The Best Hedging Strategy in the Presence of Transaction Costs

2008 ◽  
Author(s):  
Valeri Zakamouline
Keyword(s):  
Transaction Costs ◽  
Hedging Strategy

UNDERSTANDING BID-ASK SPREADS OF DERIVATIVES UNDER UNCERTAIN VOLATILITY AND TRANSACTION COSTS

2001 ◽  
Vol 04 (03) ◽  
pp. 467-489 ◽  
Author(s):  
THIERRY ANÉ ◽  
VINCENT LACOSTE
Keyword(s):  
Transaction Costs ◽  
Portfolio Diversification ◽  
Uncertain Parameters ◽  
Price Determination ◽  
Options Markets ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Equilibrium Prices ◽  
Bid Ask Spreads ◽  
Random Nature

The classical option valuation models assume that the option payoff can be replicated by continuously adjusting a portfolio consisting of the underlying asset and a risk-free bond. This strategy implies a constant volatility for the underlying asset and perfect markets. However, the existence of non-zero transaction costs, the consequence of trading only at discrete points in time and the random nature of volatility prevent any portfolio from being perfectly hedged continuously and hence suppress any hope of completely eliminating all risks associated with derivatives. Building upon the uncertain parameters framework we present a model for pricing and hedging derivatives where the volatility is simply assumed to lie between two bounds and in the presence of transaction costs. It is shown that the non-arbitrageable prices for the derivatives, which arise in this framework, can be derived by a non-linear PDE related to the convexity of the derivatives. We use Monte Carlo simulations to investigate the error in the hedging strategy. We show that the standard arbitrage is exposed to such large risks and transaction costs that it can only establish very wide bounds on equilibrium prices, obviously in contradiction with the very tight bid-ask spreads of derivatives observed on the market. We explain how the market spreads can be compatible with our model through portfolio diversification. This has important implications for price determination in options markets as well as for testing of valuation models.

ON THE NUMERICAL ASPECTS OF OPTIMAL OPTION HEDGING WITH TRANSACTION COSTS

2017 ◽  
Vol 20 (01) ◽  
pp. 1750002
Author(s):  
NORMAN JOSEPHY ◽  
LUCIA KIMBALL ◽  
VICTORIA STEBLOVSKAYA
Keyword(s):  
Transaction Costs ◽  
Numerical Study ◽  
Market Model ◽  
Hedging Strategy ◽  
Market Data ◽  
Option Hedging ◽  
Black Scholes ◽  
Real Market ◽  
Delta Hedge ◽  
The Impact

We present a numerical study of non-self-financing hedging of European options under proportional transaction costs. We describe an algorithmic approach based on a discrete time financial market model that extends the classical binomial model. We review the analytical basis for our algorithm and present a variety of empirical results using real market data. The performance of the algorithm is evaluated by comparing to a Black–Scholes delta hedge with transaction costs incorporated. We also evaluate the impact of recalibrating the hedging strategy one or more times during the life of the option using the most recent market data. These results are compared to a recalibrated Black–Scholes delta hedge modified for transaction costs.

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