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.

QUADRATIC HEDGING FOR THE BATES MODEL

2007 ◽  
Vol 10 (05) ◽  
pp. 873-885 ◽  
Author(s):  
FRIEDRICH HUBALEK ◽  
CARLO SGARRA
Keyword(s):  
Option Pricing ◽  
Explicit Expression ◽  
Martingale Measure ◽  
Risk Minimization ◽  
Hedging Strategy ◽  
Preliminary Results ◽  
Quadratic Hedging ◽  
The Mean ◽  
Mean Variance ◽  
Martingale Case

In the present paper we give some preliminary results for option pricing and hedging in the framework of the Bates model based on quadratic risk minimization. We provide an explicit expression of the mean-variance hedging strategy in the martingale case and study the Minimal Martingale measure in the general case.

Bifractional Black-Scholes Model for Pricing European Options and Compound Options

2020 ◽  
Vol 8 (4) ◽  
pp. 346-355
Author(s):  
Feng Xu
Keyword(s):  
Empirical Studies ◽  
Asset Price ◽  
European Options ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Bifractional Brownian Motion ◽  
Compound Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Delta Hedging

AbstractRecent empirical studies show that an underlying asset price process may have the property of long memory. In this paper, it is introduced the bifractional Brownian motion to capture the underlying asset of European options. Moreover, a bifractional Black-Scholes partial differential equation formulation for valuing European options based on Delta hedging strategy is proposed. Using the final condition and the method of variable substitution, the pricing formulas for the European options are derived. Furthermore, applying to risk-neutral principle, we obtain the pricing formulas for the compound options. Finally, the numerical experiments show that the parameter HK has a significant impact on the option value.

scholarly journals On the performance of delta hedging strategies in exponential Lévy models

2013 ◽  
Vol 13 (8) ◽  
pp. 1173-1184 ◽  
Author(s):  
STEPHAN DENKL ◽  
MARTINA GOY ◽  
JAN KALLSEN ◽  
JOHANNES MUHLE-KARBE ◽  
ARND PAUWELS
Keyword(s):  
Hedging Strategies ◽  
Exponential Lévy Models ◽  
Delta Hedging

scholarly journals FINANCIAL MODELING AND OPTION THEORY WITH THE TRUNCATED LEVY PROCESS

2000 ◽  
Vol 03 (01) ◽  
pp. 143-160 ◽  
Author(s):  
ANDREW MATACZ
Keyword(s):  
High Frequency ◽  
Lévy Process ◽  
Levy Process ◽  
Hedging Strategy ◽  
Financial Modeling ◽  
Option Hedging ◽  
Market Index ◽  
Delta Hedging ◽  
Option Theory ◽  
Finite Moments

In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed excess kurtosis at short timescales, along with the slow convergence to Gaussian at longer timescales. In this paper I further test the truncated Levy paradigm using high frequency data from the Australian All Ordinaries share market index. I then consider an optimal option hedging strategy which is appropriate for the early Levy dominated regime. This is compared with the usual delta hedging approach and found to differ significantly.

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