Implied integrated variance and hedging

If the volatility is stochastic, stock price returns and European option prices depend on the time average of the variance, i.e. the integrated variance, not on the path of the volatility. Applying a Bayesian statistical approach, we compute a forward-looking estimate of this variance, an option-implied integrated variance. Simultaneously, we obtain estimates of the correlation coefficient between stock price and volatility shocks, and of the parameters of the volatility process. Due to the convexity of the Black–Scholes formula with respect to the volatility, pricing and hedging with Black–Scholes-type formulas and the implied volatility often lead to inaccuracies if the volatility is stochastic. Theoretically, this problem can be avoided by using Hull–White-type option pricing and hedging formulas and the integrated variance. We use the implied integrated variance and Hull–White-type formulas to hedge European options and certain volatility derivatives.     

企业运用衍生品的风险管理效果分析——来自中国上市公司的证据

现有文献较少关注企业运用衍生品的风险管理效果,以至于不能准确地解释运用衍生品的行为与功能。以沪深两市上市公司在2005～2011年间运用过衍生品的企业为样本,分析其运用衍生品的风险管理效果,研究发现中国企业运用衍生品的风险管理效果很弱。因此,可以认为中国企业运用衍生品的行为主要是套期获利,而不是名义上宣称的套期保值。     

基于VaR模型的最优套期保值比例探析——以美元远期套保为例

VaR模型被认为是兼顾投机套利与套期保值两大动机的衍生工具决策模型。国内文献对此讨论较少。基于其理论推导,可以归纳地认为VaR模型具有兼容性、一般性、"期权"特征和可操作性。以美元远期套保为例,研究发现,基于VaR模型的最优套保比较之传统最优套保比、最小方差最优套保比更有优势,能够解释中国企业运用衍生工具失败的原因。但据此推论,基于VaR模型确定最优套保比在实践中仍然存在一些问题,如非正态分布、现货头寸不确定、损益报告困难等。     

The QLBS Q-Learner goes NuQLear: fitted Q iteration,inverse RL,and option portfolios

The QLBS model is a discrete-time option hedging and pricing model that is based on Dynamic Programming (DP) and Reinforcement Learning (RL). It combines the famous Q-Learning method for RL with the Black–Scholes (–Merton) (BSM) model's idea of reducing the problem of option pricing and hedging to the problem of optimal rebalancing of a dynamic replicating portfolio for the option, which is made of a stock and cash. Here we expand on several NuQLear (Numerical Q-Learning) topics with the QLBS model. First, we investigate the performance of Fitted Q Iteration for an RL (data-driven) solution to the model, and benchmark it versus a DP (model-based) solution, as well as versus the BSM model. Second, we develop an Inverse Reinforcement Learning (IRL) setting for the model, where we only observe prices and actions (re-hedges) taken by a trader, but not rewards. Third, we outline how the QLBS model can be used for pricing portfolios of options, rather than a single option in isolation, thus providing its own, data-driven and model-independent solution to the (in)famous volatility smile problem of the Black–Scholes model.     

Machine learning for quantitative finance: fast derivative pricing,hedging and fitting

In this paper, we show how we can deploy machine learning techniques in the context of traditional quant problems. We illustrate that for many classical problems, we can arrive at speed-ups of several orders of magnitude by deploying machine learning techniques based on Gaussian process regression. The price we have to pay for this extra speed is some loss of accuracy. However, we show that this reduced accuracy is often well within reasonable limits and hence very acceptable from a practical point of view. The concrete examples concern fitting and estimation. In the fitting context, we fit sophisticated Greek profiles and summarize implied volatility surfaces. In the estimation context, we reduce computation times for the calculation of vanilla option values under advanced models, the pricing of American options and the pricing of exotic options under models beyond the Black–Scholes setting.     

套期保值的交易费用与交易策略选择研究

套期保值可以对冲股市的系统风险，评价套期保值绩效时，以往研究通常使用方差减小率，并得出动态套保策略优于静态套保策略的结论。但方差减小率忽视了交易费用，容易误导投资者选择错误的套保策略。文章基于实际情况，分析了套期保值的交易费用，并提出了修正的套保绩效，用来评价套保策略。实证分析表明，只有在交易费用较低时动态套保策略才更...     

The exchange rate effect of multi-currency risk arbitrage

Carry trade arbitrage strategies typically involve multiple currencies. Limits to arbitrage in such a setting not only slow the adjustment to the fundamental equilibrium, but can also generate transitory over- or undershooting of each exchange rate in accordance with the marginal risk contribution of each speculative position to the overall arbitrage risk. The paper uses a natural experiment to identify a particular global arbitrage opportunity and shows that arbitrage risk hedging modifies the exchange rate dynamics in the predicted manner. New spectral methods are applied to obtain a more precise inference on the cross-sectional trading pattern of the arbitrageurs.     

Time and frequency dynamics of connectedness and hedging performance in global stock markets: Bitcoin versus conventional hedges

Some studies have revealed the hedging ability of Bitcoin against stock markets, but the knowledge of how it compares with other hedges is in its infancy. This paper presents the first study on time-frequency domain connectedness and hedging among five hedges (Bitcoin, crude oil, commodities, gold and the U.S. dollar (USD) index) and four stock indices (developed markets ex U.S., emerging markets ex China, U.S. and China). We find that the connectedness between hedges and stock markets varies by time across time horizons. Specifically, the connectedness between Bitcoin and stock indices is the smallest among all hedges, especially for the short horizon. Gold and USD are isolated from other markets at longer horizons. The hedging ratio, optimal portfolio weights and hedging effectiveness also vary across investment horizons. For short-term investment, gold has better hedging effectiveness, especially for emerging stock markets and the U.S. stock market. For median- and long-term investment, USD has better performance, especially for developed markets ex U.S. and emerging stock markets. Additionally, although Bitcoin has good hedging properties, it has high volatility compared with other hedging assets. In other words, if Bitcoin is included in a portfolio, investors should pay attention to its wide variation. These empirical findings highlight the important role that gold and USD play in hedging against global stock markets.     

Investigating the dynamic relationship between cryptocurrencies and conventional assets: Implications for financial investors

Cryptocurrencies are gradually establishing themselves as a new class of assets with unique features, although there remains skepticism and a lack of understanding of their nature. In this study, we compare the financial properties of these new digital assets and investigate their dynamic relationship with major financial securities and commodities. Furthermore, we evaluate the economic and financial potential benefits of cryptocurrencies for financial investors. Using different time-varying copula approaches and bivariate dynamic conditional correlation GARCH models, we find that the cross-correlation with conventional assets is changing over time but weak, supporting the idea that these cryptocurrencies can be suitable for financial diversification. However, our analysis of portfolios shows that cryptocurrencies are poor hedging instruments in most of the considered cases. Moreover, we find that the relationship between cryptocurrencies and conventional assets is sensitive to external economic and financial shocks.     

Deep hedging

We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We discuss how standard reinforcement learning methods can be applied to non-linear reward structures, i.e. in our case convex risk measures. As a general contribution to the use of deep learning for stochastic processes, we also show in Section 4 that the set of constrained trading strategies used by our algorithm is large enough to ε-approximate any optimal solution. Our algorithm can be implemented efficiently even in high-dimensional situations using modern machine learning tools. Its structure does not depend on specific market dynamics, and generalizes across hedging instruments including the use of liquid derivatives. Its computational performance is largely invariant in the size of the portfolio as it depends mainly on the number of hedging instruments available. We illustrate our approach by an experiment on the S&P500 index and by showing the effect on hedging under transaction costs in a synthetic market driven by the Heston model, where we outperform the standard ‘complete-market’ solution.