Alexander M. G. Cox

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Double no-touch options, contracts which pay out a fixed amount provided an underlying asset remains within a given interval, are commonly traded, particularly in FX markets. In this work, we establish model-free bounds on the price of these options based on the prices of more liquidly traded options (call and digital call options). Key steps are the(More)
Recent work of Dupire and Carr and Lee has highlighted the importance of understanding the Skorokhod embedding originally proposed by Root for the model-independent hedging of variance options. Root’s work shows that there exists a barrier from which one may define a stopping time which solves the Skorokhod embedding problem. This construction has the(More)
We consider model-free pricing of digital options, which pay out if the underlying asset has crossed both upper and lower barriers. We make only weak assumptions about the underlying process (typically continuity), but assume that the initial prices of call options with the same maturity and all strikes are known. Under such circumstances, we are able to(More)
2004 COPYRIGHT Attention is drawn to the fact that copyright of this thesis rests with its author. This copy of the thesis has been supplied on the condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without the(More)
The Skorokhod embedding problem was first proposed, and then solved, by Skorokhod (1965), and may be described as follows. Given a Brownian motion (Bt) t>0 and a centred target law can we find a ‘small’ stopping time T such that BT has distribution ? Skorokhod gave an explicit construction of the stopping time T in terms of independent random variables, and(More)
In this paper we consider the Skorokhod embedding problem for target distributions with non-zero mean. In the zero-mean case, uniform integrability provides a natural restriction on the class of embeddings, but this is no longer suitable when the target distribution is not centred. Instead we restrict our class of stopping times to those which are minimal,(More)
The approach to pricing and hedging of options through considering the dual problem of finding the expected value of the payoff under a risk-neutral measure is both classical and well understood. In a complete market setting it is simply the way to compute the hedging price, as argued by Black and Scholes [4]. In incomplete markets, the method originated in(More)
We present a constructive probabilistic proof of the fact that if B = (Bt)t≥0 is standard Brownian motion started at 0 and μ is a given probability measure on IR such that μ({0}) = 0 then there exists a unique left-continuous increasing function b : (0,∞) → IR∪{+∞} and a unique left-continuous decreasing function c : (0,∞) → IR ∪ {−∞} such that B stopped at(More)