Abstract
The assumption of constant correlation between the underlyings cannot be satisfied in market. In this paper, we find the multi-asset option price intervals assuming the correlation lies within a given interval. First we transform this financial problem to a stochastic optimal control problem, then obtain options' maximum and minimum price models through dynamic programming principle. We further discuss how to solve the Black-Scholes-Barenblatt equation through finite difference schemes. We conclude this paper by giving its applications in multi asset option market, comparing with the analytical solutions, and giving a method how to identify arbitrage opportunity in multi-asset option markets.
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