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

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

An Analysis of American Options under Heston Stochastic Volatility and Jump-Diffusion Dynamics

This paper considers the problem of pricing American options when the dynamics of the underlying are driven by both stochastic volatility following a square root process as used by Heston (1993), and by a Poisson jump process as introduced by Merton (1976). Probability arguments are invoked to find a representation of the solution in terms of expectations over the joint distribution of the underlying process. A combination of Fourier transform in the log stock price and Laplace transform in the volatility is then applied to find the transition probability density function of the underlying process. It turns out that the price is given by an integral dependent upon the early exercise surface, for which a corresponding integral equation is obtained. The solution generalises in an intuitive way the structure of the solution to the corresponding European option pricing problem in the case of a call option and constant interest rates obtained by Scott (1997).American options; stochastic volatility; jump-diffusion processes; Volterra integral equations; free boundary problem; method of lines

Multi-Systemic Biological Risk and Cancer Mortality: The NHANES III Study.

Multi-systemic biological risk (MSBR), a proxy for allostatic load, is a composite index of biomarkers representing dysregulation due to responses to chronic stress. This study examined the association of an MSBR index with cancer mortality. The sample included n = 13,628 adults aged 20-90 from the NHANES III Linked Mortality File (1988-1994). The MSBR index included autonomic (pulse rate, blood pressure), metabolic (HOMAir, triglycerides, waist circumference), and immune (white blood cell count, C-reactive protein) markers. We fit Cox proportional hazards models to estimate hazard ratios (HRs) and 95% confidence intervals (CI) of overall cancer mortality risk, according to quartiles (q) of the index. In multivariable models, compared to those in q1, q4 had a 64% increased risk for cancer mortality (HR = 1.64, 95% CI:1.13-2.40). The immune domain drove the association (HR per unit = 1.19, 95% CI:1.07-1.32). In stratified analyses, the HR for those with a BMI ≥ 25 was 1.12 per unit (95% CI:1.05-1.19) and those with a BMI < 25 was 1.04 per unit (95% CI:0.92-1.18). MSBR is positively associated with risk for cancer mortality in a US sample, particularly among those who are overweight or obese. The utilization of standard clinical measures comprising this index may inform population cancer prevention strategies

The Evaluation of American Option Prices Under Stochastic Volatility and Jump-Diffusion Dynamics Using the Method of Lines

This paper considers the problem of numerically evaluating American option prices when the dynamics of the underlying are driven by both stochastic volatility following the square root process of Heston (1993), and by a Poisson jump process of the type originally introduced by Merton (1976). We develop a method of lines algorithm to evaluate the price as well as the delta and gamma of the option, thereby extending the method developed by Meyer (1998) for the case of jump-diffusion dynamics. The accuracy of the method is tested against two numerical methods that directly solve the integro-partial differential pricing equation. The first is an extension to the jump-diffusion situation of the componentwise splitting method of Ikonen & Toivanen (2007). The second method is a Crank-Nicolson scheme that is solved using projected successive over relaxation which is taken as the benchmark. The relative efficiency of these methods for computing the American call option price, delta, gamma and free boundary is analysed. If one seeks an algorithm that gives not only the price but also the delta and gamma to the same level of accuracy for a given computational effort then the method of lines seems to perform best amongst the methods considered.American options; stochastic volatility; jump-diffusion processes; Volterra integral equations; free boundary problem; method of lines

Evaluation of American Strangles

This paper presents a generalisation of McKean's free boundary value problem for American options by considering an American strangle position, where the early exercise of one side of the payoff will knock-out the out-of-the-money side. When attempting to evaluate the price of this American strangle, it is not correct to simply price the component American call and put options which make up the strangle, and take the sum of their values. The Fourier transform technique is used to derive the integral equation for the price of our American strangle. From this expression, a coupled integral equation system for the strangle's call- and put-side free boundaries is found. While the equation for the price of the strangle is simply the sum of its component American call and put option equations, the free boundary for each side is shown to have a more complex nature. Anumerical algorithm for solving the coupled integral equation system for the free boundaries is provided, and the resulting approximations are used to determine the price of the American strangle position. Numerical comparisons between the strangle price and the price of a portfolio formed from a long position in both an American call an American put option are presented.american options; volterra integral equation; free-bondary problem

Mentoring and Coaching in Transport and Logistics Higher Education: Issues and Challenges

Mentoring is widely accepted as a developmental process for personal growth and career advancement. Its functions are often carried out within the context of a long-term, continuous and supportive relationship between a skilled or more experienced person (mentor) who serves as a role model to teach, sponsor, encourage and counsel and a less experienced individual (mentee). Although some evidence exists to support the idea that, where mentoring practices are applied in higher education, students tend to perform better as scholars and experience higher confidence and morale, mentoring is still under-utilised when used as a way to help support individuals’ personal and professional development. Meanwhile, larger organisations tend to invest significant resources on talent management activities, as a means to identify how such activities are being utilised to develop current assets within organisations, develop leadership, support change or bridge the gap of insufficiently qualified graduates in industry. This paper presents a structured literature review on mentoring and coaching including similarities and differences in each approach and their appropriateness in transport and logistics higher education. It provides an understanding of each concept and suggests relevant applications as an effective means of maximising the potential of existing and prospective students and employees. Finally, it discusses the extent to which “mentoring and coaching” can be used in transport and logistics higher education as a developmental approach to provide students with a competitive edge when entering the workplace

Rationale, Study Design, and Cohort Characteristics for the Markers for Environmental Exposures (MEE) Study.

Environmental factors have been linked to many diseases and health conditions, but reliable assessment of environmental exposures is challenging. Developing biomarkers of environmental exposures, rather than relying on self-report, will improve our ability to assess the association of such exposures with disease. Epigenetic markers, most notably DNA methylation, have been identified for some environmental exposures, but identification of markers for additional exposures is still needed. The rationale behind the Markers for Environmental Exposures (MEE) Study was to (1) identify biomarkers, especially epigenetic markers, of environmental exposures, such as pesticides, air/food/water contaminants, and industrial chemicals that are commonly encountered in the general population; and (2) support the study of potential relationships between environmental exposures and health and health-related factors. The MEE Study is a cross-sectional study with potential for record linkage and follow-up. The well-characterized cohort of 400 postmenopausal women has generated a repository of biospecimens, including blood, urine, and saliva samples. Paired data include an environmental exposures questionnaire, a breast health questionnaire, dietary recalls, and a food frequency questionnaire. This work describes the rationale, study design, and cohort characteristics of the MEE Study. In addition to our primary research goals, we hope that the data and biorepository generated by this study will serve as a resource for future studies and collaboration

Association of Frequent Aspirin Use With Ovarian Cancer Risk According to Genetic Susceptibility

IMPORTANCE: Frequent aspirin use is associated with reduced ovarian cancer risk, but it is unknown whether genetic factors modify this association. Understanding effect modifiers is important given that any use of aspirin for ovarian cancer chemoprevention will likely need to focus on specific higher-risk subgroups. OBJECTIVE: To evaluate whether the association between frequent aspirin use and ovarian cancer is modified by a polygenic score (PGS) for nonmucinous ovarian cancer. DESIGN, SETTING, AND PARTICIPANTS: We pooled individual-level data from 8 population-based case-control studies from the Ovarian Cancer Association Consortium conducted in the US, UK, and Australia between 1995 and 2009. We included case patients and control participants with both genetic data and data on frequent aspirin use. Case patients with mucinous ovarian cancer were excluded. Data were analyzed between November 1, 2021, and July 31, 2022. EXPOSURES: Frequent aspirin use, defined as daily or almost daily use for 6 months or longer. MAIN OUTCOMES AND MEASURES: The main outcome was nonmucinous epithelial ovarian cancer. We used logistic regression to estimate odds ratios (ORs) and 95% CIs and likelihood ratio tests to investigate effect modification by the PGS. RESULTS: There were 4476 case patients with nonmucinous ovarian cancer and 6659 control participants included in this analysis. At study enrollment, the median (IQR) age was 58 (50-66) years for case patients and 57 (49-65) years for control participants. Case patients and control participants self-reported that they were Black (122 [3%] vs 218 [3%]), White (3995 [89%] vs 5851 [88%]), or of other race and ethnicity (348 [8%] vs 580 [9%]; race and ethnicity were unknown for 11 [0%] vs 10 [0%]). There were 575 case patients (13%) and 1030 control participants (15%) who reported frequent aspirin use. The 13% reduction in ovarian cancer risk associated with frequent aspirin use (OR, 0.87 [95% CI, 0.76-0.99]) was not modified by the PGS. Consistent ORs were observed among individuals with a PGS less than (0.85 [0.70-1.02]) and greater than (0.86 [0.74-1.01]) the median. Results were similar by histotype. CONCLUSIONS AND RELEVANCE: The findings of this study suggest that genetic susceptibility to ovarian cancer based on currently identified common genetic variants does not appear to modify the protective association between frequent aspirin use and ovarian cancer risk. Future work should continue to explore the role of aspirin use for ovarian cancer prevention among individuals who are at higher risk for ovarian cancer

Robust Tests for Additive Gene-Environment Interaction in Case-Control Studies Using Gene-Environment Independence

There have been recent proposals advocating the use of additive gene-environment interaction instead of the widely used multiplicative scale, as a more relevant public health measure. Using gene-environment independence enhances statistical power for testing multiplicative interaction in case-control studies. However, under departure from this assumption, substantial bias in the estimates and inflated type I error in the corresponding tests can occur. In this paper, we extend the empirical Bayes (EB) approach previously developed for multiplicative interaction, which trades off between bias and efficiency in a data-adaptive way, to the additive scale. An EB estimator of the relative excess risk due to interaction is derived, and the corresponding Wald test is proposed with a general regression setting under a retrospective likelihood framework. We study the impact of gene-environment association on the resultant test with case-control data. Our simulation studies suggest that the EB approach uses the gene-environment independence assumption in a data-adaptive way and provides a gain in power compared with the standard logistic regression analysis and better control of type I error when compared with the analysis assuming gene-environment independence. We illustrate the methods with data from the Ovarian Cancer Association Consortium.Multiple funders listed on paper