Local Risk Minimization of Contingent Claims Simultaneously Exposed to Endogenous and Exogenous Default Times

2021 ◽  
Author(s):  
Ramin Okhrati ◽  
Nikolaos Karpathopoulos
Keyword(s):  
Contingent Claims ◽  
Risk Minimization ◽  
Local Risk

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.

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.

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.

LOCAL RISK-MINIMIZATION UNDER MARKOV-MODULATED EXPONENTIAL LÉVY MODEL

2015 ◽  
Vol 18 (05) ◽  
pp. 1550033
Author(s):  
OLIVIER MENOUKEU-PAMEN ◽  
ROMUALD MOMEYA
Keyword(s):  
Regime Switching ◽  
Risk Minimization ◽  
Martingale Representation ◽  
Option Hedging ◽  
Hedging Strategies ◽  
Local Risk ◽  
Hedging Problem ◽  
Markov Modulated ◽  
Martingale Representation Theorem ◽  
Minimization Approach

In this paper, the option hedging problem for a Markov-modulated exponential Lévy model is examined. We use the local risk-minimization approach to study optimal hedging strategies for Europeans derivatives when the price of the underlying is given by a regime-switching Lévy model. We use a martingale representation theorem result to construct an explicit local risk minimizing strategy.

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