A Comment on No-Arbitrage Pricing

Abstract

In this short notice we present critical comments on no-arbitrage principle. We show that no-arbitrage pricing is complete in a pricing theory which ignores market risk and is dealing with the deterministic implied price of instruments. There is a unique price of a derivative in deterministic setting. The no-arbitrage pricing approach picks risk free bond which used as upfront funding instrument for financing deals. In such approach the underlying of the derivatives in deterministic setting becomes risk free bond. In stochastic setting no-arbitrage pricing replace real underlying on a virtual underlying that has risk free expected return and the original volatility. From our point of view this interpretation of the price of a derivative is incorrect. The derivatives pricing contains two steps. On the first step we define the ‘market price.’ This is the price for each admissible market scenario. On the second step we define a spot derivatives price. In some cases spot price can be implied price. In more complex situations for example such as options pricing construction of the spot price does not so simple. Given market and spot derivative prices we arrive at the market risk. The market risk by definition is the probability of scenarios that counterparty pays or loses more than it is implied by the spot price. Market and spot prices along with correspondent market risk is what we call derivatives price. We illustrate this approach by considering a forward contract pricing.