scholarly journals A note on the existence of unique equivalent martingale measures in a Markovian setting

1997 ◽  
Vol 1 (3) ◽  
pp. 251-257 ◽  
Author(s):  
Tina Hviid Rydberg
Keyword(s):  
Martingale Measures ◽  
Equivalent Martingale Measures ◽  
Equivalent Martingale

scholarly journals Option Pricing Driven by a Telegraph Process with Random Jumps

2012 ◽  
Vol 49 (3) ◽  
pp. 838-849 ◽  
Author(s):  
Oscar López ◽  
Nikita Ratanov
Keyword(s):  
Option Pricing ◽  
Financial Market ◽  
Option Prices ◽  
Martingale Measures ◽  
Market Models ◽  
Telegraph Process ◽  
Equivalent Martingale Measures ◽  
Hedging Strategies ◽  
Random Jumps ◽  
Equivalent Martingale

In this paper we propose a class of financial market models which are based on telegraph processes with alternating tendencies and jumps. It is assumed that the jumps have random sizes and that they occur when the tendencies are switching. These models are typically incomplete, but the set of equivalent martingale measures can be described in detail. We provide additional suggestions which permit arbitrage-free option prices as well as hedging strategies to be obtained.

scholarly journals Complications with stochastic volatility models

1998 ◽  
Vol 30 (01) ◽  
pp. 256-268 ◽  
Author(s):  
Carlos A. Sin
Keyword(s):  
Stochastic Volatility ◽  
Stock Price ◽  
Local Martingale ◽  
Stochastic Volatility Models ◽  
Martingale Measures ◽  
Equivalent Martingale Measures ◽  
Volatility Models ◽  
Equivalent Martingale

We show a class of stock price models with stochastic volatility for which the most natural candidates for martingale measures are only strictly local martingale measures, contrary to what is usually assumed in the finance literature. We also show the existence of equivalent martingale measures, and provide one explicit example.

scholarly journals Finitely Additive Equivalent Martingale Measures

2010 ◽  
Vol 26 (1) ◽  
pp. 46-57 ◽  
Author(s):  
Patrizia Berti ◽  
Luca Pratelli ◽  
Pietro Rigo
Keyword(s):  
Martingale Measures ◽  
Equivalent Martingale Measures ◽  
Equivalent Martingale

Structure-preserving equivalent martingale measures for ℋ-SII models

2018 ◽  
Vol 55 (1) ◽  
pp. 1-14 ◽  
Author(s):  
David Criens
Keyword(s):  
Financial Models ◽  
Martingale Measures ◽  
Structure Preserving ◽  
Mild Conditions ◽  
Equivalent Martingale Measures ◽  
Independent Increments ◽  
Integrable Functions ◽  
Equivalent Martingale

Abstract In this paper we relate the set of structure-preserving equivalent martingale measures ℳsp for financial models driven by semimartingales with conditionally independent increments to a set of measurable and integrable functions 𝒴. More precisely, we prove that ℳsp ≠ ∅ if and only if 𝒴 ≠ ∅, and connect the sets ℳsp and 𝒴 to the semimartingale characteristics of the driving process. As examples we consider integrated Lévy models with independent stochastic factors and time-changed Lévy models and derive mild conditions for ℳsp ≠ ∅.

scholarly journals Regime-Switching Risk: To Price or Not to Price?

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Tak Kuen Siu
Keyword(s):  
Relative Entropy ◽  
Regime Switching ◽  
Martingale Measure ◽  
Martingale Measures ◽  
Equivalent Martingale Measure ◽  
Equivalent Martingale Measures ◽  
Black Scholes ◽  
Normative Issues ◽  
Equivalent Martingale ◽  
Markovian Regime Switching

Should the regime-switching risk be priced? This is perhaps one of the important “normative” issues to be addressed in pricing contingent claims under a Markovian, regime-switching, Black-Scholes-Merton model. We address this issue using a minimal relative entropy approach. Firstly, we apply a martingale representation for a double martingale to characterize the canonical space of equivalent martingale measures which may be viewed as the largest space of equivalent martingale measures to incorporate both the diffusion risk and the regime-switching risk. Then we show that an optimal equivalent martingale measure over the canonical space selected by minimizing the relative entropy between an equivalent martingale measure and the real-world probability measure does not price the regime-switching risk. The optimal measure also justifies the use of the Esscher transform for option valuation in the regime-switching market.

scholarly journals Equivalent or absolutely continuous probability measures with given marginals

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Patrizia Berti ◽  
Luca Pratelli ◽  
Pietro Rigo ◽  
Fabio Spizzichino
Keyword(s):  
Probability Measures ◽  
Mass Transportation ◽  
Martingale Measures ◽  
Absolutely Continuous ◽  
Equivalent Martingale Measures ◽  
Equivalent Martingale

AbstractLet (X,A) and (Y,B) be measurable spaces. Supposewe are given a probability α on A, a probability β on B and a probability μ on the product σ-field A ⊗ B. Is there a probability ν on A⊗B, with marginals α and β, such that ν ≪ μ or ν ~ μ ? Such a ν, provided it exists, may be useful with regard to equivalent martingale measures and mass transportation. Various conditions for the existence of ν are provided, distinguishing ν ≪ μ from ν ~ μ.

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