American binary FX options: from theoretical value to market price

[Truncated abstract] There is no universally accepted benchmark model for pricing exotic FX options to market, such as that for European vanilla FX options. The use of not only different models but also of different methodologies, results in widely dispersed model-dependent exotic option prices for any given set of market and contract inputs. The severity of the resultant model price dispersion is strong evidence of model risk. Model risk is especially acute for price-makers in sell-side banks who, owing to the heterogeneity of over-the-counter (OTC) exotic options, do not have actual traded daily closing mark-to-market prices for all exotic options in their book, and so must mark-to-model instead. If the model does not perform well, it will not reflect market reality, and neither will the reported daily profit and loss. Given that sell-side banks use models throughout the price-making process, from pricing market risk to identifying hedging strategies, defining risk limits, reporting to key stakeholders internally and externally, as well as determining trader bonuses and Basel II capital retention levels, model risk is an important consideration in the OTC exotic option space. The orthodox response to model risk is price centric. Orthodoxy develops models that rely on complex and esoteric mathematics in order to improve pricing accuracy, even if it results in models that are opaque and inaccessible to most price-makers and risk managers who use them. In contrast, this research focuses on hedging strategies. This is because price-makers, irrespective of the model used to price, hedge unwanted imbalances in exotic FX option risk with liquid, traded European vanilla FX option strategies like butterflies and risk reversals.