Immunizing Foreign Exchange Contracts Against Swap Rate and Volatility Risks

Swap rate risk, also called the problem of' "maturity gaps," originates from foreign currency holdings whenever the involved contracts have differing maturities. Such differing maturities give rise to a sensitivity of the portfolio values with respect to the "swap rate," or differential between the relative interest rates in two countries. Volatility risk, which typically affects only currency contracts having asymmetric payoffs (such as currency options), gives rise to a sensitivity of portfolio values with respect to changes in the exchange rate volatility. In this article we show how currency portfolios may be immunized , or made insensitive, to both swap rate risk and volatility risk, in the sense of Macaulay's (1938) classical treatment of interest rate risk. The European currency option contract is the primary subject of our discussion, since we show that both ordinary forward contracts and other complicated currency contracts are equivalent to suitable combinations of European currency options.     

The dynamic impact of oil price shocks on the stock market and the USD/RMB exchange rate: Evidence from implied volatility indices

Using daily data from March 16, 2011, to September 9, 2019, we explore the dynamic impact of the oil implied volatility index (OVX) changes on the Chinese stock implied volatility index (VXFXI) changes and on the USD/RMB exchange rate implied volatility index (USDCNYV1M) changes. Through a TVP-VAR model, we analyse the time-varying uncertainty transmission effects across the three markets, measured by the changes in implied volatility indices. The empirical results show that the OVX changes are the dominant factor, which has a positive impact on the USDCNYV1M changes and the VXFXI changes during periods of important political and economic events. Moreover, USDCNYV1M changes are the key factor affecting the impact of OVX changes on VXFXI changes. When the oil crisis, exchange rate reform, and stock market crash occurred during 2014–2016, the positive effects of uncertainty transmission among the oil market, the Chinese stock market, and the bilateral exchange rate are significantly strengthened. Finally, we find that the positive effects are significant in the short term but diminish over time.     

Implied volatility and the risk-free rate of return in options markets

We numerically solve systems of Black–Scholes formulas for implied volatility and implied risk-free rate of return. After using a seemingly unrelated regressions (SUR) model to obtain point estimates for implied volatility and implied risk-free rate, the options are re-priced using these parameters. After repricing, the difference between the market price and model price is increasing in time to expiration, while the effect of moneyness and the bid-ask spread are ambiguous. Our varying risk-free rate model yields Black–Scholes prices closer to market prices than the fixed risk-free rate model. In addition, our model is better for predicting future evolutions in model-free implied volatility as measured by the VIX.     

Path dependent volatility

We propose a general class of non-constant volatility models with dependence on the past. The framework includes path-dependent volatility models such as that by Hobson and Rogers and also path dependent contracts such as options of Asian style. A key feature of the model is that market completeness is preserved. Some empirical analysis, based on the comparison with standard local volatility and Heston models, shows the effectiveness of the path dependent volatility. In particular, it turns out that, when large market movements occur, the tracking errors of Heston minimum-variance hedging are up to twice the hedging errors of a path dependent volatility model.      

Options and earnings announcements: an empirical study for the European Options Exchange

In this paper we give an introduction in option pricing theory and explicitly specify the Black-Scholes model. Although market participants use this and similar models to price options, they violate one of the fundamental assumptions of the model. They do not set a constant value for the volatility of the underlying asset over time, but change the volatility even during a day. By means of event study methodology we investigate the volatility of the underlying asset and the volatility implicit in option prices around earnings announcements by firms. We find that the volatility in option prices increases before the announcement date and drops sharply afterwards. The volatility of the underlying stocks is higher only at the announcement dates and we do not observe a higher volatility around these dates. Hence, the constant volatility of the underlying asset, which is one of the assumptions in the Black-Scholes model, does not hold. However, the market seems to correctly anticipate the change in volatility, by correcting option prices.     

Option pricing with discrete time jump processes

In this paper we propose new option pricing models based on class of models with jumps contained in the Lévy-type based models (NIG-Lévy, Schoutens, 2003, Merton-jump, Merton, 1976 and Duan based model, Duan et al., 2007). By combining these different classes of models with several volatility dynamics of the GARCH type, we aim at taking into account the dynamics of financial returns in a realistic way. The associated risk neutral dynamics of the time series models is obtained through two different specifications for the pricing kernel: we provide a characterization of the change in the probability measure using the Esscher transform and the Minimal Entropy Martingale Measure. We finally assess empirically the performance of this modelling approach, using a dataset of European options based on the S&P 500 and on the CAC 40 indices. Our results show that models involving jumps and a time varying volatility provide realistic pricing and hedging results for options with different kinds of time to maturities and moneyness. These results are supportive of the idea that a realistic time series model can provide realistic option prices making the approach developed here interesting to price options when option markets are illiquid or when such markets simply do not exist.     

An empirical application of stochastic volatility models

This paper studies the empirical performance of stochastic volatility models for twenty years of weekly exchange rate data for four major currencies. We concentrate on the effects of the distribution of the exchange rate innovations for both parameter estimates and for estimates of the latent volatility series. The density of the log of squared exchange rate innovations is modelled as a flexible mixture of normals. We use three different estimation techniques: quasi-maximum likelihood, simulated EM, and a Bayesian procedure. The estimated models are applied for pricing currency options. The major findings of the paper are that: (1) explicitly incorporating fat-tailed innovations increases the estimates of the persistence of volatility dynamics; (2) the estimation error of the volatility time series is very large; (3) this in turn causes standard errors on calculated option prices to be so large that these prices are rarely significantly different from a model with constant volatility. © 1998 John Wiley & Sons, Ltd.     

The impact of idiosyncratic uncertainty when investment opportunities are endogenous

This paper develops a general equilibrium model to study the impact of aggregate fluctuations in idiosyncratic volatility that incorporates the endogenous determination of investment opportunities. By making investment options more valuable, an increase in volatility encourages the creation of new investment options. I find the response of the economy to a volatility shock depends on how investment opportunities are obtained. If potential entrants are allowed to invest in new idiosyncratic technologies, thereby acquiring options for further investment, the volatility shock increases overall investment and results in an economic boom. On the other hand, if such an investment in option creation is precluded and investment opportunities are exogenously given, the volatility shock decreases aggregate investment.     

Approximate analytic solution for Asian options with stochastic volatility

The valuation of Asian options is complicated because the arithmetic average of lognormal random variables is no longer lognormal. Furthermore, the stochastic volatility inherent in financial asset prices is easily observed. However, few academic studies consider the pricing and hedging of Asian options with stochastic volatility, despite the popularity of such options. This study extends the work of Hull and White (1987) and integrates the Taylor series expansion technique to derive an approximate analytic solution for Asian options with stochastic volatility. Numerical experiments show that the proposed approximate analytic solution performs favorably and is computationally efficient compared with large-sample simulations. The approximate analytic solution provides a practical approach for pricing and hedging Asian options with stochastic volatility and is both easy to implement and desirable in terms of computing speed.     

Modelling the conditional volatility of commodity index futures as a regime switching process

Commodity index futures offer a versatile tool for gaining different forms of exposure to commodity markets. Volatility is a critical input in many of these applications. This paper examines issues in modelling the conditional variance of futures returns based on the Goldman Sachs Commodity Index (GSCI). Given that commodity markets tend to be ‘choppy’ (Webb, 1987 ), a general econometric model is proposed that allows for abrupt changes or regime shifts in volatility, transition probabilities which vary explicitly with observable fundamentals such as the basis, GARCH dynamics, seasonal variations and conditional leptokurtosis. The model is applied to daily futures returns on the GSCI over 1992–1997. The results show clear evidence of regime shifts in conditional mean and volatility. Once regime shifts are accounted for, GARCH effects are minimal. Consistent with the theory of storage, returns are more likely to switch to the high‐variance state when the basis is negative than when the basis is positive. The regime switching model also performs well in forecasting the daily volatility compared to standard GARCH models without regime switches. The model should be of interest to sophisticated traders who base their trading strategies on short‐term volatility movements, managed commodity funds interested in hedging an underlying diversified portfolio of commodities and investors of options and other derivatives tied to GSCI futures contracts. Copyright © 2001 John Wiley & Sons, Ltd.     

Parametric pricing of higher order moments in S&P500 options

A general parametric framework based on the generalized Student t‐distribution is developed for pricing S&P500 options. Higher order moments in stock returns as well as time‐varying volatility are priced. An important computational advantage of the proposed framework over Monte Carlo‐based pricing methods is that options can be priced using one‐dimensional quadrature integration. The empirical application is based on S&P500 options traded on select days in April 1995, a total sample of over 100,000 observations. A range of performance criteria are used to evaluate the proposed model, as well as a number of alternative models. The empirical results show that pricing higher order moments and time‐varying volatility yields improvements in the pricing of options, as well as correcting the volatility skew associated with the Black–Scholes model. Copyright © 2004 John Wiley & Sons, Ltd.     

Forecasting risk in the US Dollar exchange rate under volatility shifts

Recent evidence suggests that volatility shifts (i.e. structural breaks in volatility) in returns increases kurtosis which significantly contributes to the observed non-normality in market returns. In this paper, we endogenously detect significant shifts in the volatility of US Dollar exchange rate and incorporate this information to estimate Value-at-Risk (VaR) to forecast large declines in the US Dollar exchange rate. Our out-of-sample performance results indicate that a GARCH model with volatility shifts produces the most accurate VaR forecast relative to several benchmark methods. Our contribution is important as changes in US Dollar exchange rate have a substantial impact on the global economy and financial markets.     

Time series properties of ARCH processes with persistent covariates

We investigate the time series properties of a volatility model, whose conditional variance is specified as in ARCH with an additional persistent covariate. The included covariate is assumed to be an integrated or nearly integrated process, with its effect on volatility given by a wide class of nonlinear volatility functions. In the paper, such a model is shown to generate many important characteristics that are commonly observed in financial time series. In particular, the model yields persistence in volatility, and also well predicts leptokurtosis. This is true for any type of volatility functions considered in the paper, as long as the covariate is integrated or nearly integrated. Stationary covariates cannot produce important characteristics observed in many financial time series. We present two empirical applications of the model, which show that the default premium (the yield spread between Baa and Aaa corporate bonds) affects stock return volatility and the interest rate differential between two countries accounts for exchange rate return volatility. The forecast evaluation shows that the model generally outperforms GARCH and FIGARCH at relatively lower frequencies.     

基于实物期权法的风险投资项目估价方法——一个文献综述

本文理清了实物期权及其在风险投资项目估价中应用的发展脉络,并提出了实物期权在风险投资项目估价应用中需要发展的地方。     

Dupire’s formulas in the Piterbarg option pricing model

In this paper we derive an expression for the local volatility of an underlying asset, given the prices of liquid European call options under the Piterbarg framework. The Piterbarg framework is a multi-curve derivative pricing model which extends the well known Black–Scholes–Merton model by relaxing the assumption of a risk-free interest rate, and includes collateral payments. The expressions for the local volatility is a function of the option price surface, and is then transformed to become a function of the implied volatility surface.     

Modeling volatility in sector index returns with GARCH models using an iterated algorithm

Financial market participants are interested in knowing what events can alter the volatility pattern of financial assets and how unanticipated shocks determine the persistence of volatility over time. The present paper studies these issues by detecting time periods of sudden changes in volatility by using the iterated cumulated sums of squares (ICSS) algorithm. Examining five major sectors from January 1992 to August 2003, we found that accounting for volatility shifts in the standard GARCH model considerably reduces the estimated volatility persistence. Our results have important implications regarding asset pricing, risk management, and portfolio selection. (JEL G110, G120)     

The credibility of the Colombian exchange rate target zone: Its impact over the volatility of interest rate differentials

This paper analyzes the credibility of Colombia’s exchange rate target zone, and in particular its impact on the volatility of interest rate differentials. Bertola and Caballeros’ (1995) model of a target zone with imperfect credibility is used to derive the impact of a reduction in credibility over the variance of the interest rate differential. It is theoretically shown, that as credibility decreases the variance of the interest rate differential increases. This theoretical argument is used to estimate credibility in Colombia’s exchange rate target zone. Using a SWARCH model, the probability of being in a regime with high interest rate volatility is estimated, and is related with events in the exchange rate market. Results suggest that there is evidence of lack of credibility even before the recent international financial turmoil was triggered.     

Time-series properties and predictability of Greek exchange rates

This paper explores the time-series properties and predictability of weekly percentage changes in the Greek drachma exchange rates with respect to the currencies of major trading-partner countries, such as the USA, Germany, the UK, France, Italy and Japan. The analysis is carried out using the EGARCH-M model along with the power exponential distribution. Percentage changes in the Greek drachma with respect to the German mark, the French franc, the Italian lira and Japanese yen are predictable using past information. The volatility of Greek exchange rates is best represented by an EGARCH process and as such is predictable using past volatility measures. Moreover, volatility of the Greek drachma with respect to the German mark and Italian lira positively influences future movements in these exchange rates. The hypothesis that volatility is an asymmetric function of past innovations is rejected in all cases. Following the inclusion of the Greek drachma in the ECU currency basket, its value has been depreciating at a higher rate with respect to the German mark and Italian lira and at a lower rate with respect to the US dollar. Also, its volatility with respect to the German mark, the French franc, and the Italian lira has decreased, whereas its volatility with respect to the US dollar has increased.     

Stock market volatility,the news,and monetary policy

The dynamic relationship linking the volatility of equity prices with “the news” and the expected path for monetary policy is investigated. Previous results that link the impact of the news about real activity to changes in current and future interest rates are employed in developing a positive link between changes in volatility and the news. Empirically, our results uncover a positive and statistically significant response of the CBOE volatility index, VIX, to unanticipated changes in employment, but not to inflation. Hence, agents' expectations for the policy response to news have an important influence on the expected volatility of stock prices. (JEL E44, E52)     

The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange,stock, and bond markets

We study the forecasting of future realized volatility in the foreign exchange, stock, and bond markets from variables in our information set, including implied volatility backed out from option prices. Realized volatility is separated into its continuous and jump components, and the heterogeneous autoregressive (HAR) model is applied with implied volatility as an additional forecasting variable. A vector HAR (VecHAR) model for the resulting simultaneous system is introduced, controlling for possible endogeneity issues. We find that implied volatility contains incremental information about future volatility in all three markets, relative to past continuous and jump components, and it is an unbiased forecast in the foreign exchange and stock markets. Out-of-sample forecasting experiments confirm that implied volatility is important in forecasting future realized volatility components in all three markets. Perhaps surprisingly, the jump component is, to some extent, predictable, and options appear calibrated to incorporate information about future jumps in all three markets.