Hi, This is a question from the book of Skiadas(2009) "Asset Pricing Theory" 1.Chapter; Q18

capital. 18. (Bid-Ask Spreads) This exercise models bid-ask spreads by regarding the purchase and the sale of an asset as separate contracts on which short positions are not possible. (The approach is limited to the single-period case.) A long spot position in asset D is the contract (-Sa, D), the scalar Sa representing the ask spot price of the asset. A short spot position in asset D is the contract (Sb, -D), the scalar Sy representing the bid spot price of the asset. In particular, a long spot position in a unit discount bond (-Pa, 1) implements default-free lending with interest rate n = (1/pa) 1, and a short position in a unit discount bond (Pb, 1) implements default-free borrowing with interest rate rb = (1/pb) -- 1. Bid- ask spreads in the forward market for an asset D are modeled analogously through the contracts (0, D Fal) and (0, F11 D), representing long and short forward positions, respectively. The prices Fa and Fy are the ask and bid forward prices of the asset, respectively. (a) Show that in an arbitrage-free market the following restrictions must hold: n