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.

CROSS HEDGING WITHIN A LOG MEAN REVERTING MODEL

2007 ◽  
Vol 10 (05) ◽  
pp. 887-914 ◽  
Author(s):  
SAMUEL NJOH
Keyword(s):  
Energy Markets ◽  
Financial Asset ◽  
Risk Minimization ◽  
No Arbitrage ◽  
Spot Prices ◽  
Quadratic Minimization ◽  
Hedging Strategies ◽  
Local Risk ◽  
Cross Hedging ◽  
Quadratic Criteria

We hedge options on electricity spot prices by cross hedging, i.e., by using another financial asset. We calculate hedging strategies by quadratic minimization and local risk minimization. In our model of energy markets, we have done a deep study of no arbitrage and of the existence of martingale measures with square integrable density. Then we have established tools for efficient hedges. Nevertheless, we have clearly proved possible limitations of the expiry of options with quadratic criteria.

scholarly journals SOME NOTES ABOUT THE MARTINGALE REPRESENTATION THEOREM AND THEIR APPLICATIONS

2020 ◽  
Vol 6 (2) ◽  
pp. 76
Author(s):  
Reza Habibi
Keyword(s):  
Representation Theorem ◽  
Stochastic Dynamics ◽  
Real Data ◽  
Sensitivity Analyses ◽  
Data Sets ◽  
Martingale Representation ◽  
Hedging Strategies ◽  
Martingale Representation Theorem ◽  
Dynamics Models ◽  
Theoretical Results

An important theorem in stochastic finance field is the martingale representation theorem. It is useful in the stage of making hedging strategies (such as cross hedging and replicating hedge) in the presence of different assets with different stochastic dynamics models. In the current paper, some new theoretical results about this theorem including derivation of serial correlation function of a martingale process and its conditional expectations approximation are proposed. Applications in optimal hedge ratio and financial derivative pricing are presented and sensitivity analyses are studied. Throughout theoretical results, simulation-based results are also proposed. Two real data sets are analyzed and concluding remarks are given. Finally, a conclusion section is given.

scholarly journals Weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain

2021 ◽  
Vol 58 (2) ◽  
pp. 372-393
Author(s):  
H. M. Jansen
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
The State ◽  
Stochastic Integrals ◽  
Occupation Measure ◽  
Generator Matrix ◽  
Markov Modulated ◽  
Erlang Loss

AbstractOur aim is to find sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain. First, we study properties of the state indicator function and the state occupation measure of a Markov chain. In particular, we establish weak convergence of the state occupation measure under a scaling of the generator matrix. Then, relying on the connection between the state occupation measure and the Dynkin martingale, we provide sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure. We apply our results to derive diffusion limits for the Markov-modulated Erlang loss model and the regime-switching Cox–Ingersoll–Ross process.

Continuous-time mean-variance portfolio selection with regime-switching financial market: Time-consistent solution

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ishak Alia ◽  
Farid Chighoub
Keyword(s):  
Portfolio Selection ◽  
Regime Switching ◽  
Optimal Time ◽  
Uniqueness Results ◽  
State Dependent ◽  
Consistent Solution ◽  
Game Theoretic ◽  
Markov Modulated ◽  
Mean Variance Portfolio ◽  
Mean Variance

Abstract This paper studies optimal time-consistent strategies for the mean-variance portfolio selection problem. Especially, we assume that the price processes of risky stocks are described by regime-switching SDEs. We consider a Markov-modulated state-dependent risk aversion and we formulate the problem in the game theoretic framework. Then, by solving a flow of forward-backward stochastic differential equations, an explicit representation as well as uniqueness results of an equilibrium solution are obtained.

scholarly journals An Analytic Approach for Pricing American Options with Regime Switching

2021 ◽  
Vol 14 (5) ◽  
pp. 188
Author(s):  
Leunglung Chan ◽  
Song-Ping Zhu
Keyword(s):  
Regime Switching ◽  
American Options ◽  
Option Price ◽  
Switching Model ◽  
Homotopy Analysis ◽  
State Regime ◽  
Markov Modulated ◽  
Appreciation Rate ◽  
The Interest Rate ◽  
Hidden States

This paper investigates the American option price in a two-state regime-switching model. The dynamics of underlying are driven by a Markov-modulated Geometric Wiener process. That means the interest rate, the appreciation rate, and the volatility of underlying rely on hidden states of the economy which can be interpreted in terms of Markov chains. By means of the homotopy analysis method, an explicit formula for pricing two-state regime-switching American options is presented.

scholarly journals Weather Risk Management in Agriculture

2016 ◽  
Vol 64 (4) ◽  
pp. 1303-1309 ◽  
Author(s):  
Martina Bobriková
Keyword(s):  
Financial Risk ◽  
Weather Conditions ◽  
Option Hedging ◽  
Put Option ◽  
Hedging Strategies ◽  
Weather Risk ◽  
High Volatility ◽  
Unfavourable Weather ◽  
Agricultural Industries ◽  
Weather Risk Management

The paper focuses on valuation of a weather derivative with payoffs depending on temperature. We use historical data from the weather station in the Slovak town Košice to obtain unique prices of option contracts in an incomplete market. Numerical examples of prices of some contracts are presented, using the Burn analysis. We provide an example of how a weather contract can be designed to hedge the financial risk of a suboptimal temperature condition. The comparative comparison of the selected option hedging strategies has shown the best results for the producers in agricultural industries who hedges against an unfavourable weather conditions. The results of analysis proved that by buying put option or call option, the farmer establishes the highest payoff in the case of temperature decrease or increase. The Long Straddle Strategy is the most expensive but is available to the farmer who hedges against a high volatility in temperature movement. We conclude with the findings that weather derivatives could be useful tools to diminish the financial losses for agricultural industries highly dependent for temperature.

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