No Arbitrage and Valuation in Markets with Realistic Transaction Costs
证明在包含市场冲击、卖空成本等现实(非比例)交易成本的市场中,无套利条件仍等价于存在定价算子,并建立了均衡价格与成本函数的关系。
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.