Linear vector optimization and European option pricing under proportional transaction costs

A method for pricing and superhedging European options under proportional transaction costs based on linear vector optimisation and geometric duality developed by Lohne & Rudloff (2014) is compared to a special case of the algorithms for American type derivatives due to Roux & Zastawniak (2014). An equivalence between these two approaches is established by means of a general result linking the support function of the upper image of a linear vector optimisation problem with the lower image of the dual linear optimisation problem

Pricing high-dimensional American options by kernel ridge regression

In this paper, we propose using kernel ridge regression (KRR) to avoid the step of selecting basis functions for regression-based approaches in pricing high-dimensional American options by simulation. Our contribution is threefold. Firstly, we systematically introduce the main idea and theory of KRR and apply it to American option pricing for the first time. Secondly, we show how to use KRR with the Gaussian kernel in the regression-later method and give the computationally efficient formulas for estimating the continuation values and the Greeks. Thirdly, we propose to accelerate and improve the accuracy of KRR by performing local regression based on the bundling technique. The numerical test results show that our method is robust and has both higher accuracy and efficiency than the Least Squares Monte Carlo method in pricing high-dimensional American options

Game options with gradual exercise and cancellation under proportional transaction costs

Game (Israeli) options in a multi-asset market model with proportional transaction costs are studied in the case when the buyer is allowed to exercise the option and the seller has the right to cancel the option gradually at a mixed (or randomised) stopping time, rather than instantly at an ordinary stopping time. Allowing gradual exercise and cancellation leads to increased flexibility in hedging, and hence tighter bounds on the option price as compared to the case of instantaneous exercise and cancellation. Algorithmic constructions for the bid and ask prices, and the associated superhedging strategies and optimal mixed stopping times for both exercise and cancellation are developed and illustrated. Probabilistic dual representations for bid and ask prices are also established

American options with gradual exercise under proportional transaction costs

American options in a multi-asset market model with proportional transaction costs are studied in the case when the holder of an option is able to exercise it gradually at a so-called mixed (randomized) stopping time. The introduction of gradual exercise leads to tighter bounds on the option price when compared to the case studied in the existing literature, where the standard assumption is that the option can only be exercised instantly at an ordinary stopping time. Algorithmic constructions for the bid and ask prices and the associated superhedging strategies and optimal mixed stopping times for an American option with gradual exercise are developed and implemented, and dual representations are established

Options under proportional transaction costs: An algorithmic approach to pricing and hedging

Abstract 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 position) in an American option with an arbitrary payoff settled by physical delivery. The seller's price representation as the expectation of the stopped payoff under an approximate martingale measure is also considered. The algorithms cover and extend the various special cases considered in the literature to-date. Any specific restrictions that were imposed on the form of the payoff, the magnitude of transaction costs or the discrete market model itself are relaxed. The pricing algorithm under transaction costs can be viewed as a natural generalisation of the iterative Snell envelope construction