Large Traders and Illiquid Options: Hedging vs. Manipulation
Holger Kraft
Goethe University (Frankfurt) & UCLA
Wednesday, Jan 20, 2010
4:30 - 5:30 PM
Terman Engineering Center, Room 453
Abstract:
In this paper, we study the effects on derivative pricing arising from price impacts by large traders. When a large trader issues a derivative and (partially) hedges his risk by trading in the underlying, he influences both his hedge portfolio and the derivative's payoff. In a Black-Scholes model with price impact, we analyze the resulting trade-off by explicitly solving the utility maximization problem of a large investor endowed with an illiquid contingent claim. We find several interesting phenomena which cannot occur in frictionless markets. Firstly, the indifference price is a convex function of the contingent claim -- and not concave as in frictionless markets -- implying that for any claim the buyer's indifference price is larger than the seller's indifference price. Secondly, indifference prices of large positions in derivatives exceed the Black-Scholes replication costs and tend to the maximum payoffs of the derivatives if the position sizes become very big. Therefore, a large trader might have an incentive to issue options if they are traded at Black-Scholes prices. Furthermore, he hedges option positions only partly if he has a negative price impact and thus exploits his ability to manipulate the option's payoff. For a positive price impact he overhedges the option position leading to an extra profit from the stock position exceeding a perfect hedge. Finally, a large trader's price impact induces a smile in his marginal indifference prices.
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