Papers, wiki, Option Blackboard, encyclopedia, and cards.
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…
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…
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and our implied volatility approximations are fully explicit (ie, they require no special functions, no infinite series and no numerical integration). As such, approximate prices can be …
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…
We consider the problem of calculating risk-neutral implied volatilities of European options without relying on option mid prices but solely on bid and ask prices. We provide an approach, based on the conic finance paradigm, that allows to uniquely strip risk-neutral implied volatilities from bid and ask quotes, and that does not require restrictive assumptions. Our methodology also allows to jointly calculate the im…
Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and risk-analysis applications. We break this circularity with a pipeline in which implied volatility emerges as an output of a structural model of equity returns. A Jump Hidden Markov …
This paper investigates short-term behaviors of implied volatility of derivatives written on indexes in equity markets when the index processes are constructed by using a ranking procedure. Even in simple market settings where stock prices follow geometric Brownian motion dynamics, the ranking mechanism can produce the observed term structure of at-the-money (ATM) implied volatility skew for equity indexes. Our propo…
In this study, we predict next-day movements of stock end-of-day implied volatility using random forests. Through an ablation study, we examine the usefulness of different sources of predictors and expose the value of attention and sentiment features extracted from Twitter. We study the approach on a stock universe comprised of the 165 most liquid US stocks diversified across the 11 traditional market sectors using a…
Recent literature seek to forecast implied volatility derived from equity, index, foreign exchange, and interest rate options using latent factor and parametric frameworks. Motivated by increased public attention borne out of the financialization of futures markets in the early 2000s, we investigate if these extant models can uncover predictable patterns in the implied volatility surfaces of the most actively traded …
In this paper we develop a novel neural network model for predicting implied volatility surface. Prior financial domain knowledge is taken into account. A new activation function that incorporates volatility smile is proposed, which is used for the hidden nodes that process the underlying asset price. In addition, financial conditions, such as the absence of arbitrage, the boundaries and the asymptotic slope, are emb…
We consider implied volatilities in asset pricing models, where the discounted underlying is a strict local martingale under the pricing measure. Our main result gives an asymptotic expansion of the right wing of the implied volatility smile and shows that the strict local martingale property can be determined from this expansion. This result complements the well-known asymptotic results of Lee and Benaim-Friz, which…
This paper examines the possibility of using derivative-implied risk premia to explain stock returns. The rapid development of derivative markets has led to the possibility of trading various kinds of risks, such as credit and interest rate risk, separately from each other. This paper uses credit default swaps and equity options to determine risk premia which are then used to form portfolios that are regressed agains…
One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS). The usual approach consists of Þtting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data. However, recent empirical evidence suggests that the parameters characterizing the IVS change over time. In this paper we study whe…
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…
The computation of Black-Scholes implied volatility is a fundamental task in quantitative finance, underpinning option valuation, model calibration and risk management. Although implied volatility is routinely used in practice, the inversion of the Black-Scholes pricing formula remains a challenging numerical problem, particularly in asymptotic regimes corresponding to extreme option prices, strikes or maturities, wh…
W-shaped smiles appear in near-expiry options around binary events such as earnings, and have been associated with bimodal risk-neutral densities. The three-parameter eSSVI slice cannot produce them. This paper defines WSVI, a parametric family for implied volatility that admits negative at-the-forward curvature and bimodal implied densities, and develops its static no-arbitrage structure. The construction factorizes…
We propose an arbitrage-aware latent flow-matching framework for unconditional implied volatility surface generation. The method first compresses high-dimensional surfaces into a low-dimensional latent space using a variational autoencoder regularized by differentiable calendar-spread, call-spread and butterfly-arbitrage penalties. A flow-matching model then learns to transport a Gaussian prior toward the empirical l…
A CTA that is structurally short implied volatility — harvesting VRP with futures options, and owning a jump left tail.
Black-Scholes is the European option formula under lognormal spot, constant vol, and continuous hedging — a quoting convention more than a belief about the world.
Implied volatility is the σ you plug into Black-Scholes to match the market price — a quote of the option, not a forecast you must believe.
Implied Volatility Surface — Strike and tenor structure of implied vol, the core object for vol trading and risk.
The MOVE Index tracks implied volatility in the U.S. Treasury market and serves as a benchmark for rates uncertainty and macro stress.
Skew measures the relative richness of downside versus upside implied volatility, helping track hedging demand and asymmetry in market risk pricing.
Vega is the sensitivity of option value to implied volatility — the vol-dollar you are long or short.
Vega Exposure — Sensitivity to implied volatility changes — core risk for vol books and structured products.
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 Carry Trade — Selling implied vol or rolling VIX futures in contango — crowded but regime-sensitive.
Volatility Smile — Strike-dependent implied vol pattern reflecting crash and demand premia.
FX Implied Volatility — Option-implied uncertainty for currency pairs, key for hedging and risk budgeting.
Long the convertible and short the delta in the stock — harvest cheap implied vol / credit, with funding and squeeze risk.
Sell implied volatility and buy realized — harvest the gap that insurance buyers pay, with a jump left tail.
Long the convertible and short the delta in the stock — harvest cheap implied vol / credit, with funding and squeeze risk.
A CTA that is structurally short implied volatility — harvesting VRP with futures options, and owning a jump left tail.
FX Implied Volatility — Option-implied uncertainty for currency pairs, key for hedging and risk budgeting.
Implied volatility is the σ you plug into Black-Scholes to match the market price — a quote of the option, not a forecast you must believe.
Implied Volatility Surface — Strike and tenor structure of implied vol, the core object for vol trading and risk.
The MOVE Index tracks implied volatility in the U.S. Treasury market and serves as a benchmark for rates uncertainty and macro stress.
Skew measures the relative richness of downside versus upside implied volatility, helping track hedging demand and asymmetry in market risk pricing.
Vega is the sensitivity of option value to implied volatility — the vol-dollar you are long or short.
Vega Exposure — Sensitivity to implied volatility changes — core risk for vol books and structured products.
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 Carry Trade — Selling implied vol or rolling VIX futures in contango — crowded but regime-sensitive.
Sell implied volatility and buy realized — harvest the gap that insurance buyers pay, with a jump left tail.
Volatility Smile — Strike-dependent implied vol pattern reflecting crash and demand premia.