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arXiv · arXiv q-fin · 2019

Market Price of Trading Liquidity Risk and Market Depth

Price impact of a trade is an important element in pre-trade and post-trade analyses. We introduce a framework to analyze the market price of liquidity risk, which allows us to derive an inhomogeneous Bernoulli ordinary differential equation. We obtain two closed form solutions, one of which reproduces the linear function of the order flow in Kyle (1985) for informed traders. However, when traders are not as asymmetr…

Masaaki Kijima, Christopher Ting

OpenAlex · The Journal of Finance · 2014 · cites 837

A Pyrrhic Victory? Bank Bailouts and Sovereign Credit Risk

ABSTRACT We model a loop between sovereign and bank credit risk. A distressed financial sector induces government bailouts, whose cost increases sovereign credit risk. Increased sovereign credit risk in turn weakens the financial sector by eroding the value of its government guarantees and bond holdings. Using credit default swap (CDS) rates on European sovereigns and banks, we show that bailouts triggered the rise o…

Viral V. Acharya, Itamar Drechsler, Philipp Schnabl

OpenAlex · National Bureau of Economic Research · 2007 · cites 233

How Sovereign is Sovereign Credit Risk?

We study the nature of sovereign credit risk using an extensive sample of CDS spreads for 26 developed and emerging-market countries.Sovereign credit spreads are surprisingly highly correlated, with just three principal components accounting for more than 50 percent of their variation.Sovereign credit spreads are generally more related to the U.S. stock and high-yield bond markets, global risk premia, and capital flo…

Francis A. Longstaff, Jun Pan, Lasse Heje Pedersen, Kenneth J. Singleton

OpenAlex · Journal of Financial and Quantitative Analysis · 2016 · cites 124

Real Economic Shocks and Sovereign Credit Risk

Abstract We provide new empirical evidence that U.S. expected growth and consumption volatility are closely related to the strong comovement in sovereign spreads. We rationalize these findings in an equilibrium model with recursive utility for credit default swap (CDS) spreads. The framework links a reduced-form default process with country-specific sensitivity to expected growth and macroeconomic uncertainty. Exploi…

Patrick Augustin, Roméo Tédongap

arXiv · arXiv · 2014

Option Pricing, Historical Volatility and Tail Risks

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…

Samuel E. Vazquez

OpenAlex · Review of Financial Studies · 2003 · cites 1020

Delta-Hedged Gains and the Negative Market Volatility Risk Premium

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 empirical t…

Gurdip Bakshi, Nikunj Kapadia

OpenAlex · The Journal of Derivatives · 2003 · cites 153

Volatility Risk Premiums Embedded in Individual Equity Options

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…

Gurdip Bakshi, Nikunj Kapadia

OpenAlex · 2002 · cites 74

Portfolio construction and risk budgeting.

CONTENTS This book aims at providing a comprehensive treatment of alternative portfolio construction techniques ranging from traditional mean variance and lower partial moments based methods over Bayesian techniques to more recent developments as portfolio resampling or stochastic programming solutions using scenario optimization. 1. Traditional Portfolio Construction: Selected Issues - Starts with a review of Markow…

Bernd Scherer

OpenAlex · Journal of Financial and Quantitative Analysis · 2005 · cites 60

The Volatility Risk Premium Embedded in Currency Options

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…

Buen Sin Low, Shaojun Zhang

arXiv · arXiv · 2026

Harvesting the Volatility Risk Premium: A Learning-to-Rank Approach

This paper develops the first end-to-end application of cross-sectional learning-to-rank to the S&P 500 weekly options (SPXW) zero-day-to-expiration surface, integrated with margin-aware position sizing, an abstention rule driven by model uncertainty, and a strict out-of-time integrity check. A LightGBM LambdaRank ranker scores a daily nine-strategy cross-section composed of eight delta-targeted short-put positions a…

Maciej Wysocki

arXiv · arXiv · 2025

Sizing the Risk: Kelly, VIX, and Hybrid Approaches in Put-Writing on Index Options

This paper examines systematic put-writing strategies applied to S&P 500 Index options, with a focus on position sizing as a key determinant of long-term performance. Despite the well-documented volatility risk premium, where implied volatility exceeds realized volatility, the practical implementation of short-dated volatility-selling strategies remains underdeveloped in the literature. This study evaluates three pos…

Maciej Wysocki

arXiv · arXiv · 2021

Realized GARCH, CBOE VIX, and the Volatility Risk Premium

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…

Peter Reinhard Hansen, Zhuo Huang, Chen Tong, Tianyi Wang

arXiv · arXiv q-fin · 2018

Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations

We review recent progress in modeling credit risk for correlated assets. We start from the Merton model which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the stock prices are used whose correlations have a strong impact on the loss distribution, particularly on its tails. These correlations are non-stationary which also influences the …

Andreas Mühlbacher, Thomas Guhr

arXiv · arXiv · 2015

Local risk-minimization for Barndorff-Nielsen and Shephard models with volatility risk premium

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…

Takuji Arai

arXiv · arXiv q-fin · 2009

Analytical Framework for Credit Portfolios. Part I: Systematic Risk

Analytical, free of time consuming Monte Carlo simulations, framework for credit portfolio systematic risk metrics calculations is presented. Techniques are described that allow calculation of portfolio-level systematic risk measures (standard deviation, VaR and Expected Shortfall) as well as allocation of risk down to individual transactions. The underlying model is the industry standard multi-factor Merton-type mod…

Mikhail Voropaev

arXiv · arXiv · 2023

A stochastic control perspective on term structure models with roll-over risk

In this paper, we consider a generic interest rate market in the presence of roll-over risk, which generates spreads in spot/forward term rates. We do not require classical absence of arbitrage and rely instead on a minimal market viability assumption, which enables us to work in the context of the benchmark approach. In a Markovian setting, we extend the control theoretic approach of Gombani & Runggaldier (2013) and…

Claudio Fontana, Simone Pavarana, Wolfgang J. Runggaldier

arXiv · arXiv · 2021

Liquidity Stress Testing in Asset Management -- Part 3. Managing the Asset-Liability Liquidity Risk

This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers the modeling of the liability liquidity risk (or funding liquidity), the second dimension is dedicated to the modeling of the asset liquidity risk (or market liquidity), whereas the third dimension considers the management of the asset-liability liquidi…

Thierry Roncalli

Wiki Entities · 36

Bank CDS Index

Bank CDS Index tracks the cost of insuring major bank credit risk and serves as a real-time indicator of banking-system stress and confidence.

Fractional-Reserve Banking

Fractional-reserve banking is taking deposits and holding only a fraction in reserves or liquid assets — credit creation with a run risk.

Leverage Ratio Constraint

Leverage Ratio Constraint — Non-risk-weighted capital floor binding balance-sheet capacity.

Regional Bank ETF

Regional Bank ETF performance helps track stress in smaller and mid-sized banks, especially around deposit stability, asset quality, and local credit conditions.

Systemic Risk Indicator

Systemic Risk Indicator — Aggregate capital shortfall under stress — connects banking to macro hedges.

CDX HY Index

CDX HY Index tracks the cost of insuring a basket of North American high-yield corporate credit and serves as a sensitive gauge of credit risk appetite and stress.

Credit Rating

A credit rating is an agency’s opinion of relative default risk — a letter grade that gates mandates, not a market price.

Credit Valuation Adjustment

Credit Valuation Adjustment — Adjustment to derivative value for counterparty default risk.

Default Risk

Default risk is the chance the issuer misses a contractual payment — the event credit spread is trying, noisily, to price.

High Yield OAS

High Yield OAS measures the spread of high-yield corporate bonds over risk-free Treasuries after adjusting for embedded options, serving as a key gauge of speculative credit stress.

Junk Bond

A junk bond is a high-yield, below-investment-grade credit — more equity-like default risk, still quoted in spread and price.

Loan Officer Survey

The Loan Officer Survey tracks bank lending standards and loan demand, providing insight into whether credit supply is tightening or easing in the real economy.

Loss Given Default

LGD is 1 minus recovery — the fraction of exposure lost when default happens.

Probability of Default

PD is the probability a name defaults over a horizon — real-world for books, risk-neutral for CDS.

AI / Machine-Learning CTA

A CTA whose signals come from ML (trees, nets, representations) rather than a hand-written MA — still a futures risk engine underneath.

ATR Unit Sizing

Size each new futures position so that 1 ATR move equals a fixed fraction of equity — the Turtle risk unit, still the cleanest per-trade language.

CTA Correlation-Adjusted Sizing

Shrink size when markets are moving together so that ‘20 commodities’ are not one energy-risk factor wearing 20 tickers.

CTA Long/Short Symmetry

Whether the program treats shorts with the same rules and risk as longs — the difference between a two-way CTA and a long-biased TAA in a futures wrapper.

CTA Options Strategy

Express views with listed options on futures — defined-risk directional, calendars, or vol — still a CTA if the underlying is a commodity interest.

CTA Pyramiding / Scale-In

Add units as the trend extends — more risk on a working trade — instead of a single full-size entry.

CTA Volatility Targeting

Scale the whole book (or each market) so forecast σ hits a target — the reason a 15% vol CTA is not ‘more leveraged crude’ in a quiet month.

Diversified CTA

A program that risks money across the four big futures groups — equity indices, bonds/STIR, FX, and commodities — rather than a single pit.

Multi-Strategy CTA

A single platform that allocates risk across trend, carry, short-term, RV, and sometimes options — a house of sleeves, not a style-pure trend shop.

Implied Volatility Surface

Implied Volatility Surface — Strike and tenor structure of implied vol, the core object for vol trading and risk.

Move Index

The MOVE Index tracks implied volatility in the U.S. Treasury market and serves as a benchmark for rates uncertainty and macro stress.

Option Greeks

Greeks are the sensitivities of option value to spot, vol, time, and rates — the risk report of a non-linear book.

Risk Reversal

Risk Reversal — Call-put spread package measuring directional skew in FX and equity options.

Skew

Skew measures the relative richness of downside versus upside implied volatility, helping track hedging demand and asymmetry in market risk pricing.

Variance Risk Premium

Variance Risk Premium — Gap between implied and realized volatility that systematic vol sellers harvest.

Vega Exposure

Vega Exposure — Sensitivity to implied volatility changes — core risk for vol books and structured products.

VIX Index

VIX Index measures implied volatility in S&P 500 options and is widely used as a shorthand for equity market fear and risk aversion.

CS01

CS01 is the dollar value of one basis point of credit spread — how much the book makes or loses if the name or index OAS/CDS widens by 1 bp.

DV01

DV01 is the dollar value of one basis point: how much the position’s mark changes if the yield (or the curve point you risk on) moves by 0.01%.

Risk-On Risk-Off

Risk-on / risk-off (RORO) is a one-factor tape: the same risk appetite impulse hits credit, EM, high-beta equity, and vol in one direction while Treasuries, the dollar, and gold take the other side.

TINA

TINA — There Is No Alternative — was the 2010s slogan that zero rates left no choice but equities (or credit), compressing risk premia because cash paid nothing.

Wrong-Way Risk

Wrong-way risk is when exposure rises at the same time the counterparty’s credit worsens — the hedge or the receivable fails exactly when you need it.

Option Blackboard · 1

strategy

Defined-Risk Bridge Playbook

Strategy bridge from Blackboard scanner cards into Options Lab templates without implying live broker execution.

Encyclopedia · 24

AI / Machine-Learning CTA

A CTA whose signals come from ML (trees, nets, representations) rather than a hand-written MA — still a futures risk engine underneath.

Quant · Foundations

Alpha

Alpha is return not explained by the risk factors you chose — a residual, not a personality.

Emerging Markets · Foundations

ATR Unit Sizing

Size each new futures position so that 1 ATR move equals a fixed fraction of equity — the Turtle risk unit, still the cleanest per-trade language.

Banking · Foundations

Bank CDS Index

Bank CDS Index tracks the cost of insuring major bank credit risk and serves as a real-time indicator of banking-system stress and confidence.

Equity · Foundations

Blue Chip

A blue chip is a large, established, usually profitable listed company — a reputation, not a risk-free claim.

BTP-Bund Spread

BTP-Bund spread measures the yield difference between Italian and German government bonds and is a key indicator of euro-area sovereign stress and fragmentation risk.

Quant · Foundations

Capital Asset Pricing Model

CAPM says expected excess return is beta times the market risk premium — one factor, one line, many violations.

Credit · Foundations

CDX HY Index

CDX HY Index tracks the cost of insuring a basket of North American high-yield corporate credit and serves as a sensitive gauge of credit risk appetite and stress.

Fixed Income · Foundations

Commercial Mortgage Delinquency

Commercial Mortgage Delinquency — Office and retail stress feeding through CRE credit and regional bank risk.

Strategies · Foundations

Convertible Arbitrage

Long the convertible and short the delta in the stock — harvest cheap implied vol / credit, with funding and squeeze risk.

Fixed Income · Foundations

Convexity Risk

Convexity Risk — Non-linear price response to yield changes, especially relevant in MBS and long bonds.

Fixed Income · Foundations

Credit Default Swap Spread

Credit Default Swap Spread — Market-implied default risk premium for single names and indices.

Credit · Foundations

Credit Rating

A credit rating is an agency’s opinion of relative default risk — a letter grade that gates mandates, not a market price.

Credit · Foundations

Credit Valuation Adjustment

Credit Valuation Adjustment — Adjustment to derivative value for counterparty default risk.

CTA Correlation-Adjusted Sizing

Shrink size when markets are moving together so that ‘20 commodities’ are not one energy-risk factor wearing 20 tickers.

CTA Long/Short Symmetry

Whether the program treats shorts with the same rules and risk as longs — the difference between a two-way CTA and a long-biased TAA in a futures wrapper.