求教HULL 里面关于B-S 一道题目

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12.12 Assume that a non-dividend-paying stock has an expected return of U and a volatility of Q, an innovative financial institution has just announced that it will trade a derivative that pays off a dollar amount equal to 1/T* ln(ST/S0) at time T. the variables S0 and ST denote the value of the stock price at time zero and time T

A. Describe the payoff from this derivative.

B. use the risk-neutral valuation to calculate the price of the derivative at time zero.

不太明白第二步求的是derivative 的价格，用分布得到的期望只是其增长率，怎么才是它的价格，我看了答案里有道题和它很象，题目里的return 是 ln(ST)， 这个在算的时候就是把增长率的期望乘上时间因素就是答案了，不是很清楚，望高人指点一下。

[此贴子已经被作者于2007-9-5 12:31:30编辑过]

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关键词：hull B-S hul Institution Derivative 题目 求教 hull

你怎么知道他要用BS的？

题目是否抄全了？Pay off scheme不是很清楚啊。

题目说的很清楚，用risk neutral valuation to value the derivative.
Risk-neutral valuation 通常分三布：
1. Assume that the expected return from the underlying asset is the risk-free interest rate, i (ie, assume mu = r)
2. Calculate the expected payoff from the derivative.
3. Discount the expected payoff at the risk-free interest rate.
需要注意的是，risk-neutral valuation只是一个工具来解BS方程。它的结构不仅在risk-neutral世界里适用，在实际世界里也适用。

能不能告诉我，在什么点，pay什么价格吗？

是什么类型的Option？

能不能具体点？

以下是引用stevensym在2007-9-6 9:21:00的发言：

能不能告诉我，在什么点，pay什么价格吗？

是什么类型的Option？

能不能具体点？

不是option

到期payoff就是1/T * log(S_T / S_0)

好比forward，到期payoff就是S_T - F_0

God, a dollar amount equal to...就是美元价值等于。。。。。

我还以为，pays a dollar。。。。。

另外，出题者为什么要强调是BS模型呢？BS有其他解释吗？

[此贴子已经被作者于2007-9-6 15:12:20编辑过]

The problem itself doesn't mention BS model.

It just asks you to use risk-neutral valuation to price this derivative.

Remember,risk-neutral valuation is a very important tool. The BS model can be solved by risk-neutral valuation.

以下是引用qdzhang在2007-9-6 22:43:00的发言：

Remember,risk-neutral valuation is a very important tool. The BS model can be solved by risk-neutral valuation.

faint to death...

Black-Scholes "IS" risk neutral pricing. That's why they were awarded Nobel prize, not for option pricing, but for risk neutral pricing.

Or do you have your way to solve it using risk-averse or risk-seeking valuation? You'll be nominated.

[此贴子已经被作者于2007-9-7 1:50:26编辑过]

以下是引用irvingy在2007-9-7 1:42:00的发言：

faint to death...

Black-Scholes "IS" risk neutral pricing. That's why they were awarded Nobel prize, not for option pricing, but for risk neutral pricing.

Or do you have your way to solve it using risk-averse or risk-seeking valuation? You'll be nominated.

Did I say BS model can be solved using risk-averse or risk-seeking valuation?

The BS model's contribution is not for option pricing, but for its partial-derivative equation. The pricing formulation generated by risk-neutral valuation satisfies the BS equation.

[此贴子已经被作者于2007-9-7 5:03:28编辑过]

以下是引用qdzhang在2007-9-7 5:02:00的发言：

Did I say BS model can be solved using risk-averse or risk-seeking valuation?

No, you just said "risk-neutral valuation is a very important tool. The BS model can be solved by risk-neutral valuation".

This sounds like "The BS model can also be solved by some other tools, although maybe less important than risk-neutral valuation".

So I wonder if you can solve it by risk-averse or risk-seeking. Looks like you can't, or you have risk-fourth something to show us.

Admit now you don't really understand what you're talking about, okay? Better than being pointed out in an interview, as that would be a slap in your face.