scholarly journals Risk minimization for game options in markets imposing minimal transaction costs

2016 ◽  
Vol 48 (3) ◽  
pp. 926-946 ◽  
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.

Portfolio Selection with Transaction Costs and Jump-Diffusion Asset Dynamics I: A Numerical Solution

2016 ◽  
Vol 06 (04) ◽  
pp. 1650018 ◽  
Author(s):  
Michal Czerwonko ◽  
Stylianos Perrakis
Keyword(s):  
Diffusion Process ◽  
Transaction Costs ◽  
Portfolio Selection ◽  
Discrete Time ◽  
Continuous Time ◽  
Jump Diffusion ◽  
Numerical Approach ◽  
Proportional Transaction Costs ◽  
Asset Portfolio ◽  
Time Formulation

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.

A note on super-replicating strategies

1994 ◽  
Vol 347 (1684) ◽  
pp. 485-494 ◽  
Keyword(s):  
Option Pricing ◽  
Transaction Costs ◽  
Continuous Time ◽  
Black Scholes ◽  
Alternative Approaches

The standard Black-Scholes option pricing methodology fails in the presence of transaction costs because portfolios that exactly replicate the option pay-off no longer exist. Several alternative approaches have been proposed; our purpose is to examine one of them which is based on the idea of ‘super-replicating’ portfolios. It is argued that this approach does not lead to a viable theory of option pricing in continuous time.

scholarly journals PRICING AND HEDGING GAME OPTIONS IN CURRENCY MODELS WITH PROPORTIONAL TRANSACTION COSTS

2016 ◽  
Vol 19 (07) ◽  
pp. 1650043 ◽  
Author(s):  
ALET ROUX
Keyword(s):  
Transaction Costs ◽  
Proportional Transaction Costs ◽  
Numerical Examples ◽  
Dual Representations ◽  
Optimal Hedging ◽  
Game Options

The pricing, hedging, optimal exercise and optimal cancellation of game or Israeli options are considered in a multi-currency model with proportional transaction costs. Efficient constructions for optimal hedging, cancellation and exercise strategies are presented, together with numerical examples, as well as probabilistic dual representations for the bid and ask price of a game option.

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

1999 ◽  
Vol 36 (1) ◽  
pp. 163-178 ◽  
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.

SHORTFALL RISK MINIMIZATION UNDER FIXED TRANSACTION COSTS

2018 ◽  
Vol 21 (05) ◽  
pp. 1850034
Author(s):  
NIV NAYMAN
Keyword(s):  
Analytical Solution ◽  
Transaction Costs ◽  
Dynamic Programming Algorithm ◽  
Control Policy ◽  
Programming Algorithm ◽  
Main Question ◽  
Risk Minimization ◽  
Shortfall Risk ◽  
Markov Decision ◽  
Augmented State

In this work, we deal with market frictions which are given by fixed transaction costs independent of the volume of the trade. The main question that we study is the minimization of shortfall risk in the Black–Scholes (BS) model under constraints on the initial capital. This problem does not have an analytical solution and so numerical schemes come into the picture. The Cox–Ross–Rubinstein (CRR) binomial models are an efficient tool for approximating the BS model. In this paper, we study in detail the CRR models with fixed transaction costs. In particular, we construct an augmented state-action space forming a Markov decision process (MDP) and provide a proof for the existence of optimal control/policy. We further suggest a dynamic programming algorithm for calculating the optimal hedging strategy and its corresponding shortfall risk. In the absence of transaction costs, there is an analytical solution in both CRR and BS models, and so we use them for testing our algorithm and its convergence. Moreover, we point out various insights provided by our numerical results, for example, regarding the change in the investor’s activity in the presence of friction.

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