Investigating nonlinear speculation in cattle, corn, and hog futures markets using logistic smooth transition regression models

This article explores nonlinearities in the response of speculators’ trading activity to price changes in live cattle, corn, and lean hog futures markets. Analyzing weekly data from March 4, 1997 to December 27, 2005, we reject linearity in all of these markets. Using smooth transition regression models, we find a similar structure of nonlinearities with regard to the number of different regimes, the choice of the transition variable, and the value at which the transition occurs.Futures markets, speculation, nonlinear dynamics, smooth transition regression model

American Call Options on Jump-Diffusion Processes: A Fourier Transform Approach

This paper considers the Fourier transform approach to derive the implicit integral equation for the price of an American call option in the case where the underlying asset follows a jump-diffusion process. Using the method of Jamshidian (1992), we demonstrate that the call option price is given by the solution to an inhomogeneous integro-partial differential equation in an unbounded domain, and subsequently derive the solution using Fourier transforms. We also extend McKean’s incomplete Fourier transform approach to solve the free boundary problem under Merton’s framework, for a general jump size distribution. We show how the two methods are related to each other, and also to the Geske-Johnson compound option approach used by Gukhal (2001). The paper also derives results concerning the limit for the free boundary at expiry, and presents a numerical algorithm for solving the linked integral equation system for the American call price, delta and early exercise boundary. This scheme is applied to Merton’s jump-diffusion model, where the jumps are log-normally distributed.American options; jump-diffusion; Volterra integral equation; free boundary problem

Small Traders in Currency Futures Markets Format

This study examines the interrelation between small traders' open interest and large hedging and speculation in the Canadian dollar, Swiss franc, British pound, and Japanese yen futures markets. The results, based on Granger-causality tests and vector autoregressive models, suggest that small traders' open interest is closely related to large speculators' open interest. Small traders and speculators tend to herd, which means that small traders are long [short] when speculators are long [short] as well. Moreover, small traders and speculators are positive feedback traders whereas hedgers are contrarians. Regarding information flows, speculators lead small traders in three of the four currency futures markets. The results therefore suggest that small traders ares mall speculators who follow the large speculators, indicating that they are less well informed than the large speculators.currency futures; small traders; speculation; hedging

A Modern View on Merton's Jump-Diffusion Model

Merton has provided a formula for the price of a European call option on a single stock where the stock price process contains a continuous Poisson jump component, in addition to a continuous log-normally distributed component. In Merton's analysis, the jump-risk is not priced. Thus the distribution of the jump-arrivals and the jump-sizes do not change under the change of measure. We go onto introduce a Radon-Nikodym derivative process that induces the change of measure from the market measure to an equivalent martingale measure. The choice of parameters in the Radon-Nikodym derivative allows us to price the option under different financial-economic scenarios. We introduce a hedging argument that eliminates the jump-risk in some sort of averaged sense, and derive an integro-partial differential equation of the option price that is related to the one obtained by Merton.financial derivatives; compound Poisson processes; equivalent martingale measure; hedging portfolio

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Two Stochastic Volatility Processes - American Option Pricing

In this paper we consider the pricing of an American call option whose underlying asset dynamics evolve under the influence of two independent stochastic volatility processes of the Heston (1993) type. We derive the associated partial differential equation (PDE) of the option price using hedging arguments and Ito's lemma. An integral expression for the general solution of the PDE is presented by using Duhamel's principle and this is expressed in terms of the joint transition density function for the driving stochastic processes. We solve the Kolmogorov PDE for the joint transition density function by first transforming it to a corresponding system of characteristic PDEs using a combination of Fourier and Laplace transforms. The characteristic PDE system is solved by using the method of characteristics. With the full price representation in place, numerical results are presented by first approximating the early exercise surface with a bivariate log linear function. We perform numerical comparisons with results generated by the method of lines algorithm and note that our approach is very competitive in terms of accuracy.American options; Fourier transform; Laplace transform; method of characteristics

Investigating Nonlinear Speculation in Cattle, Corn and Hog Futures Markets Using Logistic Smooth Transition Regression Models

This article explores nonlinearities in the response of speculators’ trading activity to price changes in live cattle, corn, and lean hog futures markets. Analyzing weekly data from March 4, 1997 to December 27, 2005, we reject linearity in all of these markets. Using smooth transition regression models, we find a similar structure of nonlinearities with regard to the number of different regimes, the choice of the transition variable, and the value at which the transition occurs.futures marktes; speculation; nonlinear dynamics; smooth transition regression model

The Evaluation of American Compound Option Prices Under Stochastic Volatility Using the Sparse Grid Approach

A compound option (the mother option) gives the holder the right, but not obligation to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we demonstrate a partial differential equation (PDE) approach to pricing American-type compound options where the underlying dynamics follow Heston’s stochastic volatility model. This price is formulated as the solution to a two-pass free boundary PDE problem. A modified sparse grid approach is implemented to solve the PDEs, which is shown to be accurate and efficient compared with the results from Monte Carlo simulation combined with the Method of Lines.American compound option; stochastic volatility; free boundary problem; sparse grid; combination technique; Monte Carlo simulation; method of lines

Pricing American Options on Jump-Diffusion Processes using Fourier Hermite Series Expansions

This paper presents a numerical method for pricing American call options where the underlying asset price follows a jump-diffusion process. The method is based on the Fourier-Hermite series expansions of Chiarella, El-Hassan & Kucera (1999), which we extend to allow for Poisson jumps, in the case where the jump sizes are log-normally distributed. The series approximation is applied to both European and American call options, and algorithms are presented for calculating the option price in each case. Since the series expansions only require discretisation in time to be implemented, the resulting price approximations require no asset price interpolation, and for certain maturities are demonstrated to produce both accurate and efficient solutions when compared with alternative methods, such as numerical integration, the method of lines and finite difference schemes.American options; jump-diusion; Fourier-Hermite series expansions; free boundary problem

Diagnostic testing for earnings simulation engines in the Australian electricity market

This study has endeavoured to propose and implement a series of diagnostic tests to determine the appropriateness of electricity simulation engines (ESEs) for generating electricity load and price paths to be used as input in the determination of a retailer’s earnings distribution and the assessment of earnings-at-risk (EaR) measures. Additional diagnostic measures require development before a routine can be developed whereby a complete diagnostic report can be generated as output using simulated and historical data as input. This work includes: (1) Further partitioning of output load and prices from an ESE into off-peak, peak and weekend periods to determine the subsequent effect on earnings. (2) The diagnosis of simulated load paths. As simulated load was not supplied for all engines, the diagnostics developed in this report did not include an analysis of load. (3) The building of a response surface to capture the interaction between temperature, load and price. (4) Examination of the convergence behaviour of an ESE. Convergence in this context means the determination of the minimum number of load and price paths required from a simulator in order to return expected profiles that conform to industry expectations. This would involve the sequential testing of an increasing number of simulated paths from an ESE in order to determine the number required. In conclusion, it is important to understand that each of the simulators that were diagnosed in this study were criticised according to industry expectations, and to the degree that the diagnostics employed here reflect those expectations. In fact, all simulators will attract criticism given that they are calibrated on historical data and are expected to generate future prices for market conditions that are unknown. The mark of an appropriate ESE is that the future load and pricing structure it generates is not too much at variance with industry expectations. A critical function of a simulator is for it not to overestimate or underestimate load and prices such that the risk metrics used to govern earnings risk faced by an electricity retailer are compromised to the extent that their book is either grossly over-hedged or under-hedged