic short-vol strategies.
Volatility of Volatility — Uncertainty about future volatility, critical for tail hedges and vol-of-vol products.
Realized Volatility — Historical return variation that determines PnL for delta-hedged option positions.
GARCH Volatility Model — Conditional heteroskedasticity framework for forecasting volatility clusters.
Local Volatility Model — Strike-dependent diffusion used to fit vanilla surfaces consistently.
Stochastic Volatility Model — Models where volatility itself is random, capturing smile dynamics and VRP.
SVI Parameterization — Arbitrage-aware parameterization of volatility smiles for interpolation and trading.
Volatility Arbitrage — Trading discrepancies between implied, realized, and cross-asset volatility.
Dispersion Trading — Index vol versus single-name vol — a pure play on implied correlation.
Variance Swap — Contract paying realized variance versus strike, core institutional vol transfer instrument.
VIX Futures Term Structure — Curve shape driving roll yield for vol ETNs and systematic short-vol carry.
Volatility Carry Trade — Selling implied vol or rolling VIX futures in contango — crowded but regime-sensitive.
Gamma Scalping — Trading realized vol against a long gamma book via delta hedging.
Iron Condor Structure — Short vol range trade expressing view of subdued movement between strikes.
Calendar Spread — Relative vol trade across expiries exploiting term structure dislocations.
FX Implied Volatility — Option-implied uncertainty for currency pairs, key for hedging and risk budgeting.
Low Volatility Anomaly — Empirical outperformance of low-beta stocks, crowded in risk-off regimes.
Target Volatility — Dynamic scaling of exposure to maintain constant portfolio volatility.
Tail Risk Hedging — Explicit protection against left-tail moves via options, vol, or convex instruments.
Market Depth — Volume available near best prices — collapses precede volatility spikes.
Dark Pool Volume — Off-exchange trading share influencing price discovery and lit-market toxicity.
Intraday Volatility — Within-day return variation informing execution timing and gamma scalping.
Implied Volatility — Market-implied expected volatility embedded in option prices.
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.
Code-linked scanner pattern that maps front-vol stress, ATM IV, and dealer gamma context into Blackboard + Options Lab actions.
Vol-structure note for classifying rich vs cheap ATM IV and surface dispersion before choosing credit or debit templates.
Strategy bridge from Blackboard scanner cards into Options Lab templates without implying live broker execution.
Educational IV × Greeks × surface sandbox already mounted on the Blackboard — synthetic regimes for pedagogy beside the live scanner.
Amihud Illiquidity — Average absolute return per unit volume as an illiquidity proxy.
Butterfly FX Vol (FX).
Calendar Spread — Relative vol trade across expiries exploiting term structure dislocations.
Core PCE Inflation — The Fed's preferred inflation gauge, stripping volatile food and energy components.
Crypto Realized Vol Regime — Shifts in realized volatility that redefine sizing and carry.
CVOL Index (Derivatives).
Dark Pool Volume — Off-exchange trading share influencing price discovery and lit-market toxicity.
Dispersion Trading — Index vol versus single-name vol — a pure play on implied correlation.
Event Vol Crush (Derivatives).
Forward Points AUDUSD — Currency valuation, flow, or FX-vol concept for FX desks.
Forward Points EURUSD — Currency valuation, flow, or FX-vol concept for FX desks.
Forward Points GBPUSD — Currency valuation, flow, or FX-vol concept for FX desks.
Forward Points NZDUSD — Currency valuation, flow, or FX-vol concept for FX desks.
Forward Points USDBRL — Currency valuation, flow, or FX-vol concept for FX desks.
Forward Points USDCAD — Currency valuation, flow, or FX-vol concept for FX desks.
Forward Points USDCHF — Currency valuation, flow, or FX-vol concept for FX desks.
Forward Points USDCNH — Currency valuation, flow, or FX-vol concept for FX desks.
Forward Points USDINR — Currency valuation, flow, or FX-vol concept for FX desks.
Forward Points USDJPY — Currency valuation, flow, or FX-vol concept for FX desks.
Forward Points USDKRW — Currency valuation, flow, or FX-vol concept for FX desks.
Forward Points USDMXN — Currency valuation, flow, or FX-vol concept for FX desks.
Forward Points USDTRY — Currency valuation, flow, or FX-vol concept for FX desks.
Forward Points USDZAR — Currency valuation, flow, or FX-vol concept for FX desks.
FX Implied Volatility — Option-implied uncertainty for currency pairs, key for hedging and risk budgeting.
A funding-stress monitor can warn before equity volatility reprices.
A liquidity premium monitor can separate default risk from liquidity-driven spread widening.
A card for handling fast markets, wide spreads, liquidity air pockets, and broken execution assumptions.