Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns

We develop a model in which the volatility of risky assets is subject to random and discontinuous shifts over time. We derive prices of claims contingent on such assets and analyze options-based trading strategies to hedge against the risk of jumps in the return volatility. Unsystematic and systematic events such as takeovers, major changes in business plans, or shifts in economic policy regimes may drastically alter firms' risk profiles. Our model captures the effect of such events on options markets.     

Dynamic factor long memory volatility

In this paper, we develop a long memory orthogonal factor (LMOF) multivariate volatility model for forecasting the covariance matrix of financial asset returns. We evaluate the LMOF model using the volatility timing framework of Fleming et al. [J. Finance, 2001, 56, 329–352] and compare its performance with that of both a static investment strategy based on the unconditional covariance matrix and a range of dynamic investment strategies based on existing short memory and long memory multivariate conditional volatility models. We show that investors should be willing to pay to switch from the static strategy to a dynamic volatility timing strategy and that, among the dynamic strategies, the LMOF model consistently produces forecasts of the covariance matrix that are economically more useful than those produced by the other multivariate conditional volatility models, both short memory and long memory. Moreover, we show that combining long memory volatility with the factor structure yields better results than employing either long memory volatility or the factor structure alone. The factor structure also significantly reduces transaction costs, thus increasing the feasibility of dynamic volatility timing strategies in practice. Our results are robust to estimation error in expected returns, the choice of risk aversion coefficient, the estimation window length and sub-period analysis.     

Static and dynamic connectedness between NFTs,Defi and other assets: Portfolio implication

The paper examines the return and volatility transmission between NFTs, Defi assets, and other assets (oil, gold, Bitcoin, and S&P 500) using the TVP-VAR framework. The results report weak static return and volatility spillovers between NFTs and Defi assets and selected markets, showing that these new digital assets are still relatively decoupled from traditional asset classes. Bitcoin, oil, and half of the NFTs and Defi assets are net transmitters of return and volatility spillovers, whereas rest of the markets are net recipients of spillovers. Our findings show that the dynamic return and volatility connectedness become higher during the initial phase of the COVID-19 pandemic and the cryptocurrency bubble of 2021. We also compute the static and dynamic optimal weights, hedge ratios, and hedging effectiveness for the portfolios of NFTs/other asset and Defi asset/other asset and show that investors and portfolio managers should consider adding NFTs and Defi assets in their portfolios of gold, oil, and stock markets to achieve diversification benefits.     

Trading volatility spreads: a test of index option market efficiency

If returns on two assets share common volatility components, the prices of options on the assets should be interdependent and the implied volatility spread should mean revert. We first demonstrate, using the canonical correlation method, that there is a common component in the volatilities of the returns on S&P 100 and S&P 500 indices. We then exploit this commonality by trading on the volatility spread between tick-by-tick OEX and SPX call options listed on the CBOE. Our vega-delta-neutral strategies generated significant profits, even after transaction costs are taken into account. The results suggest that the two options markets are not jointly efficient.     

Optimal investment under multi-factor stochastic volatility

We consider a model for multivariate intertemporal portfolio choice in complete and incomplete markets with a multi-factor stochastic covariance matrix of asset returns. The optimal investment strategies are derived in closed form. We estimate the model parameters and illustrate the optimal investment based on two stock indices: S&P500 and DAX. It is also shown that the model satisfies several stylized facts well known in the literature. We analyse the welfare losses due to suboptimal investment strategies and we find that investors who invest myopically, ignore derivative assets, model volatility by one factor and ignore stochastic covariance between asset returns can incur significant welfare losses.     

金融资产综合风险价值动态评估研究

为综合度量金融资产损失的市场风险与流动性风险,采用GARCH-VaR模型度量了日市场风险价值,用日内相对波动幅度调整为日LA-VaR,并利用时间延展槡T规则将它转换为变现期间的综合风险价值,构建了金融资产综合风险价值的全方位动态评估模型。通过以中国股指期货为例的实证研究证明,该模型能够有效评估金融资产综合风险价值,适用于金融资产公允价值的期末估算。     

Investigating the nature of interaction between crypto-currency and commodity markets

This paper investigates the dynamic relationship and volatility spillovers between cryptocurrency and commodity markets using different multivariate GARCH models. We take into account the nature of interaction between these markets and their transmission mechanisms when analyzing the conditional cross effects and volatility spillovers. Our results confirm the presence of significant returns and volatility spillovers, and we identify the GO-GARCH (2,2) as the best-fit model for modeling the joint dynamics of various financial assets. Our findings show significant dynamic linkages and volatility spillovers between gold, natural gas, crude oil, Bitcoin, and Ethereum prices. We find that gold can serve as a safe haven in times of economic uncertainty, as it is a good hedge against natural gas and crude oil price fluctuations. We also find evidence of bidirectional causality between crude oil and natural gas prices, suggesting that changes in one commodity's price can affect the other. Furthermore, we observe that Bitcoin and Ethereum are positively correlated with each other, but negatively correlated with gold and crude oil, indicating that these cryptocurrencies may serve as useful diversification tools for investors seeking to reduce their exposure to traditional assets. Our study provides valuable insights for investors and policymakers regarding asset allocation and risk management, and sheds light on the dynamics of financial markets.     

The economic value of range-based covariance between stock and bond returns with dynamic copulas

The covariance between stock and bond returns plays important roles in the setting up of asset allocation strategies and portfolio diversification. In the present study, we propose a multivariate range-based volatility model incorporating dynamic copulas into a range-based volatility model to describe the volatility and dependence structures of stock and bond returns. We then go on to assess the economic value of the covariance forecasts based on our proposed model under a mean-variance framework. The out-of-sample forecasting performance reveals that investors would be willing to pay between 39 and 2081 basis points per year to switch from a dynamic trading strategy under the return-based volatility model to a dynamic trading strategy under the range-based volatility model, with more risk-averse investors being willing to pay even higher switching fees. Furthermore, additional economic gains of between 33 and 1471 annualized basis points are achieved when taking the leverage effect into consideration.     

Pricing Currency Risks

The currency market features a small cross-section, and conditional expected returns can be characterized by few signals: interest differential, trend, and mean reversion. We exploit these properties to construct the ex ante mean-variance efficient portfolio of individual currencies. The portfolio is updated in real time and prices all prominent currency trading strategies, conditionally and unconditionally. The fraction of risk in these assets that does not affect their risk premiums is at least 85%. Extant explanations of carry strategies based on intermediary capital or global volatility are related to these unpriced components, while consumption growth is related to the priced component of returns.     

Sequential real rainbow options

We develop two models to value European sequential rainbow options. The first model is a sequential option on the better of two stochastic assets, where these assets follow correlated geometric Brownian motion processes. The second model is a sequential option on the mean-reverting spread between two assets, which is applicable if the assets are co-integrated. We provide numerical solutions in the form of finite difference frameworks and compare these with Monte Carlo simulations. For the sequential option on a mean-reverting spread, we also provide a closed-form solution. Sensitivity analysis provides the interesting results that in particular circumstances, the sequential rainbow option value is negatively correlated with the volatility of one of the two assets, and that the sequential option on the spread does not necessarily increase in value with a longer time to maturity. With given maturity dates, it is preferable to have less time until expiry of the sequential option if the current spread level is way above the long-run mean.     

Can we forecast the implied volatility surface dynamics of equity options? Predictability and economic value tests

We examine whether the dynamics of the implied volatility surface of individual equity options contains exploitable predictability patterns. Predictability in implied volatilities is expected due to the learning behavior of agents in option markets. In particular, we explore the possibility that the dynamics of the implied volatility surface of individual stocks may be associated with movements in the volatility surface of S&P 500 index options. We present evidence of strong predictable features in the cross-section of equity options and of dynamic linkages between the volatility surfaces of equity and S&P 500 index options. Moreover, time-variation in stock option volatility surfaces is best predicted by incorporating information from the dynamics in the surface of S&P 500 options. We analyze the economic value of such dynamic patterns using strategies that trade straddle and delta-hedged portfolios, and find that before transaction costs such strategies produce abnormal risk-adjusted returns.     

An evolutionary CAPM under heterogeneous beliefs

Heterogeneity and evolutionary behaviour of investors are two of the most important characteristics of financial markets. This paper incorporates the adaptive behaviour of agents with heterogeneous beliefs and establishes an evolutionary capital asset pricing model (ECAPM) within the mean-variance framework. We show that the rational behaviour of agents switching to better-performing trading strategies can cause large deviations of the market price from the fundamental value of one asset to spill over to other assets. Also, this spill-over effect is associated with high trading volumes and persistent volatility characterized by significantly decaying autocorrelations of, and positive correlation between, price volatility and trading volume.     

Determinants of idiosyncratic volatility: Evidence from the Indian stock market

This paper investigates whether firm-specific characteristics explain idiosyncratic volatility in the stocks of non-financial firms traded in the Indian stock market. It employs the linear time series five-factor model, augmented with a liquidity factor and the conditional EGARCH model, to extract yearly idiosyncratic volatility. We estimate a panel data regression to quantify the relationship between firm-specific characteristics and the volatility of individual securities. The results show that idiosyncratic volatility is significant in emerging markets such as India, and that cross-sectional return variations of firms are associated with firm-specific characteristics such as firm size, book-to-market ratio, momentum, liquidity, cash flow-to-price ratio, and returns on assets. We find that the idiosyncratic risk documented in this study is associated with smaller size of company, higher liquidity, low momentum, high book-to-market ratio, and low cash flow-to-price ratio. The findings suggest need to develop alternative tools to make investment decisions in emerging markets.     

Dynamic correlations and volatility linkages between stocks and sukuk: Evidence from international markets

An understanding of volatility and co-movements in financial markets is important for portfolio allocation and risk management practices. The current financial crisis caused a shrinkage in values of most assets, an increased volatility and a threat to the survival of several institutional investors. Managing risks and returns within the classic portfolio theory, when correlations across securities soar, is increasingly challenging. In this paper, we investigate the volatility behavior and the co-movements between sukuk and international stock indexes. Symmetric multivariate GARCH models with dynamic conditional correlations (DCC) were estimated under Student-t distribution. We provide evidence of high correlations between sukuk and US and EU stock markets, without finding the well-known flight to quality behavior affecting Islamic bonds. We also show that volatility linkages between sukuk and regional market indexes are higher during financial crisis. We argue that investors could obtain diversification benefits including sukuk in a well-diversified equity portfolio, given their lower volatility compared to equity. But higher volatility linkages and dynamic correlations during financial crises show that they are hybrid instruments between bonds and equity. Our findings are relevant for institutional investors and asset managers that include Islamic bonds in a diversified portfolio.     

Modeling Time-Varying Correlations in Volatility Between BRICS and Commodity Markets

This article investigates the asymmetric and long memory volatility properties and dynamic conditional correlations (DCCs) between Brazilian, Russian, Indian, Chinese, and South African (BRICS) stock markets and commodity (gold and oil) futures markets, using the trivariate DCC-fractionally integrated asymmetric power autoregressive conditional heteroskedasticity (FIAPARCH) model. We identify significant asymmetric and long memory volatility properties and DCCs for pairs of BRICS stock and commodity markets, and variability in DCCs and Markov Switching regimes during economic and financial crises. Finally, we analyze optimal portfolio weights and time-varying hedge ratios, demonstrating the importance of overweighting optimal portfolios between BRICS stock and commodity assets.     

Correlation risk

Investors hold portfolios of assets with different risk-reward profiles for diversification benefits. Conditional on the volatility of assets, diversification benefits can vary over time depending on the correlation structure among asset returns. The correlation of returns between assets has varied substantially over time. To insure against future “low diversification” states, investors might demand securities that offer higher payouts in these states. If this is the case, then investors would pay a premium for securities that perform well in regimes in which the correlation is high. We empirically test this hypothesis and find that correlation carries a significantly negative price of risk, after controlling for asset volatility and other risk factors.     

Robustly Hedging Variable Annuities With Guarantees Under Jump and Volatility Risks

Recent variable annuities offer participation in the equity market and attractive protection against downside movements. Accurately quantifying this additional equity market risk and robustly hedging options embedded in the guarantees of variable annuities are new challenges for insurance companies. Due to sensitivities of the benefits to tails of the account value distribution, a simple Black–Scholes model is inadequate in preventing excessive liabilities. A model which realistically describes the real world price dynamics over a long time horizon is essential for the risk management of the variable annuities. In this article, both jump risk and volatility risk are considered for risk management of lookback options embedded in guarantees with a ratchet feature. We evaluate relative performances of delta hedging and dynamic discrete risk minimization hedging strategies. Using the underlying as the hedging instrument, we show that, under a Black–Scholes model, local risk minimization hedging can be significantly better than delta hedging. In addition, we compare risk minimization hedging using the underlying with that of using standard options. We demonstrate that, under a Merton's jump diffusion model, hedging using standard options is superior to hedging using the underlying in terms of the risk reduction. Finally, we consider a market model for volatility risks in which the at‐the‐money implied volatility is a state variable. We compute risk minimization hedging by modeling at‐the‐money Black–Scholes implied volatility explicitly; the hedging effectiveness is evaluated, however, under a joint model for the underlying price and implied volatility. Our computational results suggest that, when implied volatility risk is suitably modeled, risk minimization hedging using standard options, compared to hedging using the underlying, can potentially be more effective in risk reduction under both jump and volatility risks.     

The intertemporal capital asset pricing model with dynamic conditional correlations

The intertemporal capital asset pricing model of Merton (1973) is examined using the dynamic conditional correlation (DCC) model of Engle (2002). The mean-reverting DCC model is used to estimate a stock’s (portfolio’s) conditional covariance with the market and test whether the conditional covariance predicts time-variation in the stock’s (portfolio’s) expected return. The risk-aversion coefficient, restricted to be the same across assets in panel regression, is estimated to be between two and four and highly significant. The risk premium induced by the conditional covariation of assets with the market portfolio remains positive and significant after controlling for risk premia induced by conditional covariation with macroeconomic, financial, and volatility factors.     

Macroeconomic volatility and external imbalances

Does macroeconomic volatility/uncertainty affects accumulation of net foreign assets? In OECD economies over the period 1970–2012, changes in country specific aggregate volatility are, after controlling for a wide array of factors, significantly positively associated with net foreign asset position. A standard open economy model with time varying macroeconomic uncertainty can quantitatively account for this relationship. The key mechanism is precautionary motive: more uncertainty induces residents to save more, and higher savings are in part channeled into foreign assets. Data and theory suggest that volatility is an important determinant of the medium/long run evolution of external imbalances in developed countries.     

Multiscaling and rough volatility: An empirical investigation

Pricing derivatives goes back to the acclaimed Black and Scholes model. However, such a modelling approach is known not to be able to reproduce some of the financial stylised facts, including the dynamics of volatility. In the mathematical finance community, it has therefore emerged a new paradigm, named rough volatility modelling, that represents the volatility dynamics of financial assets as a fractional Brownian motion with Hurst exponent very small, which indeed produces rough paths. At the same time, prices’ time series have been shown to be multiscaling, characterised by different Hurst scaling exponents. This paper assesses the interplay, if present, between price multiscaling and volatility roughness, defined as the (low) Hurst exponent of the volatility process. In particular, we perform extensive simulation experiments by using one of the leading rough volatility models present in the literature, the rough Bergomi model. A real data analysis is also conducted to test if the rough volatility model reproduces the same relationship. We find that the model can reproduce multiscaling features of the prices’ time series when a low value of the Hurst exponent is used, but it fails to reproduce what the real data says. Indeed, we find that the dependency between prices’ multiscaling and the Hurst exponent of the volatility process is diametrically opposite to what we find in real data, namely a negative interplay between the two.