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Asset Pricing with Volume-Dependent Trading Costs

Article arXiv papers · Author: Erindi Allaj
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Summary

This paper extends arbitrage pricing theory to markets where execution prices depend on trade size. Investors buy at the ask and sell at the bid, and implicit transaction costs include both the bid–ask spread and price impact. The authors also redefine what it means for a portfolio to be self-financing under these costs.

The framework permits specified predictable trading strategies with càdlàg or càglàd paths and bounded quadratic variation, including certain infinite-variation strategies with finitely many jumps. For càglàd predictable strategies, the paper establishes an equivalence between the existence of an equivalent probability measure and the absence of arbitrage, yielding a version of the first fundamental theorem of asset pricing. It also argues that continuous, bounded-variation strategies can improve hedging efficiency. Linear and nonlinear order-size examples illustrate the theory, but the supplied description gives no empirical evaluation or quantitative measure of the hedging improvement.

Key ideas

  • Execution prices depend on traded volume in the market model.
  • Implicit costs combine the bid–ask spread with price impact.
  • The self-financing condition allows specified predictable strategies with finite jumps and bounded quadratic variation.
  • For càglàd predictable strategies, absence of arbitrage is equivalent to an equivalent probability measure.
  • Continuous bounded-variation strategies may improve hedging efficiency under implicit costs.

Tags

ArbitrageMarket microstructureRisk management
Full text
# Implicit transaction costs and the fundamental theorems of asset pricing


# Implicit transaction costs and the fundamental theorems of asset pricing









This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded volume. The investors in the market always buy at the ask and sell at the bid price. Implicit transaction costs are composed of two terms, one is able to capture the bid-ask spread, and the second the price impact. Moreover, a new definition of a self-financing portfolio is obtained. The self-financing condition suggests that continuous trading is possible, but is restricted to predictable trading strategies having cádlág (right-continuous with left limits) and cáglád (left-continuous with right limits) paths of bounded quadratic variation and of finitely many jumps. That is, cádlág and cáglád predictable trading strategies of infinite variation, with finitely many jumps and of finite quadratic variation are allowed in our setting. Restricting ourselves to cáglád predictable trading strategies, we show that the existence of an equivalent probability measure is equivalent to the absence of arbitrage opportunities, so that the first fundamental theorem of asset pricing (FFTAP) holds. It is also shown that the use of continuous and bounded variation trading strategies can improve the efficiency of hedging in a market with implicit transaction costs. To better understand how to apply the theory proposed we provide an example of an implicit transaction cost economy that is linear and non-linear in the order size.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.