When You Hedge Discretely: Optimization of Sharpe Ratio for Delta-Hedging Strategy under Discrete Hedging and Transaction Costs

2012 ◽  
Author(s):  
Artur Sepp
Keyword(s):  
Transaction Costs ◽  
Sharpe Ratio ◽  
Hedging Strategy ◽  
Delta Hedging ◽  
Discrete Hedging

scholarly journals TRACKING ERRORS FROM DISCRETE HEDGING IN EXPONENTIAL LÉVY MODELS

2011 ◽  
Vol 14 (06) ◽  
pp. 803-837 ◽  
Author(s):  
MATS BRODÉN ◽  
PETER TANKOV
Keyword(s):  
Tracking Errors ◽  
Hedging Strategy ◽  
Squared Error ◽  
Hedging Portfolio ◽  
Exponential Lévy Models ◽  
Delta Hedging ◽  
Quadratic Hedging ◽  
Market Practice ◽  
Discrete Hedging ◽  
Explicit Relation

We analyze the errors arising from discrete readjustment of the hedging portfolio when hedging options in exponential Lévy models, and establish the rate at which the expected squared error goes to zero when the readjustment frequency increases. We compare the quadratic hedging strategy with the common market practice of delta hedging, and show that for discontinuous option pay-offs the latter strategy may suffer from very large discretization errors. For options with discontinuous pay-offs, the convergence rate depends on the underlying Lévy process, and we give an explicit relation between the rate and the Blumenthal-Getoor index of the process.

scholarly journals Robustness of Delta Hedging for Path-Dependent Options in Local Volatility Models

2007 ◽  
Vol 44 (04) ◽  
pp. 865-879 ◽  
Author(s):  
Alexander Schied ◽  
Mitja Stadje
Keyword(s):  
Payoff Function ◽  
Hedging Strategy ◽  
Local Volatility ◽  
Directional Convexity ◽  
Volatility Models ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Black Scholes ◽  
Delta Hedging ◽  
Path Dependent

We consider the performance of the delta hedging strategy obtained from a local volatility model when using as input the physical prices instead of the model price process. This hedging strategy is called robust if it yields a superhedge as soon as the local volatility model overestimates the market volatility. We show that robustness holds for a standard Black-Scholes model whenever we hedge a path-dependent derivative with a convex payoff function. In a genuine local volatility model the situation is shown to be less stable: robustness can break down for many relevant convex payoffs including average-strike Asian options, lookback puts, floating-strike forward starts, and their aggregated cliquets. Furthermore, we prove that a sufficient condition for the robustness in every local volatility model is the directional convexity of the payoff function.

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.

scholarly journals Efficient Hedging of Options with Probabilistic Haar Wavelets

2012 ◽  
Vol 2012 ◽  
pp. 1-37
Author(s):  
Pedro José Catuogno ◽  
Sebastián Esteban Ferrando ◽  
Alfredo Lázaro González
Keyword(s):  
Transaction Costs ◽  
Upper Bounds ◽  
Haar Wavelets ◽  
Efficient Hedging ◽  
Delta Hedging ◽  
Binary Options ◽  
Path Dependent ◽  
Underlying Processes ◽  
Theoretical Developments

The paper brings forward the issue of efficient representations of financial claims; in particular it addresses the problem of large transaction costs in hedging replications. Inspired by the localized properties of wavelets basis, Haar systems associated with space-time discretizations of continuous stochastic processes are proposed as a means to address the issue of efficient pathwise approximation. Theoretical developments are presented that justify the use of these approximations to construct self-financing portfolios by means of binary options. Upper bounds on the volume of transactions required to implement these portfolios are then established to illustrate the quality of the proposed approximations. The approach is applicable to general financial claims of European type, including path-dependent ones, for continuous underlying processes. Several numerical results and comparisons with delta hedging are also presented.

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