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.
|Journal||International Journal of Theoretical and Applied Finance|
|State||Published - Dec 1 2017|
- Black-Scholes model
- Riskless asset
- fractional Brownian motion
- jump-diffusion model
- stochastic volatility model