Pricing European continuous-installment currency options with mean-reversion

In this paper, we consider European continuous-installment currency option under the mean-reversion environment. Specifically, we provide efficient pricing formula of installment currency put option via a partial differential equation (PDE) approach when the exchange rate follows the mean reverting lognormal model. Using the Mellin transform techniques, we derive the integral equation representation for the optimal stopping boundary from the PDE for pricing of the option. To verify the efficiency and accuracy of our approach, we provide computational results with the least square Monte Carlo method proposed by Longstaff and Schwartz (2001). We also present some numerical examples to examine the characteristics of the optimal boundaries and prices.     

The volatility of temperature and pricing of weather derivatives

We propose an Ornstein–Uhlenbeck process with seasonal volatility to model the time dynamics of daily average temperatures. The model is fitted to approximately 45 years of daily observations recorded in Stockholm, one of the European cities for which there is a trade in weather futures and options on the Chicago Mercantile Exchange. Explicit pricing dynamics for futures contracts written on the number of heating/cooling degree-days (so-called HDD/CDD futures) and the cumulative average daily temperature (so-called CAT futures) are calculated, along with a discussion on how to evaluate call and put options with these futures as underlying.     

我国短期利率均值回复假设的实证研究

本文以银行间和交易所的1日及7日回购利率为研究对象,利用Va-sicek、CIR、CKLS利率模型检验了它们的均值回复特征,并使用TARCH、EGARCH、PARCH及ANTI-GARCH模型验证了它们的均值回复速度和条件方差的双重不对称性.发现当这4种利率处于较高水平时,其回落速度较慢,波动性较大;当处于较低水平时,其反弹速度较快,波动性较小.这种均值回复特征又以交易所市场更为明显,其回调速度明显高于银行间同类利率.     

Modelling electricity prices: a time change approach

To capture mean reversion and sharp seasonal spikes observed in electricity prices, this paper develops a new stochastic model for electricity spot prices by time changing the Jump Cox-Ingersoll-Ross (JCIR) process with a random clock that is a composite of a Gamma subordinator and a deterministic clock with seasonal activity rate. The time-changed JCIR process is a time-inhomogeneous Markov semimartingale which can be either a jump-diffusion or a pure-jump process, and it has a mean-reverting jump component that leads to mean reversion in the prices in addition to the smooth mean-reversion force. Furthermore, the characteristics of the time-changed JCIR process are seasonal, allowing spikes to occur in a seasonal pattern. The Laplace transform of the time-changed JCIR process can be efficiently computed by Gauss–Laguerre quadrature. This allows us to recover its transition density through efficient Laplace inversion and to calibrate our model using maximum likelihood estimation. To price electricity derivatives, we introduce a class of measure changes that transforms one time-changed JCIR process into another time-changed JCIR process. We derive a closed-form formula for the futures price and obtain the Laplace transform of futures option price in terms of the Laplace transform of the time-changed JCIR process, which can then be efficiently inverted to yield the option price. By fitting our model to two major electricity markets in the US, we show that it is able to capture both the trajectorial and the statistical properties of electricity prices. Comparison with a popular jump-diffusion model is also provided.     

STATISTICAL ARBITRAGE PAIRS TRADING STRATEGIES: REVIEW AND OUTLOOK

This survey reviews the growing literature on pairs trading frameworks, i.e., relative-value arbitrage strategies involving two or more securities. Research is categorized into five groups: The distance approach uses nonparametric distance metrics to identify pairs trading opportunities. The cointegration approach relies on formal cointegration testing to unveil stationary spread time series. The time-series approach focuses on finding optimal trading rules for mean-reverting spreads. The stochastic control approach aims at identifying optimal portfolio holdings in the legs of a pairs trade relative to other available securities. The category “other approaches” contains further relevant pairs trading frameworks with only a limited set of supporting literature. Finally, pairs trading profitability is reviewed in the light of market frictions. Drawing from a large set of research consisting of over 100 references, an in-depth assessment of each approach is performed, ultimately revealing strengths and weaknesses relevant for further research and for implementation.     

Re-examining forward market efficiency Evidence from fractional and Harris-Inder cointegration tests

This article investigates the forward market efficiency by testing the unbiased forward exchange rate hypothesis using nine currencies vis-à-vis the U.S. dollar. The empirical tests are conducted using monthly data during the period between January 1985 and December 1996 and two different methods of cointegration tests, a fractional (GPH) test and the Harris-Inder test. The two cointegration tests are based on two different null hypotheses. Results provide ample evidence of cointegration between the spot and the forward rate, but little evidence of the unbiased rate hypothesis, which may be due to the nonstationary risk premium.     

Long term spread option valuation and hedging

This paper investigates the valuation and hedging of spread options on two commodity prices which in the long run are in dynamic equilibrium (i.e., cointegrated). The spread exhibits properties different from its two underlying commodity prices and should therefore be modelled directly. This approach offers significant advantages relative to the traditional two price methods since the correlation between two asset returns is notoriously hard to model. In this paper, we propose a two factor model for the spot spread and develop pricing and hedging formulae for options on spot and futures spreads. Two examples of spreads in energy markets – the crack spread between heating oil and WTI crude oil and the location spread between Brent blend and WTI crude oil – are analyzed to illustrate the results.     

Modelling fundamental analysis in portfolio selection

We derive a closed-form appraisal/information ratio of the investors who are able to observe some information about security fundamentals, by solving a simple instantaneous mean-variance portfolio choice problem in a continuous-time framework. Both analytical and numerical results suggest that investors should choose securities with a more volatile mispricing, a less volatile fundamental, a higher mean-reverting speed and a larger dividend. Our model calibrated with realistic parameters easily outperforms top-percentile portfolio managers in reality, which suggests that the implementation of fundamental analysis may be impeded in practice due to limits of arbitrage. Our paper is a first, necessarily simple, step towards filling the gap of modelling fundamental analysis in portfolio selection.     

Pairs trading with a mean-reverting jump–diffusion model on high-frequency data

This paper develops a pairs trading framework based on a mean-reverting jump–diffusion model and applies it to minute-by-minute data of the S&P 500 oil companies from 1998 to 2015. The established statistical arbitrage strategy enables us to perform intraday and overnight trading. Essentially, we conduct a three-step calibration procedure to the spreads of all pair combinations in a formation period. Top pairs are selected based on their spreads’ mean-reversion speed and jump behaviour. Afterwards, we trade the top pairs in an out-of-sample trading period with individualized entry and exit thresholds. In the back-testing study, the strategy produces statistically and economically significant returns of 60.61% p.a. and an annualized Sharpe ratio of 5.30, after transaction costs. We benchmark our pairs trading strategy against variants based on traditional distance and time-series approaches and find its performance to be superior relating to risk–return characteristics. The mean-reversion speed is a main driver of successful and fast termination of the pairs trading strategy.     

A scenario-based integrated approach for modeling carbon price risk

Carbon prices are highly dependent on government emission policies and local industrial compositions. When historical data does not exist or limited price data can only be sourced from another country, scenario analysis becomes the only tool for the modelling of future carbon prices. However, various plausible but equally possible scenarios can produce large variations in forecast carbon prices. In a traditional approach of scenario analysis, investment decisions or risk management strategies are proposed and analysed for each given scenario, optimal solutions are determined. However, when the number of scenarios becomes large, it often becomes too complex and intractable to have a clear view on the selection of investment decisions or risk-management strategies because these decisions and strategies are closely linked with each of the many scenarios. In this paper, it is proposed to use a stochastic mean-reversion model to represent future carbon price movements, but this model is calibrated to the forecast carbon prices of all the scenarios. In this approach, a single model is used to capture the underlying uncertainty and expectation of the stochastic carbon prices as projected by all the scenarios, carbon price risk can thus be modeled and analysed without the need for direct references to any specific scenarios. The modelling and management of long-term carbon-price risk are therefore purely dependent on future carbon price levels and volatilities of these scenarios, instead of on the scenarios themselves. Through such an approach, the optimization of investment decisions and risk management solutions can be much simpler because the forecasted carbon prices are the only input data.