ABSTRACT Structured retail products are unsecured bonds subject to the default risk of the issuer. We analyze the price‐setting policy of issuers with respect to this default risk. Using a long‐term data set of discount certificates in the German market, we apply a time series IVX‐approach to find that (i) quoted prices do depend on issuer default risk, but (ii) this dependency is under‐proportional. Hence, retail investors are only partially compensated for bearing issuer default risk. A long‐term analysis covering the global financial crisis, the European debt crisis, and the succeeding calm period, as well as supporting evidence from the coronavirus crisis, provides patterns consistent with a fading attention hypothesis: When default risk has left the focus of retail investors, they are no longer compensated for it, even if it becomes substantial, as in the early months of the coronavirus crisis.
ABSTRACT This paper studies the shape of zero and par yield curves through the carry and convexity of zero‐bond and par–swap butterflies under instrument‐based parallel shifts : the component instruments are held fixed, and each instrument's own quote receives the same additive shock. Although this framework is a conditional scenario experiment rather than a model‐independent restriction on admissible yield‐curve shapes, it is simple and widely used in fixed‐income risk management. For zero‐coupon bonds, maturity is the natural horizontal coordinate; for par–swaps, the nonlinear bootstrap relation makes the fixed‐leg annuity, or PV01, the relevant coordinate. Under the stated instrument‐based evolution rule, an appropriately weighted zero‐cost butterfly has a nonnegative instantaneous revaluation under either direction of an admissible common shift, while convexity of the initial curve in the relevant coordinate also generates positive short‐horizon carry. These results provide a partial economic rationale for the commonly observed concavity of yield curves: convex segments can support positive‐carry, level‐neutral butterflies under the benchmark shift convention. We then examine daily US dollar par–swap rates from July 3, 2000 to October 28, 2016. The data are obtained from the Federal Reserve Bank of St. Louis FRED database. The empirical results show that convexity is more frequently detected in annuity coordinates than under maturity weighting and is concentrated primarily at the front end of the curve. Realized short‐horizon movements are seldom instrument‐parallel, and the gross advantage of convex butterflies is substantially reduced by nonlevel curve movements and transaction costs. The evidence, therefore, supports the use of annuity coordinates for constructing and evaluating swap butterflies, while also showing that the benchmark parallel‐shift scenario should be interpreted as a risk‐management device rather than as a description of typical realized curve dynamics.
This study explores the impact of the Shanghai crude oil futures (SC) market on corporate trade credit financing in China. Using data on listed firms from 2012 to 2023 and a difference-in-differences model, we find the launch of SC significantly increased trade credit financing for oil-dependent firms. Mechanism evidence suggests that SC is associated with improvements in credit risk and market information environment, which are economically consistent with suppliers' trade credit decisions. Cross-sectional analysis reveals stronger effects among firms with higher investment capacity, higher production costs, and lower transparency. Economic consequences analysis suggests the effect further stimulates corporate capital investment and technological innovation. The results demonstrate how innovations in energy finance may support the real economy and contribute to the stability of China's energy industries.
Our investigation focuses on the valuation of variance and volatility swaps by incorporating both clustered jump behaviors and liquidity-related risk factors. The proposed modeling framework characterizes stock price movements using a jump-diffusion process, where Hawkes processes govern the jump component in the absence of liquidity effects. Stochastic liquidity is further integrated through a discount factor that modifies the underlying asset value. To preserve model generality, we introduce a complete correlation framework across all Brownian motions involved. A change of measure is applied to express the dynamics under a risk-neutral pricing measure. Subsequently, the forward characteristic function associated with the log-price is expressed analytically, enabling the derivation of closed-form swap valuation formulae. Using daily data from the Brent crude oil futures continuous contract, we calibrate relevant model parameters, providing empirical evidence supporting jump clustering. Numerical implementation of the formulae further offers insights into their sensitivity to variations in model parameters.
This study examines market concentration within the client clearing services from 2008 to 2025. Our analysis reveals a significant structural shift beginning mid-2014: large bank-affiliated Futures Commission Merchants (FCMs) have consolidated their dominance as smaller entities exit the industry, while concentration has also risen among the remaining non-bank FCMs. We investigate how these structural changes affect market dynamics, price discovery, and trader behavior across commodity futures markets. While our findings indicate no systematic market-wide effects, we document significant impacts in specific markets, particularly regarding small investor participation. Several commodity futures markets exhibit reduced small trader activity when concentration levels are higher, especially during periods of elevated volatility.
This study parameterizes extreme comovement between options market ambiguity (OMA) and implied volatility using the Symmetrized Joe-Clayton copula model and a recursive estimation approach. The empirical results demonstrate that acceleration in extreme comovement (AEC) contains incremental information about future market uncertainty beyond that captured by OMA and implied volatility. Both in-sample and out-of-sample predictive tests confirm that AEC anticipates impending market declines. Incorporation of this signal into investment strategies yields significantly better performance than the traditional buy-and-hold strategy and the strategies signaled by OMA and implied volatility, providing extra evidence that AEC is a leading indicator of market slumps.
This study investigates whether equity market Capital Gains Overhang (CGO) contains predictive information for crude oil volatility. Using data from January 2000 to December 2024, we document that S&P 500 CGO negatively predicts volatility in both WTI and Brent crude oil markets, demonstrating international cross-market predictability. Higher CGO values, reflecting substantial unrealized gains among equity investors, are associated with significantly lower subsequent oil volatility. Comprehensive out-of-sample tests show that CGO-augmented models substantially outperform autoregressive benchmarks across multiple evaluation periods. The forecasting improvements remain significant after controlling for traditional macroeconomic predictors and prove robust to alternative specifications. The predictive power persists in regime-switching frameworks, with CGO enhancing both regime. Our findings highlight the importance of international cross-market behavioral linkages for volatility forecasting and risk management in energy markets.
This article examines the pricing of European options while incorporating liquidity risks, extending the classical Heston stochastic volatility framework. A new methodology is proposed by incorporating both liquidity risk and stochastic long-term variance into the model, improving its capacity to reflect market dynamics. By applying measure transformation, the model dynamics are formulated under an equivalent martingale measure, leading to an analytical expression for the characteristic function of the stock price logarithm. This yields a closed-form solution for European option pricing, which is subsequently benchmarked against existing models through numerical simulations to evaluate its pricing accuracy and parameter sensitivity. Empirical analysis is conducted to examine the performance of the model using market data.
This paper presents a robust new finding that reciprocal return risk premium, defined as the difference between the expected reciprocal of return under physical and risk-neutral measures, significantly predicts the option returns in the cross-section. Theoretical and empirical evidence underscore the pivotal role of the ex post volatility risk premium in this relation. We also find that the positive relation between reciprocal return risk premium and option return mainly resides in the component, which is by definition a natural measure for return variation under the risk-neutral measure.
This paper examines the relationship between skewness and kurtosis in Bitcoin spot and futures markets using high-frequency data. We document a strong convex skewness-kurtosis relationship consistent with theoretical moment restrictions. Trading activity is positively associated with realized kurtosis, particularly in futures markets, though sensitive to specification and driven by extreme-return episodes. Allowing the relationship to evolve over time reveals substantial curvature variation, indicating state-dependent higher-moment dynamics. The close co-movement of results across markets suggests patterns reflect broad market-wide conditions. The empirical framework is reduced-form and results should be interpreted as conditional associations rather than causal effects.
We examine day-of-the-week effects in China's SSE 50 ETF options market and uncover three main patterns. Returns are weakest in midweek and strongest on Friday; Friday and Monday returns are not significantly different; and the trough occurs on Wednesday for calls but on Tuesday for puts. These results remain after controlling for standard risk factors, volatility clustering, and COVID-19-related structural breaks. While CVIX captures the broad Friday premium, it does not explain the internal asymmetry across option types. We show that trading value is the key liquidity channel behind the anomaly: call trading reflects speculative demand, whereas put trading is more closely tied to hedging demand, and these motives follow different weekly rhythms. VAR results further indicate that high Friday trading value creates an immediate price effect and a reversal on Monday, helping explain the missing weekend effect.
Economic policy uncertainty (EPU) is a critical yet often neglected factor in derivatives pricing, leading to systematic biases in existing valuation frameworks. This study proposes an advanced pricing model that explicitly incorporates a stochastic EPU factor with a regime-switching long-term mean into the stochastic volatility framework. The principal theoretical contribution of this research is a closed-form analytical pricing formula for European options, which successfully overcomes the challenges of multiple stochastic factors and achieves substantial computational advantages over traditional numerical methods such as the Monte-Carlo simulation. A preliminary empirical study using SSE 50 ETF option data demonstrates the model's superior pricing performance compared to other benchmarks.
We explore the risk-return tradeoff of Decentralized Finance (DeFi). We construct three novel indices for different asset classes: Lending, Decentralized Exchanges, and Derivatives. Motivated by the cryptocurrency pricing framework of Liu and Tsyvinski, we investigate how DeFi assets comove with financial primitives. We document limited correlation with traditional equities, currencies, interest rates, and commodities. We further examine several DeFi-specific factors. Bitcoin and Ethereum returns show no significant association with subsequent DeFi returns, highlighting a decoupling between base-layer assets and application-layer protocols. Meanwhile, we find some in-sample associations with DeFi-specific factors such as momentum, investor attention, and performance of centralized platforms. A novel book-to-market ratio constructed using Total Value Locked and market capitalization does not display a systematic relationship with returns. Finally, we find only limited and sector-specific associations with traditional equity industries.
This paper uses GARCH-MIDAS to predict US natural gas futures volatility using national and state-level Climate Concern Indexes (CCIs). We find that both national and state-level CCIs positively affect price volatility. Notably, models using state-level data-specifically those utilizing least-squares (LS) weighting combinations-surpass the GARCH-MIDAS-GECON benchmark and models relying solely on national CCI. These findings deliver substantial statistical and economic utility gains. Our results underscore the importance of incorporating heterogeneous climate concerns across US states to capture varied demand-supply conditions when forecasting energy market volatility.
We extend binomial and trinomial trees to price European and American style Parisian and ParAsian options by keeping track of a vector of option prices under different scenarios at each tree node. We also incorporate the method for choosing the number of time-steps that will yield more precise price estimates. The vectorized tree models can easily price exotic path-dependent options such as American double barrier Parisian options and look-back options, which present challenges to other existing methods.
Using tick-by-tick data, this study examines intraday liquidity of WTI, Brent, and INE crude oil futures. US EIA inventory announcements significantly affect intraday returns and, to a lesser extent, liquidity across all three markets. We document strong commonality in intraday liquidity, largely driven by supply-side factors, and find that WTI is the dominant source of liquidity spillovers, a pattern not mirrored in return spillovers. These findings highlight different mechanisms behind liquidity commonality and return comovements. The results are robust to additional control variables and alternative liquidity measures.
This study investigates how extreme return components (MAXs) of smart beta exchange-traded funds (ETFs) influence heterogeneous investor choice. We find that extreme overnight returns (overnight MAXs) have substantial ETFs' flow predictability above and beyond that provided by standard risk, performance, and market-timing measures. This suggests that individual investors tend to choose funds based on historical overnight MAXs. The persistence of overnight MAXs supports the lottery preference theory, which posits that retail investors disproportionately focus on the likelihood of high payoff states in a fund's past return distribution. Furthermore, we demonstrate that overnight and intraday MAXs negatively and positively predict future smart beta ETFs' performance, respectively. This divergence indicates that heterogeneous investors hold varying beliefs and employ distinct trading activities with respect to those lottery-like fund return distributions. Finally, we show that investor attention is beneficial to explain our findings.
This paper explores the application of neural networks to improve pricing of American options. Focusing on both American and European options on the S&P 100 index from January 2016 to August 2023, we integrate neural networks to model the difference between market-implied and model-implied volatilities derived from the Black-Scholes and Heston models. We also employ a pure neural network which does not use pricing models. Our study compares two neural network training architectures: independent training, where the network is trained anew daily, and sequential training, which uses the previous day's network setup as starting point to retrain the network. The findings reveal that a pure neural network with sequential training significantly reduces the root mean square error (RMSE) of implied volatility predictions compared to traditional pricing models. The inclusion of European option data in the training can enhance the models' forecasting performance, though its effectiveness varies depending on market conditions.
This paper investigates how textual sentiment in analyst research reports influences commodity futures returns in China. Using the Natural Language Processing and Information Retrieval platform to analyze a comprehensive sample of reports from 2016 to 2021, we construct sentiment indices for 37 commodity futures across agriculture, metals, chemicals, and energy sectors. Our results show that text sentiment significantly explains both contemporaneous and future returns, with negative sentiment having a stronger impact. Increased optimism is associated with higher contemporaneous returns through investor sentiment and attention channels, especially for future contracts with low open interest growth, low volatility, a contango market (futures premium), and high basis-momentum. We document heterogeneous results for subsequent returns and the three main risk premium factors. The findings remain robust after controlling for established pricing factors and macroeconomic variables. This study highlights the informational value of analyst sentiment, filling a gap in text sentiment research within the commodity futures market and offering insights for investors and policymakers.
The problem of integrating the Black, Scholes, and Merton (BSM) formula with respect to the time variable is paramount for an economist. Inspired by the real options literature, Shackleton and Wojakowski offer analytic formulae for valuing finite maturity (profit) caps and floors that are contingent on continuous flows following a lognormal distribution. Alternative, but equivalent, closed-form solutions have been recently proposed in Dias et al. by solving the time integral of options using a direct approach that does not rely on the real options intuition. This paper further extends and simplifies the computation of time integrals under the BSM world, considering not only plain-vanilla but also several exotic, including path-dependent options. We also provide a new closed-form solution of the time integral under the Margrabe economy. The method proposed in this paper makes the evaluation easier, cements the "non-real options" route and opens the way for more analytical work in BSM, Margrabe, and other areas.
