提前赎回条款，二叉树怎么处理？

Chemist_MZ 发表于 2012-1-8 09:10
Binormil tree is also useful when applied to path dependent option. e.g. Asian option, barrier o ...

So you mean you don't need to consider every path when you price Asia options, barrier options and reverse convertible?

You want be careful when you say binomial tree can pricing so many path dependent option.
......You can use it to price different options does not mean it is good in terms of 1. accuracy 2. time consuming 3. generic.
Path dependent option requires large quantity of paths in order to get the pricing correct, which is the limitation of binomial tree.
In addition, if one to take volatility smile into account, it is very limited. Perhaps you can use Derman's local vol model back 13 years ago......  Not sure if Goldman ever used it after Dupire model......

spruceyang 发表于 2012-1-8 10:57
You must be careful when you say binomial tree can pricing so many path dependent option.
...... ...

Yes we don't need. This is not created by myself but the othe scholars. See the thesis:Market Pricing of Exotic Structured Products: The Case of Multi-Asset Barrier Reverse Convertibles in Switzerland, Option Pricing in a Multi-Asset, Complete Market Economy and PRICING AND HEDGING AMERICAN BARRIER OPTIONS BY A MODIFIED BINOMIAL METHOD. You can also see some recent theses of Asian option pricing. Tree technology has developed very quickly. Far surpass the original model by CRR. Accuracy and time consuming is quite amazing, especially the time is its adventage. I have writtern a code for high-demensional tree models which can price muti-asset options, which is quite efficient. Of course sometimes the convergence speed and as you say the volatility smile is a big problem. Fortunately much work have been done on these topics. Honestly, when I search for the thesis, I am shocked by the quick development and the maturity of the tree mathod. I like it. Despite of is limitation, its advantage is quite obvious.

Chemist_MZ 发表于 2012-1-8 11:13
You can see some recent theses of Asian option pricing. Tree technology has developed very quick ...

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CRR model is applied for pricing American option. In this field, you can google Longstaff's least squire method....
The binomial tree itself is slower than the MC, the high dimensional tree will be slower than simulation with correlation matrix. For more and more, I suggest you google wiki.

I just would like to give you my understanding. If you still like to use the binomial tree, I will suggest you read Derman's technical report for all non-American type options.   

spruceyang 发表于 2012-1-8 11:31
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CRR model is applied for pricing American option. In this field, you can google Longstaff' ...

And by the way, I mention Derman's paper cause I think he has some method to do path calculations. Can't remember the details of that part......

spruceyang 发表于 2012-1-8 11:36
And by the way, I mention Derman's paper cause I think he has some method to do path calculations. ...

See Option Pricing in a Multi-Asset, Complete Market Economy. It solves the problem of the correlation matrix. It is a very new mathod which have not been widely applied. MC and tree they all have their advantages. They should be applied case by case. I do not mean that we should stick to what mathod. I also use MC for other path dependent options. In my opinion I just think that the tree mathod have a very prosperous future. By the way I just mean that the tree approach has greatly surpass the CRR model, not talking about CRR. Thank you for your recommendation, I will search for this paper right away. MC is efficient, and I also use it. Tree is more attractive to me. Both of them have their own advantages. I don't mean which one is better. The one can solve the problem more efficiently and effectively is better.

Best wishes~

Regarding tree approaches, there are only binomial trees or tirnomial trees available.

You don't use CRR so you use trinomial trees?

Regarding MC method, I guess it is not suitable for the hit-and-exercise problem. In american option valuation, MC method estimate a best stopping time and modify the paths, note it is only one instead of many or infinite.

Chemist_MZ 发表于 2012-1-7 15:27
我自己想出来这么处理，不知道对不对，从最后一步开始往前rolling，只要股价高于触发条件的，都用提前赎回的 ...

very smart that you could think it out yourself...