We extend the fundamental theorem of asset pricing to a model where the risky stock is subject to proportional transaction costs in the form of bid-ask spreads and the bank account has different interest rates for borrowing and lending. We show that such a model is free of arbitrage if and only if one can embed in it a friction-free model that is itself… (More)
American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and mar-tingale representations are presented for short (seller's) and long (buyer's) positions in an American option with an arbitrary payoff.… (More)
The paper is devoted to optimal superreplication of European options in the discrete setting under proportional transaction costs on the underlying asset. In particular, general pricing and hedging algorithms are developed. This extends previous work by many authors, which has been focused on the binomial tree model and options with specific payoffs such as… (More)
We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to the trading of the underlying asset. The algorithm computes the prices on recombining binomial trees, and is designed for modern multi-core processors. Although parallel option pricing has been well studied, none of the… (More)
The pricing and hedging of a general class of options (including Amer-ican, Bermudan and European options) on multiple assets are studied in the context of currency markets where trading in all assets is subject to proportional transaction costs, and where the existence of a risk-free numéraire is not assumed. Probabilistic dual representations are obtained… (More)
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In the paper by Melnikov and Petrachenko 'On option pricing in binomial market with transaction costs,' Finance Stoch. 9 (2005), 141–149, a procedure is put forward for pricing and replicating an arbitrary European contingent claim in the binomial model with bid-ask spreads. We present a counterexample to show that the option pricing formula stated in that… (More)