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.