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This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. As such, the model can back out the market prices of convertible bonds. A prevailing belief in the market is that convertible arbitrage is mainly due to convertible underpricing. Empirically, however, we do not find evidence supporting the underpricing hypothesis. Instead, we find that convertibles have relatively large positive gammas. As a typical convertible arbitrage strategy employs delta-neutral hedging, a large positive gamma can make the portfolio highly profitable, especially for a large movement in the underlying stock price., https://ia801504.us.archive.org/8/items/pricingConvertibleBondJumpDiffusion-5/pricingConvertibleBondJumpDiffusion-5.pdf

The LIBOR Market Model has become one of the most popular models for pricing interest rate products. It is commonly believed that Monte-Carlo simulation is the only viable method available for the LIBOR Market Model. In this article, however, we propose a lattice approach to price interest rate products within the LIBOR Market Model by introducing a shifted forward measure and several novel fast drift approximation methods. This model should achieve the best performance without losing much accuracy. Moreover, the calibration is almost automatic and it is simple and easy to implement. Adding this model to the valuation toolkit is actually quite useful; especially for risk management or in the case there is a need for a quick turnaround., https://ia801403.us.archive.org/29/items/lattice-in-lmm-4/Lattice-in-LMM-4.pdf

This paper provides an assessment of the comparative effectiveness of four econometric methods in estimating the optimal hedge ratio in an emerging equity market, particularly the South African equity and futures markets. The paper bases the effectiveness of hedging on volatility reduction and minimisation of the coefficient of variation of hedged returns as well as risk-aversion based utility maximisation. The empirical analysis shows that the single equation method estimated by ordinary least squares is the most effective over daily hedging periods. However, the vector error-correction method and multivariate GARCH methods are most effective over weekly and monthly hedging periods.

This article reviews recent econometric developments in the literature on price discovery and predictability. For both areas, we discuss traditional approaches to econometric modeling, limitations to these approaches, and recent developments designed to overcome them. We also discuss the state of the art and suggest future research. Three main conclusions are drawn. First, while many recent empirical applications in price discovery and price predictability are on the frontier of econometric methods, further developments are needed to increase relaxation of relevant assumptions and push the boundaries of applications. Second, future research in econometric modeling needs to combine/synthesize recent developments across multiple econometric issues, rather than proceeding in a piecemeal manner, for instance, by integrating developments in the time series literature into panel-based frameworks. Third, recent econometric literature is generating findings that challenge long-held beliefs about apparent empirical regularities in price discovery and price predictability, thus presenting opportunities to develop relevant theory.

The Sharpe Ratio offers an excellent summary of the excess return required per unit of risk invested. This work presents an adaptation of the ex-ante Sharpe Ratio for currencies where we consider a random walk approach for the currency behavior and implied volatility as a proxy for market expectations of future realized volatility. The outcome of the proposed measure seems to gauge some information on the expected required return attached to the “peso problem”.

Empirical studies on credit spread determinants are predicated on the presence of a single-regime over the entire sample period and thus find limited explanatory power. We show that a single regime model hides the fact that the explanatory variables take on different loadings across changing patterns in credit spreads. We capture these hidden effects by modeling endogenous (rating-specific) regimes for credit spreads. We find that in a two regime-based model traditional determinants have significant explanatory power consistent with the prediction of structural models, yet their importance changes across regimes -- some variables have their effects strengthen, weaken or even reverse signs across regimes. We also investigate the differing behavior of these loadings across different specifications of the economic cycle and find that endogenous regimes best capture the hidden effects of these variables with the highest explanatory power for the same set of variables.

Market impact is one of the most important aspects of real-world trading. It is typically a major component of transaction costs, and trading strategies are carefully optimized to minimize it. But most of the research has focused on one-off trades, not the repeated series of transactions required in delta-hedging an options position. In this article, the authors explore optimal hedging in an illiquid environment for a large trader whose trades absorb a nonmarginal fraction of the standing orders in the limit order book. The trader needs to take account of both the immediate price impact of each trade and the speed at which the limit order book is restored afterward—the market’s resilience. These two aspects of market dynamics together can produce a permanent effect of a big trade and also a temporary one that dissipates over time. Depending on the parameters of the liquidity process, the optimal strategy can be the canonical Black–Scholes delta hedge (in the limiting case of infinite liquidity) or one that is distinctly less volatile (when market impact is large, but there is some resilience in prices) or even one that entails price manipulation (when there is no resilience and the price impact is permanent).

This study proposes models that can be used as shorthand analysis tools for CDS spreads and CDS spread changes. For this purpose we examine the determinants of CDS spreads and spread changes on a broad database of 718 US firms during the period from early 2002 to early 2013. Contrary to previous studies, we discover that market variables still have explanatory power after controlling for firm-specific variables inspired by structural models. Three explanatory variables appear to overshadow the other variables examined in this paper: Stock Return, ?Volatility (the change in stock return volatility) and ?MRI (change in the median CDS spread in the rating class). We also discover that models used in the event study literature to explain spread changes can be improved by using additional market variables. Further, we show that ratings explain cross-section variation in CDS spreads even after controlling for structural model variables.

Intraday return volatility is characterized by the contemporaneous presence of periodicity and long memory. This article proposes two new parameterizations of the intraday volatility process that account for both features: the Fractionally Integrated Periodic EGARCH and the Seasonal Fractional Integrated Periodic EGARCH. The analysis of hourly E-mini S&P 500 futures returns shows that the volatility is characterized by a statistically significant long-range dependence coupled with a periodic leverage effect, with negative return shocks having a larger effect on volatility during the US trading period. Long memory estimates obtained with nonperiodic long memory models are greater than those obtained with FI-PEGARCH and SFI-PEGARCH models. A simulation experiment shows that the long memory component can be strongly biased when periodic patterns are not properly modelled at the intraday level. An out-of-sample forecasting comparison with alternative models shows that a constrained version of the FI-PEGARCH provides superior forecasts.

This paper analyzes the market microstructure of the European Climate Exchange, the largest EU ETS trading venue. The ECX captures 2/3 of the screen traded market in EUA and more than 90% in CER. Volume growth has averaged 277% in EUA between 2005 and 2009 and 724% in CER since 2007. Spreads range from €0.0188 to €0.0406 for EUA and €0.0276 to €0.0796 for CER. The median proportion of the spread due to adverse selection reaches 76% for EUA and 75% for CER. Realized volatility, bid-ask spreads and adverse selection costs decline with verified emission releases. Market impact estimates imply that an average trade will move the EUA market by 1.06 euro centimes and the CER market 1.45. The ECX is providing between 75% and 88% of price discovery for EUA trading and between 64% and 72% for CER. We find imbalances in the order book help predict returns for up to three days. A simple trading strategy that enters the market long or short when the order imbalance is strong is profitable even after accounting for spreads and market impact.

Purpose – The purpose of this paper is to investigate the effect of operating leverage, and the subsequent abandonment option available to managers, on the relationship between corporate earnings and optimal financial leverage, thereby providing an alternative (rational) explanation for the observed negative relationship between these two quantities. Design/methodology/approach – Working in a dynamic capital structure setting, where corporate earnings are modelled as an exogenous stochastic process, the paper explicitly adds fixed operating costs to the firm's value optimisation. This introduces a degree of operating leverage (DOL) and a non-zero value to the implicit abandonment option of the firm's manager. Solving for the firm's optimal timing and financing decisions the paper is able to derive the relationship between current corporate earnings and optimal financial leverage for a large class of earnings uncertainty assumptions. The theoretical implications are then tested empirically using a large selection of S&P 500 firms. Findings – The analysis reveals that the manager's flexibility to abandon the project introduces nonlinearities into the valuation that are sufficient to reconcile the trade-off theory with the empirically observed negative earnings/financial leverage relationship. The paper further finds theoretical and empirical evidence of a positive relationship between operating and financial leverage. Originality/value – Previous studies have used mean-reverting earnings as an explanation for the observed negative earnings/financial leverage relationship in a trade-off theory setting. The paper shows that the relationship does not need to be process specific. Instead, it is a direct result of the financial flexibility of managers.

We analyze risk management trends in electricity commodity markets using the production and transaction data and written hedging policies of 12 Norwegian hydropower companies. The scope of our analysis is the hedging of physical electricity production using the power derivatives available at NASDAQ OMX Commodities. In their hedging policy, these companies either use a Cashflow at Risk (C-FaR) approach or a hedge ratio approach, or follow no explicitly stated approach. We find that the derivative cashflows constitute substantial profits for these companies. Furthermore, hedging contributes to reducing the C-FaR for 10 of the companies. These findings are surprising considering that we expect hedging to yield zero expected profit and to smooth the earnings. Overall, our findings reveal that a practice of incorporating market views in hedging decisions is widespread in the sample companies, as both sanctioned in their written hedging policy and as indicated by the substantial hedging profits. © 2013. This is the authors’ accepted and refereed manuscript to the article. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

This review illustrates the interaction between law and finance in the particular case of the taxation of constructive sales. The focus is on the treatment of variable prepaid forward contracts and the rules regarding these instruments articulated by Revenue Ruling 2003-7 and the recent case involving Philip Anschutz ( Anschutz Co. et al. v. Commissioner of Internal Revenue 2011 ). Simple models are used to show how the tests established by the law fail to reflect important financial considerations, such as the volatility of asset returns and the riskiness of dividend payments. These models provide examples that form the basis for a critique of the current rules and also indicate a possible path for future reform and improvement of the law, namely the addition of a delta-based test to the existing rules. The analysis presented here aims to encourage future work that applies financial theory to critique and improve legal rules in a wide range of other situations.

Using the contingent claim approach and market data on sovereign credit default swaps we assess the drivers of a country's risk perception. Deriving market-based asset values for a set of advanced economies we gain insights into the capital markets' perspectives on sovereign creditworthiness. We find the market-based asset values to be positively influenced by debt and to be an early risk indicator for economic developments. In a cross-section analysis we identify drivers of the economic risk of countries. Clustering the countries according to their debt to asset value ratios provides further insights into the market perceptions of sovereign credit risk. For example we find that the asset values of countries with higher ratios react to changes in the global equity market. Countries with a lower ratio react more to the political stability within the country.

This paper examines the behavior of beta coefficients (systematic risk) for underlying stocks around the introduction of single-stock futures (SSFs) contracts in the Pakistani market, by employing models that account for nonsynchronous and thin trading and varying market conditions as “bull” and “bear” markets. Unlike the results of earlier studies on US markets, the empirical evidence tends to support a decline in systematic risk for the majority of underlying stocks in the post-futures listings period. Nevertheless, similar to SSFs stocks, we also find empirical evidence of a decrease in systematic risk for many of the control group stocks. This indicates that changes in beta estimates for SSFs-listed stocks might not be induced by the introduction of SSFs contract trading, but could be attributed to other market-wide or industry changes that have affected the overall market. Several plausible reasons, such as lack of program trading activities normally associated with index futures, market microstructure differences between developed markets and a developing market such as Pakistan, and the capturing of the “bear” and “bull” market effects on stock betas in our estimation procedure could explain these different results for Pakistan’s market.

© 2016 Informa UK Limited, trading as Taylor & Francis Group. In this paper, we develop a methodology for simultaneous recovery of the real-world probability density and liquidity premia from observed S&P 500 index option prices. Assuming the existence of a numéraire portfolio for the US equity market, fair prices of derivatives under the benchmark approach can be obtained directly under the real-world measure. Under this modelling framework, there exists a direct link between observed call option prices on the index and the real-world density for the underlying index. We use a novel method for the estimation of option-implied volatility surfaces of high quality, which enables the subsequent analysis. We show that the real-world density that we recover is consistent with the observed realized dynamics of the underlying index. This admits the identification of liquidity premia embedded in option price data. We identify and estimate two separate liquidity premia embedded in S&P 500 index options that are consistent with previous findings in the literature.

Issues pertaining to the investor decision to sell a security and buy another (of the same type and with the same terms) with a longer period until the expiration date (the roll forward decision) are examined. In particular, a framework is developed in which it is possible to test the trade execution quality efficiency of a roll strategy against a mean–variance optimal roll strategy characterized by multiple-day roll. Applying this framework to five leading US grain futures markets (corn, wheat, soybean, soybean meal and soybean oil) demonstrates that commonly used single-day and multiple-day roll strategies (including the Goldman roll strategy) exhibit considerable inefficiencies. These are consistent over the markets and over the time of the day in which trading occurs, and vary with execution quality risk-aversion in a predictable way. A practical multiple-day roll strategy is proposed that reduces these inefficiencies.

We reconsider the issue of price discovery in spot and futures markets. We use a threshold error correction model to allow for arbitrage operations to have an impact on the return dynamics. We estimate the model using quote midpoints, and we modify the model to account for time-varying transaction costs. We find that the futures market leads in the process of price discovery. The lead of the futures market is more pronounced in the presence of arbitrage signals. Thus, when the deviation between the spot and the futures market is large, the spot market tends to adjust to the futures market.

In the years following the publication of Black and Scholes (J Political Econ, 81(3), 637-654, 1973), numerous alternative models have been proposed for pricing and hedging equity derivatives. Prominent examples include stochastic volatility models, jump-diffusion models, and models based on Lévy processes. These all have their own shortcomings, and evidence suggests that none is up to the task of satisfactorily pricing and hedging extremely long-dated claims. Since they all fall within the ambit of risk-neutral valuation, it is natural to speculate that the deficiencies of these models are (at least in part) attributable to the constraints imposed by the risk-neutral approach itself. To investigate this idea, we present a simple two-parameter model for a diversified equity accumulation index. Although our model does not admit an equivalent risk-neutral probability measure, it nevertheless fulfils a minimal no-arbitrage condition for an economically viable financial market. Furthermore, we demonstrate that contingent claims can be priced and hedged, without the need for an equivalent change of probability measure. Convenient formulae for the prices and hedge ratios of a number of standard European claims are derived, and a series of hedge experiments for extremely long-dated claims on the S&P 500 total return index are conducted. Our model serves also as a convenient medium for illustrating and clarifying several points on asset price bubbles and the economics of arbitrage. © 2012 Springer-Verlag.

Financial markets have become increasingly global in recent decades, yet the pricing of internationally traded assets continues to depend strongly upon local risk factors, leading to several observations that are difficult to explain with standard frameworks. Equity returns depend upon both domestic and global risk factors. Further, local investors tend to overweight their asset portfolios in local equity. The stock prices of firms that begin to trade across borders increase in response to this information. Foreign exchange markets also display anomalous relationships. The forward rate predicts the wrong sign of future movements in the exchange rate, implying that traders can make profits by borrowing at lower interest rate currencies and investing in higher interest rate currencies. Furthermore, the sign of the foreign exchange premium changes over time, a fact difficult to reconcile with consumption variability. In this review, I describe the implications of the current body of research for addressing these and other global asset pricing challenges.

This paper proposes a dynamic risk-based model capable of jointly explaining the term structure of interest rates, returns on the aggregate market, and the risk and return characteristics of value and growth stocks. Both the term structure of interest rates and returns on value and growth stocks convey information about how the representative investor values cash flows of different maturities. We model how the representative investor perceives risks of these cash flows by specifying a parsimonious stochastic discount factor for the economy. Shocks to dividend growth, the real interest rate, and expected inflation are priced, but shocks to the price of risk are not. Given reasonable assumptions for dividends and inflation, we show that the model can simultaneously account for the behavior of aggregate stock returns, an upward-sloping yield curve, the failure of the expectations hypothesis, and the poor performance of the capital asset pricing model.

The article empirically examines the onshor-offshore linkages of the Indian rupee using recently developed multivariate GARCH technique. The empirical results show that the offshore non-deliverable forward market does not have mean spillover impact on onshore spot, forward and futures markets while shocks and volatilities in the non-deliverable forward market influence the onshore markets. A key finding of the study is that the magnitude of volatility spillover from non-deliverable forward to spot market has accentuated after the introduction of currency futures in India. This development could be attributable to large arbitrage between futures and non-deliverable forward market in the more recent period. The finding has critical implications for exchange rate policy and management in the Indian context. There is need for close monitoring of both the onshore and offshore markets.

This study presents an empirical analysis investigating the relationship between the futures trading activities of speculators and hedgers and the potential movements of major spot exchange rates. A set of trader position measures are employed as regression predictors, including the level and change of net positions, an investor sentiment index, extremely bullish/bearish sentiments, and the peak/trough indicators. We find that the peaks and troughs of net positions are generally useful predictors to the evolution of spot exchange rates, but other trader position measures are less correlated with future market movements. In addition, speculative position measures usually forecast price-continuations in spot rates while hedging position measures forecast price-reversals in these markets. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark

The topic of this article is the analysis of the interplay between daily carbon, electricity and gas price data with the European Union Emission Trading System (EU ETS) for CO2 emissions. In a first step we have performed Granger causality tests for Phase I of the EU ETS (January 2005 until December 2007) and the first year of Phase II of the EU ETS (2008). The analysis includes both spot and forward markets—given the close interactions between the two sets of markets. The results show that during Phase I coal and gas prices, through the clean dark and spark spread, impacted CO2 futures prices, which in return Granger caused electricity prices. During the first year of the Phase II, the short-run rent capture theory (in which electricity prices Granger cause CO2 prices) prevailed. On the basis of the qualitative results of the Granger causality tests we obtained the formulation testable equations for quantitative analysis. Standard OLS regressions yielded statistically robust and theoretically coherent results.

Briere, Burgues, and Signori examine the advantages of incorporating strategic exposure to equity volatility into the investment opportunity set of a long-term equity investor. They consider two standard volatility investments: implied volatility and volatility risk premium strategies. An analytical framework, which offers pragmatic solutions for longterm investors who seek exposure to volatility, is used to calibrate and assess the risk–return profiles of portfolios. The benefit of volatility exposure for a conventional portfolio is shown through a mean-modified Value at Risk portfolio optimization. A pure volatility investment makes it possible to partially hedge downside equity risk and thus reduce the risk profile of a portfolio, while an investment in the volatility risk premium substantially increases returns for a given level of risk. A well-calibrated combination of the two strategies enhances both the absolute and risk-adjusted returns of a portfolio.

We explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. We estimate the structural parameters of the proposed model by maximum likelihood. We find that the stochastic volatility model with fat tails can generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. The model with fat tails leads to a significant increase in implied risk premia over the benchmark Gaussian model, but similar risk free rate and its volatility, as well as that of market returns and price-dividend ratios.

Market frictions such as transactions costs, funding constraints and short selling constraints limit arbitrage, but these frictions affect different stocks differently. Using intraday data on a liquid single stock futures and spot market, we examine the effect of these frictions on arbitrage efficiency of the two markets. We find evidence of significant cross-sectional variation in the size and asymmetricity of no-arbitrage bands. To the extent that market frictions affect all stocks similarly, commonality in the size of no-arbitrage bands is expected. We find that 17% of variation in the size of no-arbitrage bands is explained by the first principal component. Changes in funding liquidity is a key factor that determines variation in the common component.

We derive a general joint affine term structure model of US government bond yields and the convenience yields on physical commodities. We apply this framework separately to oil and gold. Our results show clear links between bond and commodity markets, since bond factors play a significant role in the pricing of the convenience yield term structure. Our framework allows us to decompose the term structure of futures prices into expectations of future spot prices and risk premia components. We estimate that the risk premium in oil futures has been negative over the 1980s and 1990s, and turned positive in the mid-2000s, consistent with a declining role for supply shocks in the oil market over this period. In contrast, we estimate that the gold risk premium is mostly positive throughout the sample period.

This paper proposes a novel approach to assessing volatility contagion across equity markets. I decompose the variance risk premia of three major stock indices into: crash and non-crash risk components and analyse their cross-market correlations. I find that crash-risk premia exhibit higher correlations than non-crash risk premia, implying the existence of volatility contagion. This suggests that investors believe that equity returns will be more highly correlated across countries during market crashes than during more normal times. The main result of the analysis holds when I apply other measures of co-movement as well as when I allow correlation to be time varying. Moreover I document that crash-premia constitute a large portion of the overall variance risk premia, highlighting the importance of crash-risks. Unlike the existing literature, my approach to testing the existence of volatility contagion does not rely on short periods of financial distress, but allows for crash-risk premia to be computed in tranquil times.

Currently, there are two market models for valuation and risk management of interest rate derivatives, the LIBOR and swap market models. In this paper, we introduce arbitrage-free constant maturity swap (CMS) market models and generic market models featuring forward rates that span periods other than the classical LIBOR and swap periods. We develop generic expressions for the drift terms occurring in the stochastic differential equation driving the forward rates under a single pricing measure. The generic market model is particularly apt for pricing of Bermudan CMS swaptions, fixed-maturity Bermudan swaptions, and callable hybrid coupon swaps.

PurposeThis paper aims to construct and compare various total‐return world stock indices based on daily data.Design/methodology/approachBecause of diversification, these indices are noticeably similar. A diversification theorem identifies any diversified portfolio as a proxy for the growth optimal portfolio.FindingsThe paper constructs a diversified world stock index that outperforms a number of other indices and argues that it is a good proxy for the growth optimal portfolio.Originality/valueThe diversified world stock index has applications to derivative pricing and investment management.

We propose and examine a simple model for credit migration and spread curves of a single firm both under the real-world and the risk-neutral measure. This model is a hybrid of a structural and a reduced-form model. Default is triggered either by successive downgradings of the firm or an unpredictable jump of the state process. The default time is accordingly decomposed into predictable and totally inaccessible part.

This paper considers a diversified world stock index in a continuous financial market with the growth optimal portfolio (GOP) as reference unit or benchmark. Diversified broadly based indices and portfolios, which include major world stock market indices, are shown to approximate the GOP. It is demonstrated that a key financial quantity is the trend of a world index. It turns out that it can be directly observed since the expected increments of the index equal four times those of the quadratic variation of its square root. Using a world stock index as approximation of the discounted GOP it is shown that, in reality, the trend of the discounted GOP does not vary greatly in the long term. This leads for a diversified world index to a natural model, where the index is a transformed square root process of dimension four. The squared index volatility appears then as the inverse of the square root process. This feature explains most of the properties of an index and its volatility.

This paper describes a two-factor model for a diversified index that attempts to explain both the leverage effect and the implied volatility skews that are characteristic of index options. Our formulation is based on an analysis of the growth optimal portfolio and a corresponding random market activity time where the discounted growth optimal portfolio is expressed as a time transformed squared Bessel process of dimension four. It turns out that for this index model an equivalent risk neutral martingale measure does not exist because the corresponding Radon-Nikodym derivative process is a strict local martingale. However, a consistent pricing and hedging framework is established by using the benchmark approach. The proposed model, which includes a random initial condition for market activity, generates implied volatility surfaces for European call and put options that are typically observed in real markets. The paper also examines the price differences of binary options for the proposed model and their Black-Scholes counterparts.

This paper discusses the extent to which derivatives pose threats to firms and to the economy. After reviewing the derivatives markets and putting in perspective the various measures of the size of these markets, the paper shows who uses derivatives and why. The difficulties firms face in valuing derivatives portfolios are evaluated. Although academics pay much attention to no-arbitrage pricing results, the paper points out that there can be considerable subjectivity in the pricing of derivatives that do not have highly liquid markets. It is shown that the known risks of derivatives portfolios can generally be measured and managed well at the firm level. However, derivatives can create systemic risks when a market participant becomes excessively large relative to particular derivatives markets. Overall, the benefits of derivatives outweigh the potential threats.

The following paper focuses on the incompleteness arising from model misspecification combined with trading restrictions. While asset price dynamics are assumed to be continuous time processes, the hedging of contingent claims occurs in discrete time. The trading strategies under consideration are understood to be self-financing with respect to an assumed model which may deviate from the "true" model, thus associating duplication costs with respect to a contingent claim to be hedged. Based on the robustness result of Gaussian hedging strategies, which states that a superhedge is achieved for convex payoff-functions if the "true" asset price volatility is dominated by the assumed one, the error of time discretising these strategies is analysed. It turns out that the time discretisation of Gaussian hedges gives rise to a duplication bias caused by asset price trends, which can be avoided by discretising the hedging model instead of discretising the hedging strategies. Additionally it is shown, that on the one hand binomial strategies incorporate similar robustness features as Gaussian hedges. On the other hand, the distribution of the cost process associated with the binomial hedge coincides, in the limit, with the distribution of the cost process associated with the Gaussian hedge. Together, the last results yield a strong argument in favour of discretising the hedge model instead of time-discretising the strategies.

We estimate in this paper the market risk implied by the prices of different options traded in the Brazilian stock market. The fundamental theory to handle this problem is the one implied by the Arrow-Debreu contingent claim concept. Using that theory, we are able to construct the term structure of market risk, and to obtain a surface that provides slices for a particular “volatility smile.” The methodology that we use follows the one proposed by Shimko (1993), which is able to calculate a non-lognormal probability density function (PDF) consistent with the volatility observed in a relatively small sample of option prices. This methodology goes beyond the one proposed originally by Black and Scholes (1973), since it does not require log-normality of the PDF nor that volatility remains constant.

This Paper uses currency option data from the BMF, the Commodities and Futures exchange in Sao Paulo, Brazil, to investigate market expectations on the Brazilian Real-US dollar exchange rate from October 1994 through to March 1999. Using options data, we derive implied probability density functions (PDF) for expected future exchange rates and thus measures of the credibility of the ‘crawling peg’ and target zone (‘maxiband’) regimes governing the exchange rate. Since we do not impose an exchange rate model, our analysis is based on either the risk-neutral PDF or arbitrage-based tests of target zones. The Paper, one of the first to use options data from an emerging market, finds that target zone credibility was poor prior to February 1996, improved afterwards through September 1997 and later started to worsen again. The market anticipated periodic band adjustments, and estimated distributions are very sensitive to political and economic news affecting the credibility of the regime. We also test whether devaluation intensities estimated from these option prices can be explained by standard macroeconomic factors.

A new model of a financial market is introduced extending the multidimensional Black-Scholes model to the case where several assets can interact with each other even in the absence of noise. Sufficient conditions for the existence of the equivalent martingale measure, absence of arbitrage and completeness are given. In the case of a complete market the pricing of contingent claims based on several assets (e.g. index options) is considered and explicit formulas are derived.

International audience; The current article shows that CAC 40 index options (namely PXA) display some illiquidity problems. We examine daily data on PXA trades between May 2005 and August 2012. The study evidences the presence of a considerable number of outstanding PXA contracts; most of these options are long-term maturity options and are deep in or deep out the money options. To overcome the highlighted liquidity issues, we propose first to test the generalization of Gray and Whaley reset option introduced by François-Heude and Yousfi. The main idea is to reset the strike price PXA option to a new strike price given by the CAC 40 value at a pre-agreed point of time. Then we provide some additional measures regarding the number of the PXA strike price series and the PXA expiration dates. Finally, we test them on PXA market. Results show a significant and positive effect on the PXA liquidity.

This paper implements an algorithm that can be used to solve systems of Black-Scholes equations 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 in the Black-Scholes formula. Given this re-pricing, we find that the difference between the market and model price is increasing in moneyness, and decreasing in time to expiration and the size of the bid ask spread. We ask whether the new information gained by the simultaneous solution is useful. We find that after using the SUR model, and re-pricing the options, the varying risk-free rate model yields Black-Scholes prices closer to market prices than the fixed risk-free rate model. We also find that the varying risk-free rate model is better for predicting future evolutions in model-free implied volatility as measured by the VIX. Finally, we discuss potential trading strategies based both on the model-based Black-Scholes prices and on VIX predictability.

Risk management is crucial for optimal portfolio management. One of the fastest growing areas in empirical finance is the expansion of financial derivatives. The purpose of this special issue on " Risk Management and Financial Derivatives" is to highlight some areas in which novel econometric, financial econometric and empirical finance methods have contributed significantly to the analysis of risk management, with an emphasis on financial derivatives, specifically conditional correlations and volatility spillovers between crude oil and stock index returns, pricing exotic options using the Wang transform, the rise and fall of S&P500 variance futures, predicting volatility using Markov switching multifractal model: evidence from S&P100 index and equity options, the performance of commodity trading advisors: a mean-variance-ratio test approach, forecasting volatility via stock return, range, trading volume and spillover effects: the case of Brazil, estimating and simulating Weibull models of risk or price durations: an application to ACD models, valuation of double trigger catastrophe options with counterparty risk, day of the week effect on the VIX - a parsimonious representation, equity and CDS sector indices: dynamic models and risk hedging, the probability of default in collateralized credit operations, risk premia in multi-national enterprises, solving claims replication problems in a complete market by orthogonal series expansion, downside risk management and VaR-based optimal portfolios for precious metals, oil and stocks, and implied Sharpe ratios of portfolios with options: application to Nikkei futures and listed options.

This paper provides a new way of converting risk-neutral moments into the corresponding physical moments, which are required for many applications. The main theoretical result is a new analytical representation of the expected payoffs of put and call options under the physical measure in terms of current option prices and a representative investor’s preferences. This representation is then used to derive analytical expressions for a variety of ex-ante physical return moments, showing explicitly how moment premiums depend on current option prices and preferences. As an empirical application of our theoretical results, we provide option-implied estimates of the representative stock market investor’s disappointment aversion using S&P 500 index option prices. We find that disappointment aversion has a procyclical pattern. It is high in times of high index levels and declines when the index falls. We confirm the view that investors with high risk aversion and disappointment aversion leave the stock market during times of turbulence and reenter it after a period of high returns.

The phenomenon of the frequency basis (i.e. a spread applied to one leg of a swap to exchange one oating interest rate for another of a different tenor in the same currency) contradicts textbook no-arbitrage conditions and has become an important feature of interest rate markets since the beginning of the Global Financial Crisis (GFC) in 2008. Empirically, the basis spread cannot be explained by transaction costs alone, and therefore must be due to a new perception by the market of risks involved in the execution of textbook "arbitrage" strategies. This has led practitioners to adopt a pragmatic "multi-curve" approach to interest rate modelling, which leads to a proliferation of term structures, one for each tenor. We take a more fundamental approach and explicitly model liquidity risk as the driver of basis spreads, reducing the dimensionality of the market for the frequency basis from observed spread term structures for every frequency pair down to term structures of two factors characterising liquidity risk. To this end, we use an intensity model to describe the arrival time of (possibly stochastic) liquidity shocks with a Cox Process. The model parameters are calibrated to quoted market data on basis spreads, and the improving stability of the calibration suggests that the basis swap market has matured since the turmoil of the GFC.

Using both S&P 500 option and recently introduced VIX option prices, we study pricing kernels and their dependence on multiple volatility factors. We first propose nonparametric estimates of marginal pricing kernels, conditional on the VIX and the slope of the variance swap term structure. Our estimates highlight the state-dependence nature of the pricing kernels. In particular, conditioning on volatility factors, the pricing kernel of market returns exhibit a downward sloping shape up to the extreme end of the right tail. Moreover, the volatility pricing kernel features a striking U-shape, implying that investors have high marginal utility in both high and low volatility states. This finding on the volatility pricing kernel presents a new empirical challenge to both existing equilibrium and reduced-form asset pricing models of volatility risk. Finally, using a full-fledged parametric model, we recover the joint pricing kernel, which is not otherwise identifiable.

The article examines whether commodity risk is priced in the cross-section of equity returns. Alongside a long-only equally-weighted portfolio of commodity futures, we employ as an alternative commodity risk factor a term structure portfolio that captures the propensity of commodity futures markets to be backwardated or contangoed. Equity-sorted portfolios with greater sensitivities to the two commodity risk factors command higher average returns. The two commodity portfolios are also found to explain part of the size, value and momentum anomalies. Conclusions regarding the pricing of the commodity risk factors are not an artifact driven by crude oil and are robust to the inclusion of financial and macroeconomic variables and to the addition of a composite leading indicator in the pricing model.

This paper develops an hourly forward curve for power markets where the intra-day and intra-week shapes (profiles) depend on the level of the hydrological balance. The shaping model is based on a feed-forward Artificial Neural Network (ANN), which is trained on a historical data set of hourly electricity spot prices from the Nord Pool market and weekly measurements of the Nordic hydrological balance. The yearly seasonal cycle is estimated with historical electricity forward prices from the Nasdaq OMX Commodities exchange. We calibrate the shaping model to prevailing electricity forward prices and proceed to demonstrate its most important properties. By using comparative static analysis we particulary focus on the hydro dependence of the shapes. We conclude the paper with a real world valuation task. By combining our proposed forward curve with a simple Ornstein-Uhlenbeck process we price a strip of hourly call options on the electricity spot price under different hydrological scenarios.

The basic model of financial economics is the Samuelson model of geometric Brownian motion because of the celebrated Black-Scholes formula for pricing the call option. The asset's volatility is a linear function of the asset value and the model guarantees positive asset prices. In this paper, it is shown that the pricing partial differential equation can be solved for level-dependent volatility which is a quadratic polynomial. If zero is attainable, both absorption and negative asset values are possible. Explicit formulae are derived for the call option: a generalization of the Black-Scholes formula for an asset whose volatiliy is affine, the formula for the Bachelier model with constant volatility, and new formulae in the case of quadratic volatility. The implied Black-Scholes volatilities of the Bachelier and the affine model are frowns, the quadratic specifications imply smiles.

This article empirically analyzes some properties shared by all one-dimensional diffusion option models. Using SP options are not redundant securities, nor ideal hedging instruments—puts and the underlying asset prices may go down together. Much of the extant knowledge about option pricing is based on the assumption that the underlying asset price follows a one-dimensional diffusion process. Examples of such option pricing models include the classic Black–Scholes (1973), Merton (1973), the Cox–Ross (1976) constant elasticity of variance, the ones studied in Derman and Kani (1994), Rubinstein (1994), Bergman, Grundy, and Wiener (1996), Bakshi, Cao, and Chen (1997, 2000), and Dumas, Fleming, and Whaley (1998). All models in the one-dimensional diffusion class share three basic properties. First, call prices are monotonically increasing and put prices are monotonically decreasing in the underlying asset price (the monotonicity property). Second, as the underlying asset price is the sole source of uncertainty for all of its options, option prices must be perfectly correlated with each other and with the underlying asset (the perfect

We analyze the joint convergence of sequences of discounted stock prices and Radon-Nicodym derivatives of the minimal martingale measure when interest rates are stochastic. Therefrom we deduce the convergence of option values in either complete or incomplete markets. We illustrate the general result by two main examples: a discrete time i.i.d. approximation of a Merton type pricing model for options on stocks and the trinomial tree of Hull and White for interest rate derivatives.