Properties of Options on Several Underlying Assets
نویسندگان
چکیده
It is well-known that prices of options on one underlying asset decay with time and are convex in the underlying asset if the contract function is convex. Here, options on several underlying assets are studied and we prove that if the volatility matrix is independent of time, then the option prices decay with time if the contract function is convex. However, the option prices are no longer necessarily convex in the underlying assets. If a time dependent volatility is allowed we note that the option prices do not necessarily decay with time. Moreover, we show that even if the price processes are independent, convexity is preserved only for very special volatilities including price processes driven by a Geometric Brownian motion.
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