No Arbitrage and Valuation in Markets with Realistic Transaction Costs

Abstract

One of the most fundamental results in finance is the equivalence of a no-arbitrage condition to the existence of a pricing operator in markets without transaction costs (see Ross (1978)). Garman and Ohlson (1981) extended this to markets with proportional transaction costs. The current paper further extends this result to markets with realistic (and nonproportional) transaction costs. These costs include all investors' market-impact and short-borrowing costs, large investors' institutional commissions, and for small investors only the additional cost of retail commissions. They are functions of the value of the trade and have increasing, increasing, constant, and decreasing marginal rates, respectively, in that value. Garman and Ohlson showed that equilibrium prices in their notion of a corresponding cost-free market, plus a certain factor, prevail under equilibrium in markets with proportional transaction costs. The current paper extends this to realistic transaction costs and establishes the functional relation between this factor and the form of such costs.