This thesis studies the work of Przemysław Rola on the condition of no-arbitrage in a finite discrete time market with a money account (risk-free) and bid-ask spreads. In the first chapter, we introduce the mathematical model and we state the notions of Equivalent Bid-Ask Martingale Measure (EBAMM) and consistent price system (CPS). In the second chapter, we prove some lemmas and the fundamental theorem of asset pricing using the existence of EBAMM or superCPS and subCPS as an equivalent condition for no-arbitrage. In the last chapter, as an application of our findings, we introduce the Cox-Ross-Rubinstein model with bid-ask spreads.

This thesis studies the work of Przemysław Rola on the condition of no-arbitrage in a finite discrete time market with a money account (risk-free) and bid-ask spreads. In the first chapter, we introduce the mathematical model and we state the notions of Equivalent Bid-Ask Martingale Measure (EBAMM) and consistent price system (CPS). In the second chapter, we prove some lemmas and the fundamental theorem of asset pricing using the existence of EBAMM or superCPS and subCPS as an equivalent condition for no-arbitrage. In the last chapter, as an application of our findings, we introduce the Cox-Ross-Rubinstein model with bid-ask spreads.

Arbitrage theory in discrete time markets with bid-ask spread

TARGON, ALBERTO
2022/2023

Abstract

This thesis studies the work of Przemysław Rola on the condition of no-arbitrage in a finite discrete time market with a money account (risk-free) and bid-ask spreads. In the first chapter, we introduce the mathematical model and we state the notions of Equivalent Bid-Ask Martingale Measure (EBAMM) and consistent price system (CPS). In the second chapter, we prove some lemmas and the fundamental theorem of asset pricing using the existence of EBAMM or superCPS and subCPS as an equivalent condition for no-arbitrage. In the last chapter, as an application of our findings, we introduce the Cox-Ross-Rubinstein model with bid-ask spreads.
2022
Arbitrage theory in discrete time markets with bid-ask spread
This thesis studies the work of Przemysław Rola on the condition of no-arbitrage in a finite discrete time market with a money account (risk-free) and bid-ask spreads. In the first chapter, we introduce the mathematical model and we state the notions of Equivalent Bid-Ask Martingale Measure (EBAMM) and consistent price system (CPS). In the second chapter, we prove some lemmas and the fundamental theorem of asset pricing using the existence of EBAMM or superCPS and subCPS as an equivalent condition for no-arbitrage. In the last chapter, as an application of our findings, we introduce the Cox-Ross-Rubinstein model with bid-ask spreads.
Arbitrage
Bid-Ask Spread
CPS
Martingale Measure
CRR Model
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/43091