Generic pricing of FX,inflation and stock options under stochastic interest rates and stochastic volatility

We consider the pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility, for which we use a generic multi-currency framework. We allow for a general correlation structure between the drivers of the volatility, the inflation index, the domestic (nominal) and the foreign (real) rates. Having the flexibility to correlate the underlying FX/inflation/stock index with both stochastic volatility and stochastic interest rates yields a realistic model that is of practical importance for the pricing and hedging of options with a long-term exposure. We derive explicit valuation formulas for various securities, such as vanilla call/put options, forward starting options, inflation-indexed swaps and inflation caps/floors. These vanilla derivatives can be valued in closed form under Schöbel and Zhu [Eur. Finance Rev., 1999, 4, 23–46] stochastic volatility, whereas we devise an (Monte Carlo) approximation in the form of a very effective control variate for the general Heston [Rev. Financial Stud., 1993, 6, 327–343] model. Finally, we investigate the quality of this approximation numerically and consider a calibration example to FX and inflation market data.     

Noise traders, excess volatility, and a securities transactions tax

Proponents of a securities transactions tax have suggested that such a tax may reduce stock return volatility. The argument is that, to the extent that short-term speculative trading volume is the source of excess volatility, a tax that reduces such volume will reduce volatility. In the context of a simple general equilibrium model, it is shown that this partial equilibrium argument is misleading and in large part incorrect. In the absence of a tax, the model generates equilibria in which the risky asset's price exhibits excess volatility and agents engage in excess trading activity owing to the presence of destabilizing noise traders. Within the context of the model, it is shown that, although a transactions tax can reduce the volatility of the risky asset's price, the reduction in price volatility is accompanied by a fall in the asset's price as agents discount the future tax liability associated with risky asset ownership. Consequently, although price volatility may decrease slightly, the fall in equilibrium prices more than compensates, and the volatiltiy of risky asset returns unambiguously increases with the level of the transactions tax.Board of Governors of the Federal Reserve SystemThe conclusions herein are those of the author and do not represent the views of the Federal Reserve Board or any of the Federal Reserve Banks.     

Pricing of foreign exchange options under the MPT stochastic volatility model and the CIR interest rates

We consider an extension of the model proposed by Moretto, Pasquali, and Trivellato [2010. “Derivative Evaluation Using Recombining Trees under Stochastic Volatility.” Advances and Applications in Statistical Sciences 1 (2): 453–480] (referred to as the MPT model) for pricing foreign exchange (FX) options to the case of stochastic domestic and foreign interest rates driven by the Cox, Ingersoll, and Ross dynamics introduced in Cox, Ingersoll, and Ross [1985. “A Theory of Term Structure of Interest Rates.” Econometrica 53(2): 385–408]. The advantage of the MPT model is that it retains some crucial features of Heston's stochastic volatility model but, as demonstrated in Moretto, Pasquali, and Trivellato [2010. “Derivative Evaluation Using Recombining Trees under Stochastic Volatility.” Advances and Applications in Statistical Sciences 1 (2): 453–480], it is better suited for discretization through recombining lattices, and thus it can also be used to value and hedge exotic FX products. In the model examined in this paper, the instantaneous volatility is correlated with the exchange rate dynamics, but the domestic and foreign short-term rates are assumed to be mutually independent and independent of the dynamics of the exchange rate. The main result furnishes a semi-analytical formula for the price of the FX European call option, which hinges on explicit expressions for conditional characteristic functions.     

Making money from FX volatility

As FX options become commoditized products, derivatives on the volatility itself, such as FVAs, have emerged allowing the expression of views on volatility without the burden of actively managing complex option portfolios. Stephane Knauf describes how the canny trader may seek to apply familiar trading strategies from other markets.     

Development and Functioning of FX Markets in Asia and the Pacific

Global foreign exchange (FX) trading volume in traditional FX products and derivatives in Asia and the Pacific has expanded rapidly over the last fifteen years, more so than in other regions. Asian currencies also have experienced exceptional growth in offshore turnover, including non‐deliverable forwards (NDFs). Trading activity on this scale spread across many countries and currencies underscores the need for a well‐functioning infrastructure and exceptional risk management processes. While settlement risks are mitigated for the vast majority of turnover through systems like CLS Bank, the Asia Pacific region would benefit by having more countries and currencies become CLS enabled or tradable under other Payment versus payment (PVP) systems. Though less pronounced than during the global financial crisis, FX markets in the region experienced added turbulence during the “taper tantrum” period of 2013. High turnover currencies tended to depreciate more after taper announcements; though volatility rose more sharply in currencies with low turnover. The FX market is a prominent venue for carry trades that are subject to crash risk. While there is some evidence of herding behavior exacerbating this risk over the past decade, the measures calibrated more recently do not suggest exceptional crowding into carry trades ahead of the “taper tantrum” in 2013. At the same time, our measures of crowdedness for the carry trade show considerable variation over time. Making crowdedness measures publicly available might be advisable.     

Foreign Exchange Risk,Hedging, and Tax-Motivated Outbound Income Shifting

Although outbound income shifting to low-tax jurisdictions provides tax savings, it is often accompanied by nontax costs. In this study, I examine whether foreign exchange (FX) risk constrains tax-motivated outbound income shifting by U.S. multinational corporations. My findings indicate that exposure to greater currency volatility is associated with less outbound income shifting, and this effect is stronger for firms with foreign affiliates using foreign functional currencies. I also investigate whether hedging facilitates outbound income shifting. Consistent with hedging lowering costs associated with exchange rate volatility, I find that U.S. firms that use more currency derivatives tend to shift more income to low-tax foreign jurisdictions. Overall, these findings suggest that FX risk is an important cost of outbound income shifting.     

The impact of the French securities transaction tax on market liquidity and volatility

In this paper, we assess the impact of the securities transaction tax (STT) introduced in France in 2012 on market liquidity and volatility. To identify causality, we rely on a distinctive design of the tax, which is imposed on large French firms only, all listed on Euronext. This provides two reliable control groups (smaller French firms and foreign firms listed on Euronext) and allows us to use a difference-in-difference approach in order to isolate the impact of the tax from the other economic changes that have occurred simultaneously. We find that the STT has reduced stock trading, but we find no significant effect on theoretically based measures of liquidity, such as price impact, and no significant effect on volatility. The results are robust whether we rely on different control groups (German stocks listed on the Deutsche Börse), different datasets (firm-level or aggregated data), different periods (from one to six months), or different methodologies (propensity score matching, regression discontinuity design).     

2014年10月银行间市场运行报告

10月,银行间市场的主要运行特点是：人民币市场资金面维持宽松,长期利率走低、短期利率升而不高;债券市场维持暧势,国债收益率曲线显著下移;人民币交易汇率持续走强,相对中间价偏离继续温和扩大;人民币利率互换收盘曲线整体下移,交易量同比显著增长;外汇衍生品交投活跃,外汇掉期曲线与上月持平,期权波动率继续小幅上行。     

Optimal informed trading in the foreign exchange market

We formulate a market microstructure model of exchange determination that we employ to investigate the impact of informed trading on exchange rates and on foreign exchange (FX) market conditions. With our formulation, we show how strategic informed agents influence exchange rates via both the portfolio-balance and information effects. We outline the connection which exists between the private value of information, market efficiency, liquidity and exchange rate volatility. Our model is also consistent with recent empirical research on the micro-structure of FX markets.     

A continuous time Bayesian network classifier for intraday FX prediction

Abstract

Prediction of foreign exchange (FX) rates is addressed as a binary classification problem in which a continuous time Bayesian network classifier (CTBNC) is developed and used to solve it. An exact algorithm for inference on CTBNC is introduced. The performance of an instance of these classifiers is analysed and compared to that of dynamic Bayesian network by using real tick by tick FX rates. Performance analysis and comparison, based on different metrics such as accuracy, precision, recall and Brier score, evince a predictive power of these models for FX rates at high frequencies. The achieved results also show that the proposed CTBNC is more effective and more efficient than dynamic Bayesian network classifier. In particular, it allows to perform high frequency prediction of FX rates in cases where dynamic Bayesian networks-based models are computationally intractable.     

The intended and unintended consequences of financial-market regulations: A general-equilibrium analysis

In a production economy with trade in financial markets motivated by the desire to share labor-income risk and to speculate, we show that speculation increases volatility of asset returns and investment growth, increases the equity risk premium, and reduces welfare. Regulatory measures, such as constraints on stock positions, borrowing constraints, and the Tobin tax have similar effects on financial and macroeconomic variables. However, borrowing constraints and the Tobin tax are more successful than constraints on stock positions at improving welfare because they substantially reduce speculative trading without impairing excessively risk-sharing trades.     

Short-term Dynamics in the Cyprus Stock Exchange

Abstract

This paper investigates the short-term dynamics of stock returns in an emerging stock market namely, the Cyprus Stock Exchange (CYSE). Stock returns are modelled as conditionally heteroscedastic processes with time-dependent serial correlation. The conditional variance follows an EGARCH process, while for the conditional mean three nonlinear specifications are tested, namely: (a) the LeBaron exponential autoregressive model; (b) the Sentana and Wadhwani positive feedback trading model; and finally (c) a model that nests both (a) and (b). There is an inverse relationship between volatility and autocorrelation consistent with the findings from several other stock markets, including the US. This pattern could be the manifestation of a certain form of noise trading namely positive feedback trading or, momentum trading strategies. There is little evidence that market declines are followed with higher volatility than market advances, the so-called ‘leverage effect’, that has been observed in almost all developed stock markets. In out of sample forecasts, the nonlinear specifications provide better results in terms of forecasting both first and second moments of the distribution of returns.     

Can channel pattern trading be profitably automated?

Financial markets, such as the global foreign exchange (FX) market, often exhibit trending behaviour. Within such trends, the market level oscillates with changes in market consensus. Continued oscillations of this type result in the formation of wave patterns within the underlying trend known as channels, which are used by technical analysts as trade entry signals. A sample space of such channels has been constructed from a set of US dollar/British pound Spot FX tick data from 1989–1997 using pattern recognition algorithms and the profitability of trading using such patterns has been estimated. A number of attributes of the resulting collection of channels has been subjected to statistical analysis with the aim of classifying patterns that can be traded profitably using a number of simple trading rules. Results of this analysis show that there exist statistically significant links between the channels' attributes and profitability.     

Intertemporal risk-return trade-off in foreign exchange rates

We investigate the intertemporal risk-return trade-off of foreign exchange (FX) rates for ten currencies quoted against the USD. For each currency, we use three risk measures simultaneously that pertain to that currency; its realized volatility, its realized skewness, and its value-at-risk. We apply monthly FX excess returns and risk measures calculated from daily observations. We find that there is a significant contemporaneous risk-return trade-off for the currencies under investigation. There is no evidence of noncontemporaneous risk-return trade-off. We pay special attention to the risk-return trade-off during the recent financial crisis.     

Market-maker,inventory control and foreign exchange dynamics

Abstract

This paper examines how inventory management of foreign exchange dealers may affect exchange-rate dynamics. According to empirical observations, market makers set exchange rates not only with respect to excess demand but also in recognition of their inventory. Within our model, market makers control their positions by quoting exchange rates that provoke offsetting orders of technical and fundamental traders. Our model demonstrates that such behaviour may amplify trading volume, exchange-rate volatility and deviations from fundamentals.     

Conditional volatility persistence and volatility spillovers in the foreign exchange market

I investigate the magnitudes and determinants of volatility spillovers in the foreign exchange (FX) market, using realized measures of volatility and heterogeneous autoregressive (HAR) models. I confirm both meteor shower effects (i.e., inter-regional volatility spillovers) and heat wave effects (i.e., intra-regional volatility spillovers) in the FX market. Furthermore, I find that conditional volatility persistence is the dominant channel linking the changing market states of each region to future volatility and its spillovers. Market state variables contribute to more than half of the explanatory power in predicting conditional volatility persistence, with the model that calibrates volatility persistence and spillovers conditionally on market states performing statistically and economically better. The utilization of market state variables significantly extends our understanding of the economic mechanisms of volatility persistence and spillovers and sheds new light on econometric techniques for volatility modeling and forecasting.     

Liquidity determination in an order-driven market

We exploit full order level information from an electronic FX broking system to provide a comprehensive account of the determination of its liquidity. We not only look at bid-ask spreads and trading volumes, but also study the determination of order entry rates and depth measures derived from the entire limit order book. We find strong predictability in the arrival of liquidity supply/demand events. Further, in times of low (high) liquidity, liquidity supply (demand) events are more common. In times of high trading activity and volatility, the ratio of limit to market order arrivals is high but order book spreads and depth deteriorate. These results are consistent with market order traders having better information than limit order traders.     

A simulation analysis of the microstructure of double auction markets

Abstract

We introduce an order-driven market model with heterogeneous agents trading via a central order matching mechanism. Traders set bids and asks and post market or limit orders according to exogenously fixed rules. We investigate how different trading strategies may affect the dynamics of price, bid-ask spreads, trading volume and volatility. We also analyse how some features of market design, such as tick size and order lifetime, affect market liquidity. The model is able to reproduce many of the complex phenomena observed in real stock markets.     

VOLATILITY FORECASTS,TRADING VOLUME,AND THE ARCH VERSUS OPTION‐IMPLIED VOLATILITY TRADE‐OFF

We investigate empirically the role of trading volume (1) in predicting the relative informativeness of volatility forecasts produced by autoregressive conditional heteroskedasticity (ARCH) models versus the volatility forecasts derived from option prices, and (2) in improving volatility forecasts produced by ARCH and option models and combinations of models. Daily and monthly data are explored. We find that if trading volume was low during period t?1 relative to the recent past, ARCH is at least as important as options for forecasting future stock market volatility. Conversely, if volume was high during period t?1 relative to the recent past, option‐implied volatility is much more important than ARCH for forecasting future volatility. Considering relative trading volume as a proxy for changes in the set of information available to investors, our findings reveal an important switching role for trading volume between a volatility forecast that reflects relatively stale information (the historical ARCH estimate) and the option‐implied forward‐looking estimate.