Pricing Options on an Asset with Bernoulli Jump-Diffusion Returns

The price movements of certain assets can be modeled by stochastic processes that combine continuous diffusion with discrete jumps. This paper compares values of options on assets with no jumps, jumps of fixed size, and jumps drawn from a lognormal distribution. It is shown that not only the magnitude but also the direction of the mispricing of the Black-Scholes model relative to jump models can vary with the distribution family of the jump component. This paper also discusses a methodology for the numerical valuation, via a backward induction algorithm, of American options on a jump-diffusion asset whose early exercise may be profitable. These cannot, in general, be accurately priced using analytic models. The procedure has the further advantage of being easily adaptable to nonanalytic, empirical distributions of period returns and to nonstationarity in the underlying diffusion process.     

iTV: A major opportunity for financial services,or not?

Interactive television has arrived, thanks to substantial technology investments that have been made by Sky and others. It is growing in importance as innovative interactive applications are developed for broadcast programmes (eg the BBCi service and Big Brother), and for advertising — and will develop further when broadband deployment gets to critical mass. Readers should not expect a television-variant of the world wide web, however. This was tried during 2000–2002 in the form of web look-alike, interactive ‘walled garden’ sites, and failed to attract critical mass footfall. The model has evolved and now revolves around interactive content synchronised with broadcast, which offers financial services companies an interesting new way to increase awareness and to differentiate the service presentation. Furthermore, over the next ten years, broadband is expected to usher in a new era of personalised television — in which specialised broadcasts (such as personal pensions advice programmes) can be made available on demand. The observations in this paper are mainly drawn from the UK, where digital television penetration is high; the lessons can be applied more broadly, however, and are relevant to any organisation thinking of promoting its service through entertainment channels.