The Impact of Liquidity Risk in Option Pricing Theory with a Supply Curve

Abstract: Fisher Black and Myron Scholes (Black and Scholes, 1973) presented in 1973 a valuation model for options that was intuitive and user friendly. This revolutionized the option market and made pricing an option easy.   To get a sound understanding of liquidity risk we have to specify and describe liquidity (Matz and Neu, 2007, p.5). Market liquidity and funding liquidity are two kinds of liquidity. Market liquidity can be described as good when a security is easy to trade. Easy to trade is defined as small bid ask spread, small price impact and high resilience. If a bank or investor have good funding liquidity they have good availability of funds by their own capital or from loans.   The meaning of liquidity risk can be divided into two major risks; market liquidity risk and funding liquidity risk (Pedersen, 2008). Market liquidity risk is the risk that the market liquidity gets worse when a trade needs to be made and this is the risk focused on in this paper.   Do liquidity costs in option pricing theory exist and does it depend on a real supply curve?   The main objective in this paper is to show if liquidity risk has a significant impact on option price and depends on a real supply curve. The study is based on theory and conclusions from earlier research. Built from Jarrow and Protters work in liquidity risk in option price (Jarrow and Protter, 2007) a model for the supply curve is derived.   The scientific ideal in this paper has a clear positivistic approach. The quantitative method is my choice not only because of the link between positivism, deduction and quantitative methods but gives a certain advantage when considering this problem formulation and the type of data accessible. A model is derived with a base from a model derived by Jarrow and Protter (2007) and used to show the impact of liquidity risk in the option pricing theory.   The result presented in this paper has shown that liquidity costs exist in theory and in practice, and this cost are binding. This model can be used to get exact costs in a specific case with a specific option and can help brokers to know the real liquidity risk they are exposed to.