Valuation of futures options with initial margin requirements and daily price limit

The paper presents a valuation model of futures options trading at exchanges with initial margin requirements and daily price limit, and this result gives an academic guidance to design trading rules at exchanges. Unlike the leading work of Black, certain trading rules are considered so as to be more fit for practical futures markets. The paper prices futures options with initial margin requirements and daily price limit by duplicating them with the help of the theory of backward stochastic differential equations (BSDEs, for short). Furthermore, an explicit expression of the price of the call (or the put) futures option is given and also is shown to be the unique solution of the associated nonlinear partial differential equation.