Pricing in an equilibrium based model for a large investor

Abstract

We study a financial model with a non-trivial price impact effect. In this model we consider the interaction of a large investor trading in an illiquid security, and a market maker who is quoting prices for this security. We assume that the market maker quotes the prices such that by taking the other side of the investor's demand, the market maker will arrive at maturity with the maximal expected utility of the terminal wealth. Within this model we provide an explicit recursive pricing formula for an exponential utility function, as well as an asymptotic expansion for the price for a "small" simple demand.

Stability and Analytic Expansions of Local Solutions of Systems of Quadratic BSDEs with Applications to a Price Impact Model

“…, m − 1. Theorem 1 in [12] shows that every bounded simple demand γ is viable provided that the dividends Ψ = (Ψ i ) have all exponential moments. Moreover, in this case, the price process S = S(γ) is unique and is constructed explicitly by backward induction.…”

“…The coefficients of these power series can be calculated recursively up to an arbitrary order. This work is motivated by our study in [18] of a price impact model from the market microstructure theory, which builds upon earlier works by Grossman and Miller [13], Garleanu, Pedersen, and Poteshman [11], and German [12]. In this model, a representative dealer provides liquidity for risky stocks and quotes prices in such a way that it is optimal to meet an exogenous demand for stocks.…”

A system of quadratic BSDEs arising in a price impact model

“…In this paper, we consider an inverse problem: find stock prices for which a given strategy is optimal; that is, instead of the usual task of getting "(optimal stocks') quantities from prices" we want to deduce "prices from quantities." This problem naturally arises in the market microstructure theory; see Grossman and Miller [6], Garleanu et al [4] and German [5]. Here, the strategy represents the continuous demand on the market for a set of divided-paying stocks.…”

Liquidity in Competitive Dealer Markets

“…So far, the client demand was assumed to be given exogenously as in [18,14,17,22]. We now consider how to endogenize this demand for clients that behave optimally.…”