Super-replication under proportional transaction costs: From discrete to continuous-time models

We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs. We adopt a discrete-time formulation, let the number of periods go to infinity, and show that it converges efficiently to the continuous-time solution for the cases where this solution is known. We then apply this discretization to derive numerically the boundaries of the region of no transactions. Our discrete-time numerical approach outperforms alternative continuous-time approximations of the problem.

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Hedging in discrete time under transaction costs and continuous-time limit

Journal of Applied Probability ◽

10.1239/jap/1032374239 ◽

1999 ◽

Vol 36 (1) ◽

pp. 163-178 ◽

Cited By ~ 13

Author(s):

Pierre-F. Koehl ◽

Huyên Pham ◽

Nizar Touzi

Keyword(s):

Transaction Costs ◽

Discrete Time ◽

Continuous Time ◽

Sufficient Conditions ◽

Risky Asset ◽

Market Model ◽

Upper And Lower Bounds ◽

Time Step ◽

Proportional Transaction Costs ◽

Call Options

We consider a discrete-time financial market model with L1 risky asset price process subject to proportional transaction costs. In this general setting, using a dual martingale representation we provide sufficient conditions for the super-replication cost to coincide with the replication cost. Next, we study the convergence problem in a stationary binomial model as the time step tends to zero, keeping the proportional transaction costs fixed. We derive lower and upper bounds for the limit of the super-replication cost. In the case of European call options and for a unit initial holding in the risky asset, the upper and lower bounds are equal. This result also holds for the replication cost of European call options. This is evidence (but not a proof) against the common opinion that the replication cost is infinite in a continuous-time model.

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Risk minimization for game options in markets imposing minimal transaction costs

Advances in Applied Probability ◽

10.1017/apr.2016.34 ◽

2016 ◽

Vol 48 (3) ◽

pp. 926-946 ◽

Cited By ~ 1

Author(s):

Yan Dolinsky ◽

Yuri Kifer

Keyword(s):

Transaction Costs ◽

Continuous Time ◽

Risk Minimization ◽

Proportional Transaction Costs ◽

Shortfall Risk ◽

Partial Hedging ◽

Black Scholes ◽

Fixed Transaction Cost ◽

Game Options ◽

Binomial Models

Abstract We study partial hedging for game options in markets with transaction costs bounded from below. More precisely, we assume that the investor's transaction costs for each trade are the maximum between proportional transaction costs and a fixed transaction cost. We prove that in the continuous-time Black‒Scholes (BS) model, there exists a trading strategy which minimizes the shortfall risk. Furthermore, we use binomial models in order to provide numerical schemes for the calculation of the shortfall risk and the corresponding optimal portfolio in the BS model.

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Penalty Methods for Continuous-Time Portfolio Selection with Proportional Transaction Costs

SSRN Electronic Journal ◽

10.2139/ssrn.1210105 ◽

2008 ◽

Cited By ~ 6

Author(s):

Min Dai ◽

Yifei Zhong

Keyword(s):

Transaction Costs ◽

Portfolio Selection ◽

Continuous Time ◽

Penalty Methods ◽

Proportional Transaction Costs

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Hedging in discrete time under transaction costs and continuous-time limit

Journal of Applied Probability ◽

10.1017/s0021900200016946 ◽

1999 ◽

Vol 36 (01) ◽

pp. 163-178 ◽

Cited By ~ 1

Author(s):

Pierre-F. Koehl ◽

Huyên Pham ◽

Nizar Touzi

Keyword(s):

Transaction Costs ◽

Discrete Time ◽

Continuous Time ◽

Sufficient Conditions ◽

Risky Asset ◽

Market Model ◽

Upper And Lower Bounds ◽

Time Step ◽

Proportional Transaction Costs ◽

Call Options

We consider a discrete-time financial market model with L 1 risky asset price process subject to proportional transaction costs. In this general setting, using a dual martingale representation we provide sufficient conditions for the super-replication cost to coincide with the replication cost. Next, we study the convergence problem in a stationary binomial model as the time step tends to zero, keeping the proportional transaction costs fixed. We derive lower and upper bounds for the limit of the super-replication cost. In the case of European call options and for a unit initial holding in the risky asset, the upper and lower bounds are equal. This result also holds for the replication cost of European call options. This is evidence (but not a proof) against the common opinion that the replication cost is infinite in a continuous-time model.

Download Full-text