请求高人指点一道题目，不胜感激

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在一份看涨期权合约签订后，这个合约的结果是一个零和对策，即当期权买者的收益（或者损失）为N元时，期权写者的损失（或收益）恰好为N元，从而他们的总收益为0.给的这个事实后，为什么合约的双方都预期自己有一个正的收益而签订合约？请解释。


是不是
说看涨期权的买方是预期标的证券价格上涨的，卖方式预期看涨期权标的证券价格下降。由经济人理性假设，双方预期都为正才能签订合约。
我有点不清楚，请高人指点，谢谢

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关键词：求高人指点 高人指点 不胜感激 请高人指点 经济人理性 请求 题目 指点 高人 感激

这是因为期权交易双方在对待未来证券价格上升和下降的预期不同，所以分别进入多头和空头

In theory the price of the options is determined by no arbitrage argument under some assumptions... under those assumptions the options can be replicated by  a self-financing strategy by buying/selling the underlying security together with buying/selling bond... so there is no economic difference if you buy or sell options as u can square your position by the self-financing strategy...

This is a very good question. Although it looks simple at first, but accurate understanding requires a little bit thought. I think you mentioned several truths (facts), such as 1. it's zero sum game, one's gain is the other side's loss and your explanation makes perfect sense. 2. Investors are rational, and they all have their own positive expectation.

However, when you put them together, you feel very confused. There are several aspects that can help you better understand this. First, when two sides enter a contract at time t. There are several reasons for this: a) the buyer or seller could have different view on the underlying price movement from time t to maturity T; b) the buyer or seller could enter the contract at time t because they want to realize their gains or loss based on their view at time t; c) the buyer or seller just have to take some of the positions maybe due to other hedging purpose.  Second, although the whole option game is zero sum, but it doesn't mean that whenever there are two people enter one contract, acting as the buyer or seller respectively, one gain is the other's loss. The zero sum game is considered for the overall market (all the option players at any time t).

Hope this helps.