问一道类似期权衍生品价格的题目

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MMC bank is offering a guarantee return product such that an investor invests N=$100,000 today will receive at the end of 6 months the principal N plus a return rate that is the greater of zero or 10% of the return (ST-S0)/S0 from S&P 500, assuming that the index St follows a lognormal process.

(a) Is this a good deal for the investor? i.e. Is today’s product value Vt(St,K) > $100,000?
(b) In order for this product to be priced fairly, what should be the percentage of the return offered in the product so that Vt~$100,000?
Assume that the riskfree rate is 1.73%, the average dividend yield on the index is 2.13%,and the volatility of the index is 21%.S&P 500 closed at St=1253 on 10/31/2011. (等于说S0 = 1253)


我觉得分成两部分，一部分是六个月后肯定得到的固定收益N，然后折算成present value，另一部分是面值 N/(10*S0)的期权，价值是max(0, ST-S0)，然后用
直接算出这一部分的现值。请问这样做对吗？

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关键词：衍生品 Volatility percentage lognormal PRINCIPAL percentage guarantee principal receive investor

我觉得应该没问题吧，就是相当于一个zero-coupon bill和N/(10S0)个执行价格为S0的call option

sounds fine to me.