  We price a contingent claim liability using the utility indifference
argument. We consider an agent with exponential utility, who invests in a stock
and a money market account with the goal of maximizing the utility of his
investment at the final time T in the presence of positive proportional
transaction cost in two cases with and without a contingent claim liability.
Using the computations from the heuristic argument in Whalley & Wilmott we
provide a rigorous derivation of the asymptotic expansion of the value function
in powers of the transaction cost parameter around the known value function for
the case of zero transaction cost in both cases with and without a contingent
claim liability. Additionally, using utility indifference method we derive an
asymptotic expansion of the price of the contingent claim liability. In both
cases, we also obtain a "nearly optimal" strategy, whose expected utility
asymptotically matches the leading terms of the value function.
