Seasonality and the valuation of commodity options

Price movements in many commodity markets exhibit significant seasonal patterns. However, given an observed futures price, a deterministic seasonal component at the price level is not relevant for the pricing of commodity options. In contrast, this is not true for the seasonal pattern observed in the volatility of the commodity price. Analyzing an extensive sample of soybean, corn, heating oil and natural gas options, we find that seasonality in volatility is an important aspect to consider when valuing these contracts. The inclusion of an appropriate seasonality adjustment significantly reduces pricing errors in these markets and yields more improvement in valuation accuracy than increasing the number of stochastic factors.     

The Stochastic Seasonal Behaviour of Natural Gas Prices

Previous studies have explored the seasonal behaviour of commodity prices as a deterministic factor. This paper goes further by proposing a general (n+2m)‐factor model for the stochastic behaviour of commodity prices, which nests the deterministic seasonal model by Sorensen (2002) . We consider seasonality as a stochastic factor, with n non‐seasonal and m seasonal factors. The non‐seasonal factors are as defined in Schwartz (1997) , Schwartz and Smith (2000) and Cortazar and Schwartz (2003) . The seasonal factors are trigonometric components generated by stochastic processes. The model has been applied to the Henry Hub natural gas futures contracts listed by NYMEX. We find that models allowing for stochastic seasonality outperform standard models with deterministic seasonality. We obtain similar results with other energy commodities. Moreover, we find that stochastic seasonality implies that the volatility of futures returns follows a seasonal pattern. This result has important implications in terms of option pricing.     

A unified approach to ruin probabilities with delays for spectrally negative Lévy processes

ABSTRACT

In this paper, we unify two popular approaches for the definition of actuarial ruin with implementation delays, also known as Parisian ruin. Our new definition of ruin includes both deterministic delays and exponentially distributed delays: ruin is declared the first time an excursion in the red zone lasts longer than an implementation delay with a deterministic and a stochastic component. For this Parisian ruin with mixed delays, we identify the joint distribution of the time of ruin and the deficit at ruin, therefore providing generalizations of many results previously obtained, such as in Baurdoux et al. (2016) and Loeffen et al. (in press) for the case of an exponential delay and that of a deterministic delay, respectively.     

Mean-variance cointegration and the expectations hypothesis

The present paper sheds further light on a well-known (alleged) violation of the expectations hypothesis of the term structure (EHT): the frequent finding of unit roots in interest rate spreads. We show that the EHT implies (i) that the nonstationarity stems from the holding premium, which is hence (ii) cointegrated with the spread. In a stochastic discount factor framework, we model the premium as being driven by the integrated variance of excess returns. Introducing the concept of mean-variance cointegration, we actually find cointegration relations between the conditional first and second moment of US bond data.     

Seasonal and stochastic effects in commodity forward curves

In this paper we develop a new model for the dynamics of forward curves of commodities exhibiting seasonalities, such as natural gas, electricity or agricultural commodities. In the existing literature on the subject, the first state variable in multi-factor models is the commodity price, which combines seasonal and stochastic features and may be unobservable. We propose to use instead the average forward price, which is devoid of seasonality and conveys a more robust representation of the current forward curve level. The second factor in the model is a quantity analogous to the stochastic convenience yield, which accounts for the random changes in the forward curve shape. The well-known cost-of-carry relationship is significantly improved by introducing a deterministic seasonal premium within the convenience yield. We develop model estimation procedures and apply them to a number of energy markets.     

Kernel Conditional Quantile Estimation for Stationary Processes with Application to Conditional Value-at-Risk

The paper considers kernel estimation of conditional quantilesfor both short-range and long-range-dependent processes. Undermild regularity conditions, we obtain Bahadur representationsand central limit theorems for kernel quantile estimates ofthose processes. Our theory is applicable to many price processesof assets in finance. In particular, we present an asymptotictheory for kernel estimates of the value-at-risk (VaR) of themarket value of an asset conditional on the historical informationor a state process. The results are assessed based on a smallsimulation and are applied to AT&T monthly returns.     

Validity of discrete-time stochastic volatility models in non-synchronous equity markets

The paper investigates the validity of versions of discrete-time stochastic volatility models for index series known to contain component stocks exhibiting non-synchronous trading. The efficient method of moments (EMM) is used to fit versions of the discrete-time stochastic volatility (SV) model. The EMM methodology confronts moment conditions generated by a score generator (SNP) that are valid by construction. The moment generator suggests non-linearity in the index series. The EMM construction shows that a classical discrete time stochastic volatility model is rejected. An extended model incorporating an asymmetric volatility specification validates all the moment scores. Option values from Black and Scholes (BS) and Monte Carlo simulations (MC) seem significantly different. The results suggest that BS does not price asymmetry adequately. Asymmetry suggests increased market risk inducing higher BS call prices and lower (higher) BS put pricing for ATM and OTM options (ITM) relative to MC.     

Compound trend renewal process with discounted claims: a unified approach

We derive recursive formulas for the moments of compound trend renewal sums with discounted claims. An integral expression for the moment generating function of this risk process is then obtained, from which particular distribution functions are found. We extend the compound (deterministic) trend renewal process by assuming a stochastic trend, a stochastic force of net interest and a stochastic dependence between the inter-occurrence times and the severities of the claims. Finally, stochastic dominance ordering is also observed between the compound trend renewal process and an associated non-homogeneous Poisson process.     

Nonlinearity and Low Deterministic Chaotic Behavior in Insurance Portfolio Stock Returns

This article presents new empirical evidence indicating a deterministic component in the portfolio return dynamics of life‐health and property‐liability insurance company stocks. Our research is motivated by the fact that nonlinearities are a fact of economic life for many financial applications the source of which is logically apparent, yet empirical evidence of their existence is at best weak. The primary reason attributed to the weak findings of nonlinearities reported in previous research is the use of aggregate data that can hide nonlinearities at the micro level. Insurance sector stock returns are analyzed because unique institutional characteristics indicate the possibility of identifying nonlinear dynamics. Tests based on the correlation dimension partially confirm the presence of nonlinearity. However, the more powerful Brock, Dechert, and Scheinkman (BDS) statistic strongly suggests the presence of nonlinearities in the insurance stock portfolio data. The BDS statistic applied to the standardized residuals of exponential generalized auto regressive conditional heteroskedasticity (EGARCH) models strongly rejects the null of independent and identically distributed, indicating that conditional heteroskedasticity is not responsible for the presence of the nonlinear structures in the data. In addition, tests for chaos based on locally weighted regressions indicate that insurance stock portfolio returns indicate low‐complexity chaotic behavior. This is an important result since most previous research has failed to report evidence of chaotic behavior in the time series of stock returns. Important contributions of this article are the application of tests of nonlinearities and chaos to more desegregated data sets and the findings of statistically significant evidence indicating nonlinearities and low‐deterministic chaotic behavior in insurance stock portfolio returns.     

Time zone normalization of FX seasonality

Abstract

This paper provides empirical evidence that the particular intra-day seasonality observed in the Foreign Exchange market is indeed due to the different geographical locations of its traders. Analysing more than 2 years of real transactions from a microscopic perspective, we design a procedure that accounts for the time zones from which traders operate. The resulting normalized intra-day seasonality shows a pattern akin to those observed in regulated exchanges where traders are more active at the beginning and at the end of their session.     

Central bank interventions and exchange rates: an analysis with high frequency data

We use high frequency data for the mark–dollar exchange rate for the period 1992–1995 to evaluate the effects of central bank interventions on the foreign exchange market. We estimate an unobserved component model that decomposes volatility into non-stationary and stationary parts. Stationary components in turn are decomposed into seasonal and non-seasonal intra-day parts. Our results confirm the view that interventions are not particularly effective. The exchange rate moves in the desired direction for only about 50% of the time, and often with a substantial increase in volatility. The model suggests that the two components, which are affected the most by interventions, are the permanent and the stochastic intra-day.     

Robust bootstrap procedures for the chain-ladder method

Insurers are faced with the challenge of estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A well-known and widely used technique is the chain-ladder method, which is a deterministic algorithm. To include a stochastic component one may apply generalized linear models to the run-off triangles based on past claims data. Analytical expressions for the standard deviation of the resulting reserve estimates are typically difficult to derive. A popular alternative approach to obtain inference is to use the bootstrap technique. However, the standard procedures are very sensitive to the possible presence of outliers. These atypical observations, deviating from the pattern of the majority of the data, may both inflate or deflate traditional reserve estimates and corresponding inference such as their standard errors. Even when paired with a robust chain-ladder method, classical bootstrap inference may break down. Therefore, we discuss and implement several robust bootstrap procedures in the claims reserving framework and we investigate and compare their performance on both simulated and real data. We also illustrate their use for obtaining the distribution of one year risk measures.     

Trends and random walks in macroeconmic time series: Some evidence and implications

This paper investigates whether macroeconomic time series are better characterized as stationary fluctuations around a deterministic trend or as non-stationary processes that have no tendency to return to a deterministic path. Using long historical time series for the U.S. we are unable to reject the hypothesis that these series are non-stationary stochastic processes with no tendency to return to a trend line. Based on these findings and an unobserved components model for output that decomposes fluctuations into a secular or growth component and a cyclical component we infer that shocks to the former, which we associate with real disturbances, contribute substantially to the variation in observed output. We conclude that macroeconomic models that focus on monetary disturbances as a source of purely transitory fluctuations may never be successful in explaining a large fraction of output variation and that stochastic variation due to real factors is an essential element of any model of macroeconomic fluctuations.     

Testing for constant hedge ratios in commodity markets: a multivariate GARCH approach

We develop a new multivariate generalized ARCH (GARCH) parameterization suitable for testing the hypothesis that the optimal futures hedge ratio is constant over time, given that the joint distribution of cash and futures prices is characterized by autoregressive conditional heteroskedasticity (ARCH). The advantage of the new parameterization is that it allows for a flexible form of time-varying volatility, even under the null of a constant hedge ratio. The model is estimated using weekly corn prices. Statistical tests reject the null hypothesis of a constant hedge ratio and also reject the null that time variation in optimal hedge ratios can be explained solely by deterministic seasonality and time to maturity effects.     

REGIME-SWITCHING IN AUSTRALIAN SHORT-TERM INTEREST RATES

This paper applies a generalized regime-switching (GRS) model of the short-term interest rate to Australian data. The model allows the short rate to exhibit both mean reversion and conditional heteroscedasticity and nests the popular generalized autoregressive conditional heteroscedasticity (GARCH) and regime-switching specifications. It is shown that empirical estimates of many popular interest rate models provide curious results which imply that innovations to the short rate process are extremely persistent, and that the short rate is potentially non-stationary. The source of these curious results, which are also present in US and European interest rates, is identified in the context of the GRS model, which is shown, via specification and forecasting tests, to capture the features of Australian short-term interest rate data better than existing models. The stochastic process of short-term interest rates in Australia is compared with evidence from the US and Europe, highlighting a number of important differences.     

Semi-parametric Bayesian tail risk forecasting incorporating realized measures of volatility

Realized measures employing intra-day sources of data have proven effective for dynamic volatility and tail-risk estimation and forecasting. Expected shortfall (ES) is a tail risk measure, now recommended by the Basel Committee, involving a conditional expectation that can be semi-parametrically estimated via an asymmetric sum of squares function. The conditional autoregressive expectile class of model, used to implicitly model ES, has been extended to allow the intra-day range, not just the daily return, as an input. This model class is here further extended to incorporate information on realized measures of volatility, including realized variance and realized range (RR), as well as scaled and smoothed versions of these. An asymmetric Gaussian density error formulation allows a likelihood that leads to direct estimation and one-step-ahead forecasts of quantiles and expectiles, and subsequently of ES. A Bayesian adaptive Markov chain Monte Carlo method is developed and employed for estimation and forecasting. In an empirical study forecasting daily tail risk measures in six financial market return series, over a seven-year period, models employing the RR generate the most accurate tail risk forecasts, compared to models employing other realized measures as well as to a range of well-known competitors.     

Signaling with dividends and share repurchases: a choice between deterministic and stochastic cash disbursements

We study firms signaling with cash disbursements and show thatthe choice of a deterministic or a stochastic disbursement dependson a property of the firm's production function that is analogousto absolute risk aversion for a utility function. With decreasing(increasing) absolute risk aversion, the high-quality firm prefersto distinguish itself from the low-quality firm with a stochastic(deterministic) outlay. We then study in detail two common formsof corporate cash distributions: dividends, a deterministicdisbursement, and share repurchases, a stochastic disbursement.     

The affine styled-facts price dynamics for the natural gas: evidence from daily returns and option prices

This study analyzes affine styled-facts price dynamics of Henry Hub natural gas price by incorporating the price features of jump risk, and seasonality within stochastic volatility framework. Affine styled-facts dynamics has the advantage of being able to incorporate mean reversion (MR), stochastic volatility (SV), seasonality trends (S), and jump diffusion (J) in a standardized inclusive framework. Our main finding is that models that incorporate jumps significantly improve overall out-of-sample option pricing performance. The combined MRSVJS model provides the best fit of both daily gas price returns and the related cross section of option prices. Incorporating seasonal effects tend to provide more stable pricing ability, especially for the long-term option contracts.     

Estimating stochastic volatility models using integrated nested Laplace approximations

Volatility in financial time series is mainly analysed through two classes of models; the generalized autoregressive conditional heteroscedasticity (GARCH) models and the stochastic volatility (SV) ones. GARCH models are straightforward to estimate using maximum-likelihood techniques, while SV models require more complex inferential and computational tools, such as Markov Chain Monte Carlo (MCMC). Hence, although provided with a series of theoretical advantages, SV models are in practice much less popular than GARCH ones. In this paper, we solve the problem of inference for some SV models by applying a new inferential tool, integrated nested Laplace approximations (INLAs). INLA substitutes MCMC simulations with accurate deterministic approximations, making a full Bayesian analysis of many kinds of SV models extremely fast and accurate. Our hope is that the use of INLA will help SV models to become more appealing to the financial industry, where, due to their complexity, they are rarely used in practice.     

The relationship between futures trading activity and exchange rate volatility,revisited

This paper examines the relationship between trading activity in currency futures and exchange rate volatility. In order to measure trading activity, the paper uses both volume and open interest to distinguish between speculators/day traders and hedgers. The study uses three different measures of volatility: (1) the extreme value estimator that measures intra-day volatility; (2) historical volatility; and (3) conditional volatility from the GARCH (1, 1) process. Main finding is that speculators and day traders destabilize the market for futures. Whether hedgers stabilize or destabilize the market is inconclusive. The results suggest that speculators’ demand for futures goes down in response to increased volatility. Meanwhile, the demand from hedgers shows mixed results, depending on the method used to measure volatility.