Financial market with no riskless (safe) asset

2016/12/07 by Svetlozar T. Rachev, Svetlozar Rachev, Frank J. Fabozzi +3 · 2 citations
Economics, Econometrics and Finance · #Arbitrage #Asset (computer security) #Complex Systems and Time Series Analysis #Computer science #Diffusion process #Econometrics #Economics #FOS: Economics and business #Finance #Financial Risk and Volatility Modeling #Financial economics #Financial market #Geometric Brownian motion #Jump #Mathematical Finance (q-fin.MF) #Mathematical economics #Physics #Stochastic processes and financial applications #q-fin.MF

paper · pdf · doi:10.48550/arxiv.1612.02112

arxiv created 2016/12/07 · openalex publication_date 2016/12/07 · arxiv updated 2016/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study markets with no riskless (safe) asset. We derive the corresponding Black-Scholes-Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii) jump-diffusions; (iii) diffusions with stochastic volatilities, and; (iv) geometric fractional Brownian and Rosenblatt motions. No arbitrage and market completeness conditions are derived in all four cases.

Citations

• Fractional Brownian Motions, Fractional Noises and Applications
• The Pricing of Options and Corporate Liabilities
• Capital Market Equilibrium with Restricted Borrowing
• An Intertemporal Capital Asset Pricing Model
• Debt, Deleveraging, and the Liquidity Trap: A Fisher-Minsky-Koo Approach*

Cited by

• Lévy-Driven Option Pricing without a Riskless Asset
• Innovative Extensions to Option Pricing: Asymmetric Brownian Motion and Random Walk Approaches

Related

• Arbitrage Problems with Reflected Geometric Brownian Motion
• Criteria for the absence of arbitrage in general diffusion markets
• Robust no-free lunch with vanishing risk, a continuum of assets and proportional transaction costs
• Dynamic Asset Pricing in a Unified Bachelier-Black-Scholes-Merton Model
• Black-Scholes without stochastics or PDEs