arXiv subjects

Victoria Steblovskaya

Publications and source records attributed to Victoria Steblovskaya.

3 recordsLinked to original sources

arXiv2024

Minimum Cost Super-Hedging in a Discrete Time Incomplete Multi-Asset Binomial Market

We consider a multi-asset incomplete model of the financial market, where each of $m\geq 2$ risky assets follows the binomial dynamics, and no assumptions are made on the joint distribution of the risky asset price processes. We provide explicit formulas for the minimum cost super-hedging strategies for a wide class of European type multi-asset contingent claims. This class includes European basket call and put options, among others. Since a super-hedge is a non-self-financing arbitrage strategy, it produces non-negative local residuals, for which we also give explicit formulas. This paper completes the foundation started in previous work of the authors for the extension of our results to a more realistic market model.

q-fin.MF↗

arXiv2023

Pricing multi-asset contingent claims in a multi-dimensional binomial market

We consider an incomplete multi-asset binomial market model. We prove that for a wide class of contingent claims the extremal multi-step martingale measure is a power of the corresponding single-step extremal martingale measure. This allows for closed form formulas for the bounds of a no-arbitrage contingent claim price interval. We construct a feasible algorithm for computing those boundaries as well as for the corresponding hedging strategies. Our results apply, for example, to European basket call and put options and Asian arithmetic average options.

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arXiv2023

European baskets in discrete-time continuous-binomial market models

We consider a discrete-time incomplete multi-asset market model with continuous price jumps. For a wide class of contingent claims, including European basket call options, we compute the bounds of the interval containing the no-arbitrage prices. We prove that the lower bound coincides, in fact, with Jensen's bound. The upper bound can be computed by restricting to a binomial model for which an explicit expression for the bound is known by an earlier work of the authors. We describe explicitly a maximal hedging strategy which is the best possible in the sense that its value is equal to the upper bound of the price interval of the claim. Our results show that for any $c$ in the interval of the non-arbitrage contingent claim price at time $0$, one can change the boundaries of the price jumps to obtain a model in which $c$ is the upper bound at time $0$ of this interval. The lower bound of this interval remains unaffected.

q-fin.MF↗