Price Bounds in Jump-Diffusion Markets Revisited via Market Completions

MacKay, Anne; Melnikov, Alexander

doi:10.1007/978-3-319-99719-3_50

Cited by 3 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…a non-negative local martingale (See [8]) with E[Z κ (t)] = 1 for all t ∈ [0, T]. The sufficient condition for market completeness is the uniqueness of the equivalent martingale measure.…”

Section: Pricing Contingent Claims Via Market Completion Inmentioning

confidence: 99%

Pricing Contingent Claims in a Two-Interest Rate Multi-dimensional Jump-diffusion Model via Market Completion

Melnikov,

Mohammadi Nejad

2023

Preprint

View full text Add to dashboard Cite

In this paper, we investigate a financial market in which asset prices evolve based on a multi-dimensional Brownian motion process and a multi-dimensional Poisson process with different credit and deposit rates We proceed to evaluate European options by establishing upper and lower hedging prices through a transition to a suitable auxiliary market. Additionally, we address the minimization of shortfall risk and no-arbitrage price bounds in incomplete markets within this framework.

show abstract

Section: Pricing Contingent Claims Via Market Completion Inmentioning

confidence: 99%

Pricing Contingent Claims in a Two-Interest Rate Multi-dimensional Jump-diffusion Model via Market Completion

Melnikov,

Mohammadi Nejad

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Incomplete markets typically allow for infinitely many equivalent martingale measures, leading to non-uniqueness in the no-arbitrage price of a contingent claim. Researchers address this challenge through various approaches, such as market completion by introducing specific sets of assets (refer to [18,19]). We introduce certain conditions under which a given set of assets completes the original market, enabling the determination of the range within which the no-arbitrage price can be obtained.…”

Section: Introductionmentioning

confidence: 99%

Pricing Contingent Claims in a Two-Interest-Rate Multi-Dimensional Jump-Diffusion Model via Market Completion

Melnikov,

Mohammadi Nejad

2024

AppliedMath

View full text Add to dashboard Cite

This paper investigates a financial market where asset prices follow a multi-dimensional Brownian motion process and a multi-dimensional Poisson process characterized by diverse credit and deposit rates where the credit rate is higher than the deposit rate. The focus extends to evaluating European options by establishing upper and lower hedging prices through a transition to a suitable auxiliary market. Introducing a lemma elucidates the same solution to the pricing problem in both markets under specific conditions. Additionally, we address the minimization of shortfall risk and determine no-arbitrage price bounds within the framework of incomplete markets. This study provides a comprehensive understanding of the challenges posed by the multi-dimensional jump-diffusion model and varying interest rates in financial markets.

show abstract

RVaR Hedging and Market Completions

Vasilev

Melnikov

2022

Mathematical and Statistical Methods for Actuarial Sciences and Finance

View full text Add to dashboard Cite

Price Bounds in Jump-Diffusion Markets Revisited via Market Completions

Cited by 3 publications

References 12 publications

Pricing Contingent Claims in a Two-Interest Rate Multi-dimensional Jump-diffusion Model via Market Completion

Pricing Contingent Claims in a Two-Interest Rate Multi-dimensional Jump-diffusion Model via Market Completion

Pricing Contingent Claims in a Two-Interest-Rate Multi-Dimensional Jump-Diffusion Model via Market Completion

RVaR Hedging and Market Completions

Contact Info

Product

Resources

About