scholarly journals Non Quadratic Local Risk-Minimization for Hedging Contingent Claims in Incomplete Markets

2010 ◽  
Author(s):  
Frederic Abergel ◽  
Nicolas Millot
Keyword(s):  
Incomplete Markets ◽  
Contingent Claims ◽  
Risk Minimization ◽  
Local Risk

NUMERICAL ANALYSIS ON LOCAL RISK-MINIMIZATION FOR EXPONENTIAL LÉVY MODELS

2016 ◽  
Vol 19 (02) ◽  
pp. 1650008 ◽  
Author(s):  
TAKUJI ARAI ◽  
YUTO IMAI ◽  
RYOICHI SUZUKI
Keyword(s):  
Incomplete Markets ◽  
Contingent Claims ◽  
Risk Minimization ◽  
Gamma Model ◽  
Variance Gamma ◽  
Call Options ◽  
Estimated Parameters ◽  
Exponential Lévy Models ◽  
Local Risk ◽  
Variance Gamma Model

We illustrate how to compute local risk minimization (LRM) of call options for exponential Lévy models. Here, LRM is a popular hedging method through a quadratic criterion for contingent claims in incomplete markets. Arai & Suzuki (2015) have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast Fourier transform (FFT) method suggested by by Carr & Madan (1999). Considering Merton jump-diffusion models and variance gamma models as typical examples of exponential Lévy models, we provide the forms for the FFT explicitly; and compute the values of LRM numerically for given parameter sets. Furthermore, we illustrate numerical results for a variance gamma model with estimated parameters from the Nikkei 225 index.

On Minimizing Risk in Incomplete Markets Option Pricing Models

1998 ◽  
Vol 01 (02) ◽  
pp. 227-233 ◽  
Author(s):  
Ola Hammarlid
Keyword(s):  
Incomplete Markets ◽  
Option Price ◽  
Market Model ◽  
Risk Minimization ◽  
Pricing Options ◽  
Fair Game ◽  
Local Risk ◽  
Game Condition ◽  
Stock Portfolio ◽  
Global And Local

I study the Bouchaud–Sornette, Schweizer and Schäl way of pricing options, presenting the methodology in accordance with Bouchaud–Sornette. The definitions of the wealth balance and risk from trading in options and stocks are presented. The problem of finding a risk minimizing strategy in an incomplete market model where a perfect hedge is not possible is analyzed. Using this strategy according to the approach of Bouchaud and Sornette the option is priced by a fair game condition. In this article I establish the equivalence between global and local risk minimization and prove an option price conjecture of Wolczyńska. I also investigate optimality for a stock portfolio with extra profit.

Local risk minimization and numéraire

1999 ◽  
Vol 36 (04) ◽  
pp. 1126-1139 ◽  
Author(s):  
F. Biagini ◽  
M. Pratelli
Keyword(s):  
Stochastic Process ◽  
Stochastic Volatility ◽  
Contingent Claims ◽  
Continuous Case ◽  
Risk Minimization ◽  
Complete Markets ◽  
Local Risk ◽  
The Right

The ‘change of numéraire’ technique has been introduced by Geman, El Karoui and Rochet for pricing and hedging contingent claims in the case of complete markets. In this paper we study the ‘change of numéraire’ using the ‘locally risk-minimizing approach’, when the market is not complete. We prove that, if the stochastic process which represents the prices is continuous, the l.r.m. strategy is invariant by a change of numéraire (this result is false in the right-continuous case, as is shown by some counterexamples). We also give an extension of Merton's formula to the case of stochastic volatility.

Local risk minimization and numéraire

1999 ◽  
Vol 36 (4) ◽  
pp. 1126-1139 ◽  
Author(s):  
F. Biagini ◽  
M. Pratelli
Keyword(s):  
Stochastic Process ◽  
Stochastic Volatility ◽  
Contingent Claims ◽  
Continuous Case ◽  
Risk Minimization ◽  
Complete Markets ◽  
Local Risk ◽  
The Right

The ‘change of numéraire’ technique has been introduced by Geman, El Karoui and Rochet for pricing and hedging contingent claims in the case of complete markets. In this paper we study the ‘change of numéraire’ using the ‘locally risk-minimizing approach’, when the market is not complete. We prove that, if the stochastic process which represents the prices is continuous, the l.r.m. strategy is invariant by a change of numéraire (this result is false in the right-continuous case, as is shown by some counterexamples).We also give an extension of Merton's formula to the case of stochastic volatility.

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