American options are priced and hedged in a general discrete market in the presence of arbitrary proportional transaction costs inherent in trading the underlying asset, modelled as bid-ask spreads. Pricing, hedging and optimal stopping algorithms are established for a short position (seller's...

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...

American options exercised by physical delivery of a portfolio of cash and underlying stock are considered in the binary tree model under small proportional transaction costs. Dynamic programming type recursive algorithms are developed for computing the ask and bid prices of such options,...

Dynamic programming algorithms are developed for computing the ask and bid prices of American contingent claims in a binary tree setting in the presence of small proportional transaction costs, extending the recursive construction of the Snell envelope. Associated with the pricing algorithms are...

The fact that value shares outperform glamour shares in the long term has been known for over 50 years. Why then do glamour shares remain popular? The P/E ratio was the first statistic documented to discriminate between the two. Using data for all US stocks since 1983, we find that glamour...

In the paper by Melnikov and Petrachenko published in Finance and Stochastics 9 (2005), 141--149, a procedure is put forward for pricing and replicating an arbitrary European contingent claim in the binomial market with transaction costs. We present an example to show that the option price...

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...

The pricing and hedging of a general class of options (including American, Bermudan and European options) on multiple assets are studied in the context of currency markets where trading is subject to proportional transaction costs, and where the existence of a risk-free num\'eraire is not...

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 martingale representations are presented for short (seller's) and long...