Exchangeability type properties of asset prices

In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call symmetry property and the duality principle in option pricing. A particular attention is devoted to the case of asset prices driven by Levy processes. Based on this, concrete semi-static hedging techniques for multi-asset barrier options, such as certain weighted barrier spread options, weighted barrier swap options or weighted barrier quanto-swap options are suggested.Comment: The final version of the paper "Semi-static hedging under exchangeability type conditions". To appear in Advances in Applied Probabilit

Computing general static-arbitrage bounds for European basket options via Dantzig-Wolfe decomposition

We study the problem of computing general static-arbitrage bounds for European basket options; that is, computing bounds on the price of a basket option, given the only assumption of absence of arbitrage, and information about prices of other European basket options on the same underlying assets and with the same maturity. In particular, we provide a simple efficient way to compute this type of bounds by solving a large finite non-linear programming formulation of the problem. This is done via a suitable Dantzig-Wolfe decomposition that takes advantage of an integer programming formulation of the corresponding subproblems. Our computation method equally applies to both upper and lower arbitrage bounds, and provides a solution method for general instances of the problem. This constitutes a substantial contribution to the related literature, in which upper and lower bound problems need to be treated differently, and which provides efficient ways to solve particular static-arbitrage bounds for European basket options; namely, when the option prices information used to compute the bounds is limited to vanilla and/or forward options, or when the number of underlying assets is limited to two assets. Also, our computation method allows the inclusion of real-world characteristics of option prices into the arbitrage bounds problem, such as the presence of bid-ask spreads. We illustrate our results by computing upper and lower arbitrage bounds on gasoline/heating oil crack spread options

Model-free bounds for multi-asset options using option-implied information and their exact computation

We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices. We work in a completely realistic setting, in that we only assume the knowledge of traded prices for other single- and multi-asset derivatives, and even allow for the presence of bid-ask spread in these prices. We provide a fundamental theorem of asset pricing for this market model, as well as a superhedging duality result, that allows to transform the abstract maximization problem over probability measures into a more tractable minimization problem over vectors, subject to certain constraints. Then, we recast this problem into a linear semi-infinite optimization problem, and provide two algorithms for its solution. These algorithms provide upper and lower bounds for the prices that are $\varepsilon$-optimal, as well as a characterization of the optimal pricing measures. Moreover, these algorithms are efficient and allow the computation of bounds in high-dimensional scenarios (e.g. when $d=60$). Numerical experiments using synthetic data showcase the efficiency of these algorithms, while they also allow to understand the reduction of model-risk by including additional information, in the form of known derivative prices