急！！求救！几题期权问题

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实在不知上哪找人问，就在这发帖了
烦请各路高手帮小弟我解答呗
万分感激

1. You have three European3-month XYZ call exercise prices 100, 120 and 130. The call are at $8, 5 and 3,respectively. Do you see any arbitrage opportunity?
这题没给risk-free rate, 我估计是要找出什麽样的risk-free rate可以有arbitrage opportunity.
我用boundary condition计算，但算出来挺怪的啊，r到了 700％，有木有问题啊？

2. You have XYZ trading at $42. European 6-month 40 calls and puts are traded at:

                      call        put

bid/ ask   5/ 5.5      2.75/ 3.25

Assume the risk free rate is 0%, do you see any arbitrage opportunity?

我想到Put-Call Parity。但真心不懂bid /ask 要怎麽选。

bid是我卖的价格？ask是我买的价格？

这样算出来没有arbitrage opportunity但Put-Call Parity却不成立啊！

(我有查到有人把bid/ask取平均当成option value，真是这样？)

求解惑

3. A stock priced $40, could either appreciate or depreciate by 10% . Two period and one month for each period. The risk-free rate is 2% per annum. Shout at time 1. What is the value of the shouting?

没有给原本的exercise price要怎求啊？

4. The value of a projct is $100 and cost at t=0 is $104. The project value follows a binomial model: go up to $180 or down to $60. The government posts a guarantee of $78 at time 1. What is the value of the option? RRR=20% and risk-free rate=8% per period.

ZF保证那边是指把＄60替换成＄78？

5. The value of a company is 1000 and expected to go up by 20% or go down by 10%. The company has a two-year zero-coupon debt with face value of 500. The risk-free rate is 4%. The cost of equity is 14%. What is the yield on the debt?

完全不懂

{:3_60:}

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关键词：权问题 respectively Opportunity GOVERNMENT appreciate

1. Buy 1 of x and z, sell 2.2 of y, calculate payoff of every possible price range. This question has nothing to do with interest rate.

2. I think bid is for selling, ask is for buying. Why do you wanna put this into put-call parity, which is just for theoretical price under BS? Personally, I don't find any solution. Maybe I misunderstand the question.

3.4.5. Neither do I... But I think every question is to calculate the fair value...

同求解答。

1. Construct a butterfly. Option is a convex function of S or K, so if this is violated, there is arbitrage opportunity.

2. Put-Call parity is model free, as long as it is a European option. If Put-Call parity is violated, there must be arbitrage opportunity. See one of the proof method of P-C parity (construct two portfolios, show if not equal there will be arbitrage)

3. Just assume it is ATM, stike=40.

4.  78 is the call's strike. Your option's underlying is the project's value which can go down to 60 but will be floored at 78

5.  Your company's equity is an option on your company's value. If your company's value after 2years is more than 500 which is the debt you should pay, your equity's value will be the value of firm-500, while if the value is under 500, you are unable to pay the debt and the equity price will be floored at zero. So find the present value of this option and subtract it from the current firm's value, the remaining value would be debt's present value (price). Then you can calc the yield from the price.

Chemist_MZ 发表于 2015-3-7 20:43
1. Construct a butterfly. Option is a convex function of S or K, so if this is violated, there is ar ...

thx a lot