Abstract
In this paper, we consider hedging and pricing of illiquid options on an untradable underlying asset, where an alternative instrument is used as a hedging instrument. We assume that the trade price of the hedging instrument is subject to market impacts caused by the hedger, as well as the liquidity costs paid as price spreads. This problem is important in trading illiquid options, since the price shifts together with the liquidity costs affect the hedging performance. We set the problem under a discrete time model, where the optimal hedging strategy is defined by the local risk minimization. We show algorithms to obtain the hedging strategy along with the option price by the perturbation method, and provide numerical examples. This model is useful since it can be used in estimation of the effect of both the market impacts and the liquidity costs on option prices.
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