The Optimal Alternative to the Delta Hedge in the Black and Scholes (1973) World

2010 ◽  
Author(s):  
Katarzyna Romaniuk
Keyword(s):  
Delta Hedge

scholarly journals OPTIMAL HEDGING OF DERIVATIVES WITH TRANSACTION COSTS

2006 ◽  
Vol 09 (07) ◽  
pp. 1051-1069 ◽  
Author(s):  
ERIK AURELL ◽  
PAOLO MURATORE-GINANNESCHI
Keyword(s):  
Transaction Costs ◽  
Optimization Problem ◽  
Optimal Investment ◽  
Market Model ◽  
Black Scholes ◽  
Hamilton Jacobi Bellman Equation ◽  
Finite Time Horizon ◽  
Hamilton Jacobi Bellman ◽  
Delta Hedge ◽  
Strong Control

We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton–Jacobi–Bellman equation, which by the verification theorem has well-behaved solutions if certain conditions on a potential are satisfied. In the case at hand, these conditions simply imply arbitrage-free ("Black–Scholes") pricing of the derivative. While pricing is hence not changed by friction allow a portfolio to fluctuate around a delta hedge. In the limit of weak friction, we determine the optimal control to essentially be of two parts: a strong control, which tries to bring the stock-and-derivative portfolio towards a Black–Scholes delta hedge; and a weak control, which moves the portfolio by adding or subtracting a Black–Scholes hedge. For simplicity we assume growth-optimal investment criteria and quadratic friction.

IMPLICATIONS FOR HEDGING OF THE CHOICE OF DRIVING PROCESS FOR ONE-FACTOR MARKOV-FUNCTIONAL MODELS

2013 ◽  
Vol 16 (05) ◽  
pp. 1350030
Author(s):  
JOANNE E. KENNEDY ◽  
DUY PHAM
Keyword(s):  
Markov Process ◽  
Strong Evidence ◽  
Functional Model ◽  
One Dimensional ◽  
Functional Models ◽  
Hedging Portfolio ◽  
The One ◽  
Bermudan Swaptions ◽  
Delta Hedge ◽  
Instantaneous Volatility

In this paper, we study the implications for hedging Bermudan swaptions of the choice of the instantaneous volatility for the driving Markov process of the one-dimensional swap Markov-functional model. We find that there is a strong evidence in favor of what we term "parametrization by time" as opposed to "parametrization by expiry". We further propose a new parametrization by time for the driving process which takes as inputs into the model the market correlations of relevant swap rates. We show that the new driving process enables a very effective vega-delta hedge with a much more stable gamma profile for the hedging portfolio compared with the existing ones.

What a delta hedge really does - a theoretical and pedagogical note

2008 ◽  
Vol 14 (1) ◽  
pp. 33-47 ◽  
Author(s):  
S. D. Howell
Keyword(s):  
Delta Hedge

scholarly journals Capital Structure Arbitrage under a Risk Neutral Calibration

2016 ◽  
Author(s):  
Peter Zeitsch
Keyword(s):  
Capital Structure ◽  
Simple Formulation ◽  
Volatility Risk ◽  
Arbitrage Opportunities ◽  
Risk Neutral ◽  
Historic Data ◽  
Input Variables ◽  
Arbitrage Strategy ◽  
A New Technique ◽  
Delta Hedge

By reinterpreting the calibration of structural models, a reassessment of the importance of the input variables is undertaken. The analysis shows that volatility is the key parameter to any calibration exercise by several orders of magnitude. In order to maximize the sensitivity to volatility, a simple formulation of Merton’s model is proposed that employs deep out-of-the-money option implied volatilities. The methodology also eliminates the use of historic data to specify the default barrier thereby leading to a full risk neutral calibration. Subsequently, a new technique for identifying and hedging capital structure arbitrage opportunities is illustrated. The approach seeks to hedge the volatility risk, or vega, as opposed to the exposure from the underlying equity itself, or delta. The results question the efficacy of the common arbitrage strategy of only executing the delta hedge.

The Optimal Alternative to the Delta Hedge in the Black and Scholes' (1973) World

2010 ◽  
Author(s):  
Katarzyna Romaniuk
Keyword(s):  
Delta Hedge

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.

The cross-section of average delta-hedge option returns under stochastic volatility

2008 ◽  
Vol 11 (3) ◽  
pp. 205-244
Author(s):  
Alfredo Ibáñez
Keyword(s):  
Stochastic Volatility ◽  
Cross Section ◽  
Option Returns ◽  
The Cross ◽  
Delta Hedge

CUSTO DO DELTA HEDGE: UMA AVALIAÇÃO EMPÍRICA

2008 ◽  
Author(s):  
RICARDO DE ABREU MIRANDA
Keyword(s):  
Delta Hedge
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