The Minimal Entropy Martingale Measure (MEMM) for a Markov-Modulated Lévy Model

2010 ◽  
Author(s):  
Zied Ben Salah ◽  
romuald hervé momeya
Keyword(s):  
Martingale Measure ◽  
Minimal Entropy Martingale Measure ◽  
Markov Modulated

scholarly journals The minimal entropy martingale measure in a market of traded financial and actuarial risks

2015 ◽  
Vol 282 ◽  
pp. 111-133 ◽  
Author(s):  
Jan Dhaene ◽  
Ben Stassen ◽  
Pierre Devolder ◽  
Michel Vellekoop
Keyword(s):  
Martingale Measure ◽  
Minimal Entropy Martingale Measure

The Minimal Entropy Martingale Measure for Exponential Markov Chains

2013 ◽  
Vol 50 (02) ◽  
pp. 344-358
Author(s):  
Young Lee ◽  
Thorsten Rheinländer
Keyword(s):  
Differential Equations ◽  
Markov Chains ◽  
Continuous Time ◽  
Martingale Measure ◽  
Minimal Entropy Martingale Measure ◽  
Continuous Time Markov Chains ◽  
Absence Of Arbitrage

In this article we investigate the minimal entropy martingale measure for continuous-time Markov chains. The conditions for absence of arbitrage and existence of the minimal entropy martingale measure are discussed. Under this measure, expressions for the transition intensities are obtained. Differential equations for the arbitrage-free price are derived.

scholarly journals On the minimal entropy martingale measure

2002 ◽  
Vol 30 (3) ◽  
pp. 1003-1038 ◽  
Author(s):  
Peter Grandits ◽  
Thorsten Rheinländer
Keyword(s):  
Martingale Measure ◽  
Minimal Entropy Martingale Measure

scholarly journals Pricing European options with stochastic volatility under the minimal entropy martingale measure

2015 ◽  
Vol 27 (2) ◽  
pp. 233-247 ◽  
Author(s):  
XIN-JIANG HE ◽  
SONG-PING ZHU
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Martingale Measure ◽  
Minimal Entropy Martingale Measure ◽  
Volatility Model ◽  
In Series ◽  
Expected Utility Maximization ◽  
Equivalent Martingale ◽  
The One ◽  
Pricing Formula

In this paper, a closed-form pricing formula in the form of an infinite series for European call options is derived for the Heston stochastic volatility model under a chosen martingale measure. Given that markets with the stochastic volatility are incomplete, there exists a number of equivalent martingale measures and consequently investors face a problem of making a choice of appropriate measure when they price options. The one we adopt here is the so-called minimal entropy martingale measure shown to be related to the expected utility maximization theory (Frittelli 2000 Math. Finance10(1), 39–52) and the financial rationality for choosing this measure will be further illustrated in this paper. A great advantage of our newly-derived pricing formula is that the convergence of the solution in series form can be proved theoretically; such a proof of the convergence is also complemented by some numerical examples to demonstrate the speed of convergence. To further show the validity of our formula, a comparison of prices calculated through the newly derived formula is made with those obtained directly from the Monte Carlo simulation as well as those from solving the PDE (partial differential equation) with the finite difference method.

scholarly journals On the minimal entropy martingale measure for Lévy processes

Stochastics ◽  
2019 ◽  
Vol 92 (8) ◽  
pp. 1223-1243
Author(s):  
Andrii Andrusiv ◽  
Hans-Jürgen Engelbert
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Martingale Measure ◽  
Minimal Entropy Martingale Measure
Sign in / Sign up

Export Citation Format

Share Document