“Enjoy your baby” Internet-based CBT for mothers with babies: a feasibility randomised control trial

Background: Postnatal depression is a global health problem with lasting effects on the family. Government policy is focussed on early intervention and increasing access to psychological therapies. There is a growing evidence base for the use of computerised CBT packages and this study investigated the feasibility of a CBT-based self-help internet intervention for new mothers. Objective: To assess the ability to recruit mothers, deliver an internet course, obtain follow-up data and evaluate what mothers think of the course. Design: A feasibility randomised control design was used to compare a waiting list control group (delayed access= DA) to the Enjoy Your Baby course (immediate access= IA). Measures were administered at baseline and 8 week follow-up. Methods: Adverts were placed in the Metro freesheet, on charity web pages, on social media, posters were put up in the community, and leaflets were handed out at mother and baby groups. Participants had to be 18 years old or over with a child less than 18 months old. The IA arm was given access to the course straight away. After 8 weeks all participants were asked to recomplete the original measures and those in the IA arm also gave feedback on the course. Participants in the DA arm were given access after recompleting the questionnaires. Due to a lack of follow-up data a small discussion group was conducted. Intervention: The course contains 4 core modules including helping mothers understand why they feel the way they do and helping them build closeness to their babies. Additional modules, worksheets and homework tasks were available. The DA group were given a list of additional support resources and services, and encouraged to seek additional help if required. All participants received weekly automated emails for 12 weeks as they worked through the course. It was not possible to deliver individualised support. 34 Results: Despite using a number of recruitment strategies, recruitment was lower and slower than anticipated, and attrition was high. 41 women, primarily recruited via the internet, were randomised (IA n=21, DA n=20). No significant differences were observed between participants in either arm at baseline and no statistically significant differences were identified when the demographics and baseline measures of participants who logged-on to the course were compared to those who did not, or when participants who completed follow-up measures were compared to those who did not. Pre and post intervention scores on the EPDS approached statistical significance (P=.059, r=.444) favouring the intervention arm. The discussion group suggested strengths of the course and recommended areas for improvement, including making the course more mobile friendly. Conclusion: Internet interventions show promise; however it is difficult to recruit mothers, engagement is low and attrition high. A number of recommendations are made and a further pilot or an internal pilot of a larger substantive study should be conducted to confirm recruitment and retention. Trial ID: ISRCTN90927910.

Pricing derivatives with stochastic volatility

This Ph.D. thesis contains 4 essays in mathematical finance with a focus on pricing Asian option (Chapter 4), pricing futures and futures option (Chapter 5 and Chapter 6) and time dependent volatility in futures option (Chapter 7). In Chapter 4, the applicability of the Albrecher et al.(2005)'s comonotonicity approach was investigated in the context of various benchmark models for equities and com- modities. Instead of classical Levy models as in Albrecher et al.(2005), the focus is the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and the Schwartz (1997) two-factor model. It is shown that the method delivers rather tight upper bounds for the prices of Asian Options in these models and as a by-product delivers super-hedging strategies which can be easily implemented. In Chapter 5, two types of three-factor models were studied to give the value of com- modities futures contracts, which allow volatility to be stochastic. Both these two models have closed-form solutions for futures contracts price. However, it is shown that Model 2 is better than Model 1 theoretically and also performs very well empiri- cally. Moreover, Model 2 can easily be implemented in practice. In comparison to the Schwartz (1997) two-factor model, it is shown that Model 2 has its unique advantages; hence, it is also a good choice to price the value of commodity futures contracts. Fur- thermore, if these two models are used at the same time, a more accurate price for commodity futures contracts can be obtained in most situations. In Chapter 6, the applicability of the asymptotic approach developed in Fouque et al.(2000b) was investigated for pricing commodity futures options in a Schwartz (1997) multi-factor model, featuring both stochastic convenience yield and stochastic volatility. It is shown that the zero-order term in the expansion coincides with the Schwartz (1997) two-factor term, with averaged volatility, and an explicit expression for the first-order correction term is provided. With empirical data from the natural gas futures market, it is also demonstrated that a significantly better calibration can be achieved by using the correction term as compared to the standard Schwartz (1997) two-factor expression, at virtually no extra effort. In Chapter 7, a new pricing formula is derived for futures options in the Schwartz (1997) two-factor model with time dependent spot volatility. The pricing formula can also be used to find the result of the time dependent spot volatility with futures options prices in the market. Furthermore, the limitations of the method that is used to find the time dependent spot volatility will be explained, and it is also shown how to make sure of its accuracy.