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

2008 ◽  
Vol 106 (2) ◽  
pp. 199-228 ◽  
Author(s):  
Alet Roux ◽  
Tomasz Zastawniak
Keyword(s):  
Transaction Costs ◽  
American Options ◽  
Proportional Transaction Costs

scholarly journals AMERICAN OPTIONS WITH GRADUAL EXERCISE UNDER PROPORTIONAL TRANSACTION COSTS

2014 ◽  
Vol 17 (08) ◽  
pp. 1450052 ◽  
Author(s):  
ALET ROUX ◽  
TOMASZ ZASTAWNIAK
Keyword(s):  
Transaction Costs ◽  
American Options ◽  
Option Price ◽  
Stopping Time ◽  
Market Model ◽  
Stopping Times ◽  
Asset Market ◽  
Standard Assumption ◽  
Proportional Transaction Costs ◽  
Dual Representations

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.

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