Abstract
We consider a financial market with two large investors whose trades affect prices, so they face liquidity risk. In this setting, we examine utility based prices for derivative securities in an extended version of the canonical Black—Scholes derivative pricing model. In our model the large investors’ risk preferences of are represented by an exponential utility functions. In a stylized binomial example with price impact, we show that the payoff space and the no–arbitrage pricing functional are convex but not necessarily linear, which impedes arbitrage pricing. In a continuous time framework, where large traders play a non–zero sum singular stochastic differential Cournot game, we obtain a pricing rule for derivative securities that can be characterized by a nonlinear transformation of the expectation of the distorted derivative payoff under the Markov—Nash pricing measure. Under specified assumptions, we derive a liquidity adjusted Black—Scholes equation and show that the manipulation free price coincides with the Black—Scholes price. We also implement a numerical algorithm for computing the price of European style options in a general framework.
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Contributed Presentations
- XI Conference on Mathematical & Statistical Methods for Actuarial Science & Finance
- VI QMUL Economics and Finance Workshop
- XXXII European Workshop on Economic Theory
- Royal Statistical Society International Conference