问题如下：
Derive expressions for the payoffs from a:
a.Long position in an average price call and short position in an average price put
b.A long position in an average strike call and short position in an average strike put, and
c.A long position in a plain vanilla European call and short position in a plain vanilla European put.
d.All options have the same strike price and time to maturity. Use the results to derive a relationship between the prices of the six options you have considered.
选项：
解释：
A long average price call gives a payoff of max( Save - K, 0). A short average price put gives a payoff of -max( K - Save ,0). The payoff in (a) is therefore always Save - K whether Save > K or Save <=K. Similarly, the payoff in (b) is always ST - Save and the payoff in (c) is always ST - K. From this, it follows that:
( c1 - p1) + ( c2- p2) = ( c - p)
where c1 and p1 are the prices of the average price call and put, c2 and p2 are the prices of the average strike call and put, and c and p are the prices of the plain vanilla call and put.
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