Short-Term External Debt and Foreign Exchange Rate Volatility in Emerging Economies: Evidence from the Korea Market

Abstract:

We empirically analyze the main determinants of foreign exchange rate (FX) volatility in emerging market economies using the data of Korea corporations and financial institutions. We find that short-term external debt is more important than trading volume of foreign investors in explaining FX volatility. Our results suggest that short-term debt-controlling measures, such as a tax levy on short-term borrowing, can be more effective in moderating FX volatility than can the measures affecting the trading volume, such as a Tobin tax.     

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.     

Regression Models for Bivariate Loss Data

Abstract

This case study illustrates the analysis of two possible regression models for bivariate claims data. Estimates or forecasts of loss distributions under these two models are developed using two methods of analysis: (1) maximum likelihood estimation and (2) the Bayesian method. These methods are applied to two data sets consisting of 24 and 1,500 paired observations, respectively. The Bayesian analyses are implemented using Markov chain Monte Carlo via WinBUGS, as discussed in Scollnik (2001). A comparison of the analyses reveals that forecasted total losses can be dramatically underestimated by the maximum likelihood estimation method because it ignores the inherent parameter uncertainty.     

Dynamical clustering of exchange rates

We use techniques from network science to study correlations in the foreign exchange (FX) market during the period 1991–2008. We consider an FX market network in which each node represents an exchange rate and each weighted edge represents a time-dependent correlation between the rates. To provide insights into the clustering of the exchange-rate time series, we investigate dynamic communities in the network. We show that there is a relationship between an exchange rate's functional role within the market and its position within its community and use a node-centric community analysis to track the temporal dynamics of such roles. This reveals which exchange rates dominate the market at particular times and also identifies exchange rates that experienced significant changes in market role. We also use the community dynamics to uncover major structural changes that occurred in the FX market. Our techniques are general and will be similarly useful for investigating correlations in other markets.     

A class of Lévy process models with almost exact calibration to both barrier and vanilla FX options

Vanilla (standard European) options are actively traded on many underlying asset classes, such as equities, commodities and foreign exchange (FX). The market quotes for these options are typically used by exotic options traders to calibrate the parameters of the (risk-neutral) stochastic process for the underlying asset. Barrier options, of many different types, are also widely traded in all these markets but one important feature of the FX options markets is that barrier options, especially double-no-touch (DNT) options, are now so actively traded that they are no longer considered, in any way, exotic options. Instead, traders would, in principle, like to use them as instruments to which they can calibrate their model. The desirability of doing this has been highlighted by talks at practitioner conferences but, to our best knowledge (at least within the realm of the published literature), there have been no models which are specifically designed to cater for this. In this paper, we introduce such a model. It allows for calibration in a two-stage process. The first stage fits to DNT options (or other types of double barrier options). The second stage fits to vanilla options. The key to this is to assume that the dynamics of the spot FX rate are of one type before the first exit time from a ‘corridor’ region but are allowed to be of a different type after the first exit time. The model allows for jumps (either finite activity or infinite activity) and also for stochastic volatility. Hence, not only can it give a good fit to the market prices of options, it can also allow for realistic dynamics of the underlying FX rate and realistic future volatility smiles and skews. En route, we significantly extend existing results in the literature by providing closed-form (up to Laplace inversion) expressions for the prices of several types of barrier options as well as results related to the distribution of first passage times and of the ‘overshoot’.     

The determinants of Norwegian exporters’ foreign exchange risk management

Abstract

This paper examines foreign exchange (FX) hedging by Norwegian exporting firms to provide empirical evidence on the determinants of the hedging decision. The paper contributes to prior studies by, first, focusing on exporters to ensure that the companies in the sample have FX exposure, thereby allowing a more rigorous test of the theoretical determinants of hedging, and, secondly, in contrast to most previous studies that have focused on FX external hedging instruments, the use of both internal and external instruments is examined. Univariate, multivariate and multinominal analyses all provide evidence consistent with the firm value maximization hypotheses of underinvestment and risk aversion. Also, the following characteristics of firms—size, extent of internationalization and liquidity—are found to be related to the decision to hedge FX risk. However, the evidence on the links between the firm characteristics and the decision to hedge is not consistent across internal and external FX hedgers, and also varies for individual hedging instruments. Therefore it is argued that the empirical evidence on the theoretical determinants cannot be generalized to cover the full range of FX hedging strategies (which includes internal hedging instruments). Unlike empirical studies for other countries the evidence for Norwegian firms does not support the hypothesis that the avoidance of financial distress and the need to resort to external capital markets is a significant determinant of the hedging decision. Whilst the evidence suggests that country-specific factors may play a role in determining the use of FX hedging, it does not imply that the different policies adopted are necessarily inconsistent with the firm value maximization hypothesis.     

Time-varying long-run mean of commodity prices and the modeling of futures term structures

The exploration of the mean-reversion of commodity prices is important for inventory management, inflation forecasting and contingent claim pricing. Bessembinder et al. [J. Finance, 1995, 50, 361–375] document the mean-reversion of commodity spot prices using futures term structure data; however, mean-reversion to a constant level is rejected in nearly all studies using historical spot price time series. This indicates that the spot prices revert to a stochastic long-run mean. Recognizing this, I propose a reduced-form model with the stochastic long-run mean as a separate factor. This model fits the futures dynamics better than do classical models such as the Gibson–Schwartz [J. Finance, 1990, 45, 959–976] model and the Casassus–Collin-Dufresne [J. Finance, 2005, 60, 2283–2331] model with a constant interest rate. An application for option pricing is also presented in this paper.     

Bayesian multivariate regime-switching models and the impact of correlation structure misspecification in variable annuity pricing

ABSTRACT

We develop Bayesian multivariate regime-switching models for correlated assets, comparing three different ways to flexibly structure the correlation matrix. After developing the models, we examine their relative characteristics and performance, first in a straightforward asset simulation example, and later applied to a variable annuity product with guarantees. We find that the freedom allowed by the more flexible structures enables these models to more accurately reflect the actual asset dependence structure. We also show that the correlation structures inferred by the most commonly used (and simplest) model will result in significantly larger estimates of the cost of the annuity guarantees.     

Actuarial Modeling with MCMC and BUGs

Abstract

In this paper, the author reviews some aspects of Bayesian data analysis and discusses how a variety of actuarial models can be implemented and analyzed in accordance with the Bayesian paradigm using Markov chain Monte Carlo techniques via the BUGS (Bayesian inference Using Gibbs Sampling) suite of software packages. The emphasis is placed on actuarial loss models, but other applications are referenced, and directions are given for obtaining documentation for additional worked examples on the World Wide Web.     

Spatial statistical modelling of insurance risk: a spatial epidemiological approach to car insurance

Spatial models, such as the Besag, York and Mollie (BYM) model, have long been used in epidemiology and disease mapping. A common research question in these subjects is modelling the number of disease events per region; here the BYM models provides a holistic framework for both covariates and dependencies between regions. We use these tools to assess the relative insurance risk associated with the policyholders geographical location. A Bayesian modelling approach is presented and an elastic net is used to reduce the large number of possible geographic covariates. The final inference is performed using Integrated Nested Laplace Approximation. The model is applied to car insurance data from If P&C Insurance together with spatially referenced covariate data of high resolution, provided by Insightone. The entire analysis is performed using freely available R-packages. Including spatial dependence when modelling the number of claims significantly improves on the result obtained using ordinary generalised linear models. However, the support for adding a spatial component to the model for claims cost is weaker.     

Myopic loss aversion and margin of safety: the risk of value investing

Abstract

Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the assumption of IID random order flow, and analyse it using simulation, dimensional analysis, and theoretical tools based on mean field approximations. The model makes testable predictions for basic properties of markets, such as price volatility, the depth of stored supply and demand versus price, the bid–ask spread, the price impact function, and the time and probability of filling orders. These predictions are based on properties of order flow and the limit order book, such as share volume of market and limit orders, cancellations, typical order size, and tick size. Because these quantities can all be measured directly there are no free parameters. We show that the order size, which can be cast as a non-dimensional granularity parameter, is in most cases a more significant determinant of market behaviour than tick size. We also provide an explanation for the observed highly concave nature of the price impact function. On a broader level, this work suggests how stochastic models based on zero intelligence agents may be useful to probe the structure of market institutions. Like the model of perfect rationality, a stochastic zero intelligence model can be used to make strong predictions based on a compact set of assumptions, even if these assumptions are not fully believable.     

International Yield Curves and Currency Puzzles

The currency depreciation rate is often computed as the ratio of foreign to domestic pricing kernels. Using bond prices alone to estimate these kernels leads to currency puzzles: the inability of models to match violations of uncovered interest parity and the volatility of exchange rates. This happens because of the FX bond disconnect, the inability of bonds to span exchange rates. Incorporating innovations to the pricing kernel that affect exchange rates but not bonds helps resolve the puzzles. This approach also allows one to relate news about cross-country differences between international yields to news about currency risk premiums.     

A Bayesian Generalized Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving

Abstract

This paper shows how Bayesian models within the framework of generalized linear models can be applied to claims reserving. The author demonstrates that this approach is closely related to the Bornhuetter-Ferguson technique. Benktander (1976) and Mack (2000) previously studied the Bornhuetter-Ferguson technique and advocated using credibility models. The present paper uses a Bayesian parametric model within the framework of generalized linear models.     

Continuous time and nonparametric modelling of U.S. interest rate models

In this paper we compare the forecasting performance of different models of interest rates using parametric and nonparametric estimation methods. In particular, we use three popular nonparametric methods, namely, artificial neural networks (ANN), k-nearest neighbour (k-NN), and local linear regression (LL). These are compared with forecasts obtained from two-factor continuous time interest rate models, namely, Chan, Karolyi, Longstaff, and Sanders [CKLS, J. Finance 47 (1992) 1209]; Cos, Ingersoll, and Ross [CIR, Econometrica 53 (1985) 385]; Brennan and Schwartz [BR-SC, J. Financ. Quant. Anal. 15 (1980) 907]; and Vasicek [J. Financ. Econ. 5 (1977) 177]. We find that while the parametric continuous time method, specifically Vasicek, produces the most successful forecasts, the nonparametric k-NN performed well.     

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.     

HIGH‐FREQUENCY EXCHANGE‐RATE PREDICTION WITH AN ARTIFICIAL NEURAL NETWORK

This paper examines how market microstructure variables can be used to forecast foreign exchange (FX) rates at frequencies of one to several minutes. We use a unique FX dataset of global inter‐dealer electronic transactions and applied the artificial neural network (ANN) as the predicting model. The immediately preceding bid and ask prices are significant factors in these predictions, which is in keeping with market microstructure theory. These microstructure factors have not been tested in an ANN model before. High‐frequency trading strategies based on the ANN model are shown to be profitable even when transaction costs are included. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Second-order Bayesian revision of a generalised linear model

It is well known that the exponential dispersion family (EDF) of univariate distributions is closed under Bayesian revision in the presence of natural conjugate priors. However, this is not the case for the general multivariate EDF. This paper derives a second-order approximation to the posterior likelihood of a naturally conjugated generalised linear model (GLM), i.e., multivariate EDF subject to a link function (Section 5.5). It is not the same as a normal approximation. It does, however, lead to second-order Bayes estimators of parameters of the posterior. The family of second-order approximations is found to be closed under Bayesian revision. This generates a recursion for repeated Bayesian revision of the GLM with the acquisition of additional data. The recursion simplifies greatly for a canonical link. The resulting structure is easily extended to a filter for estimation of the parameters of a dynamic generalised linear model (DGLM) (Section 6.2). The Kalman filter emerges as a special case. A second type of link function, related to the canonical link, and with similar properties, is identified. This is called here the companion canonical link. For a given GLM with canonical link, the companion to that link generates a companion GLM (Section 4). The recursive form of the Bayesian revision of this GLM is also obtained (Section 5.5.3). There is a perfect parallel between the development of the GLM recursion and its companion. A dictionary for translation between the two is given so that one is readily derived from the other (Table 5.1). The companion canonical link also generates a companion DGLM. A filter for this is obtained (Section 6.3). Section 1.2 provides an indication of how the theory developed here might be applied to loss reserving. A sequel paper, providing numerical illustrations of this, is planned.     

Hierarchical Bayesian Whittaker Graduation

Abstract

The Whittaker method of graduation has been known and used for a long time and has remained popular due to its possession of a number of ideal properties. They include being nonparametric and having an easy to understand foundation. The latter means that it makes sense and thus the user of the method has a good idea of what it can and cannot do. As well, there is a statistical derivation available that uses Bayesian notions. A problem with the derivation is that it is more intuitive than precise and as such does not provide a useful frame of reference for the graduator. Regardless of the point of view, the graduation cannot be completed until the smoothing parameter is selected and this has always relied on the judgment of the analyst.

In this paper, three tasks will be undertaken. The first is to replace the ad-hoc Bayesian derivation of the method with a formal Bayesian specification. The second is to show that with this specification it is possible to complete the graduation without making an arbitrary selection of the smoothing parameter. The third is to provide a Monte Carlo Bayesian approach for the incorporation of constraints in the graduated values. The ideas will be illustrated with a numerical example.