A setup in which a large trader has sold a certain number of American-type derivatives is considered. The large trader’s trades are assumed to have an impact on prices so that he may be tempted to minimize the payoff of the derivative by manipulating the underlying asset.
However, the option holders have the right to exercise the option, turning the pricing problem in a two-player stochastic game. It is shown that the solution of this optimization problem can be described as the solution of a double obstacle variational inequality and the optimal strategy for the large trader and the optimal exercise time for the option holder are obtained. The fact that price manipulation may force the option holders to exercise before the maturity implies that regulators must monitor stock prices and options sellers activity continuously. Our theory gives us the precise time at which a market manipulator will start manipulating prices. We also calculate a maximum number of options that can be sold so that no manipulation strategies are possible in terms of quantities such as the bid-ask spread and the price impact factor. We conclude with a sensitivity analysis in which we compare the timing and size of manipulation interventions by the large trader as well as the optimal exercise region for the options holders for different levels of liquidity.