American Options under Proportional Transaction Costs: Pricing, Hedging and Stopping Algorithms for Long and Short Positions

TY - JOUR

T1 - American Options under Proportional Transaction Costs: Pricing, Hedging and Stopping Algorithms for Long and Short Positions

AU - Roux, Alet

AU - Zastawniak, Tomasz

PY - 2009/5

Y1 - 2009/5

N2 - 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 (buyer's) positions in an American option with an arbitrary payoff. This general approach extends the special cases considered in the literature concerned primarily with computing the prices of American puts under transaction costs by relaxing any restrictions on the form of the payoff, the magnitude of the transaction costs or the discrete market model itself. The largely unexplored case of pricing, hedging and stopping for the American option buyer under transaction costs is also covered. The pricing algorithms are computationally efficient, growing only polynomially with the number of time steps in a recombinant tree model. The stopping times realising the ask (seller's) and bid (buyer's) option prices can differ from one another. The former is generally a so-called mixed (randomised) stopping time, whereas the latter is always a pure (ordinary) stopping time.

AB - 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 (buyer's) positions in an American option with an arbitrary payoff. This general approach extends the special cases considered in the literature concerned primarily with computing the prices of American puts under transaction costs by relaxing any restrictions on the form of the payoff, the magnitude of the transaction costs or the discrete market model itself. The largely unexplored case of pricing, hedging and stopping for the American option buyer under transaction costs is also covered. The pricing algorithms are computationally efficient, growing only polynomially with the number of time steps in a recombinant tree model. The stopping times realising the ask (seller's) and bid (buyer's) option prices can differ from one another. The former is generally a so-called mixed (randomised) stopping time, whereas the latter is always a pure (ordinary) stopping time.

KW - American options

KW - Transaction costs

KW - Randomised stopping

KW - Superhedging

KW - DISCRETE-TIME

KW - ARBITRAGE

KW - MARKETS

KW - REPLICATION

KW - SECURITIES

KW - THEOREM

UR - http://www.scopus.com/inward/record.url?scp=67349135257&partnerID=8YFLogxK

U2 - 10.1007/s10440-008-9290-7

DO - 10.1007/s10440-008-9290-7

M3 - Article

SN - 1572-9036

VL - 106

SP - 199

EP - 228

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

IS - 2

ER -