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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 …
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…
In this paper, a new numerical method based on adaptive gradient descent optimizers is provided for computing the implied volatility from the Black-Scholes (B-S) option pricing model. It is shown that the new method is more accurate than the close form approximation. Compared with the Newton-Raphson method, the new method obtains a reliable rate of convergence and tends to be less sensitive to the beginning point.
It is well know that, in the short maturity limit, the implied volatility approaches the integral harmonic mean of the local volatility with respect to log-strike, see [Berestycki et al., Asymptotics and calibration of local volatility models, Quantitative Finance, 2, 2002]. This paper is dedicated to a complementary model-free result: an arbitrage-free implied volatility in fact is the harmonic mean of a positive fu…
In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlying's return, whereas gradual changes in implied volatility would indicate market inefficiency. Using minute-by-minute data on S&P 500 index options, we provide evidence regarding delayed and gradual movements in implied volatility after 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…
This paper explores the effectiveness of high-frequency options trading strategies enhanced by advanced portfolio optimization techniques, investigating their ability to consistently generate positive returns compared to traditional long or short positions on options. Utilizing SPY options data recorded in five-minute intervals over a one-month period, we calculate key metrics such as Option Greeks and implied volati…
This paper derives explicit formulas for both the small and large time limits of the implied volatility in the minimal market model. It is shown that interest rates do impact on the implied volatility in the long run even though they are negligible in the short time limit.
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…
We develop a liquidity-sensitive multivariate volatility framework to improve the estimation of time-varying covariance structures under market frictions. We introduce two novel portfolio-level liquidity measures, liquidity jump and liquidity diffusion, which capture magnitude and volatility of liquidity fluctuation, respectively, and construct liquidity-adjusted return and volatility that reflect real-time liquidity…
The principal portfolios of the standard Capital Asset Pricing Model (CAPM) are analyzed and found to have remarkable hedging and leveraging properties. Principal portfolios implement a recasting of any correlated asset set of N risky securities into an equivalent but uncorrelated set when short sales are allowed. While a determination of principal portfolios in general requires a detailed knowledge of the covariance…
Market liquidity plays a vital role in the field of market micro-structure, because it is the vigor of the financial market. This paper uses a variable called convexity to measure the potential liquidity provided by order-book. Based on the high-frequency data of each stock included in the SSE (Shanghai Stock Exchange) 50 Index for the year 2011, we report several statistical properties of convexity and analyze the a…
Automated markets increasingly route order flow from learning trading agents through automated market makers (AMMs). We model trader archetypes as AI agents defined by their reward functions and analyze the feedback they create on a constant-product AMM. Herd-dominated and arbitrage-dominated markets of equal size have identical return distributions and turnover, so no rule based on volatility, value-at-risk, stress …
Mean-variance analysis is widely used in portfolio management to identify the best portfolio that makes an optimal trade-off between expected return and volatility. Yet, this method has its limitations, notably its vulnerability to estimation errors and its reliance on historical data. While shrinkage estimators and factor models have been introduced to improve estimation accuracy through bias-variance trade-offs, an…
Market Microstructure is the investigation of the process and protocols that govern the exchange of assets with the objective of reducing frictions that can impede the transfer. In financial markets, where there is an abundance of recorded information, this translates to the study of the dynamic relationships between observed variables, such as price, volume and spread, and hidden constituents, such as transaction co…
Due to the lack of reliable market information, building financial term-structures may be associated with a significant degree of uncertainty. In this paper, we propose a new term-structure interpolation method that extends classical spline techniques by additionally allowing for quantification of uncertainty. The proposed method is based on a generalization of kriging models with linear equality constraints (market-…
A CTA that is structurally short implied volatility — harvesting VRP with futures options, and owning a jump left tail.
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.
FX Implied Volatility — Option-implied uncertainty for currency pairs, key for hedging and risk budgeting.
Sell implied volatility and buy realized — harvest the gap that insurance buyers pay, with a jump left tail.
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.
Sell implied volatility and buy realized — harvest the gap that insurance buyers pay, with a jump left tail.