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FRM^®知识点：Trading and Correlation

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发布时间：2022-01-12 16:07

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means trading assets

whose prices are determined at least

in part by the comovement

of one or more asset in time.

修改后_9.jpg

Quanto option

an option that allows a domestic investor to exchange his potential option payoff in a foreign currency back into his home currency at a fixed exchange rate.

———————A quanto option therefore protects an investor against currency risk.

Example:

An American believes the Nikkei will increase, but she is worried about a decreasing yen, which would reduce or eliminate her profits from the Nikkei call option

The investor can buy a quanto call on the Nikkei, with the yen payoff being converted into dollars at a fixed (usually the post) exchange rate.

emmmm……上面的例子想表达的是：

假如有一个美国人想投资日本的股指，他认为日本的股指会涨，于是他买了一个标的为日本股指的看涨期权，但是担心日元贬值，进行汇率交换的时候要用更多的日元去换美元。所以就有了Quanto option的作用，它可以在一开始就规定好汇率的换算，由此来避免日元贬值带来的损失。

那么根据这个例子，我们还需要探讨一下这个汇率联动期权卖出方的情况。有两件事情不确定。

The financial institution that sells a quanto call does not know two things:

1.How deep in the money the call will be,i.e.,which yen amount has to be converted into dollars.

Nikkei 会涨到什么程度？

2.The exchange rate at option maturity at which the stochastic yen payoff will be converted into dollars.

到期时，日元对美元的汇率是多少？

The correlation between 1 and 2 influences the quanto call option price.

If the correlation is positive, an increasing Nikkei will also mean an increasing yen. That is favorable for the call seller. She has to settle the payoff, but only needs a small yen amount to achieve the dollar payment.

如果ρ>0，Nikkei将会上涨，期权行权，日元升值，对于卖出汇率联动期权的机构来说，用更少的日元换取美元，是一件好事，因此该期权应该卖的更便宜一些。

Therefore, the more positive the correlation coefficient, the lower the price for the quanto option.

If the correlation coefficient is negative, the opposite applies: if the Nikkei increases, the yen decreases in value. Therefore, more yen are needed to meet the dollar payment

如果ρ<0，Nikkei上涨，期权依旧行权，而日元发生贬值的情况，对于卖出汇率联动期权的机构来说，用更多的日元换取美元，并不是一件好事，因此该期权卖的更贵一点。

As a consequence, the lower the correlation coefficient, the more expensive the quanto option.

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