J*****n
发帖数: 4859 | 1 Say, I would like to price a barrier or Asian otions in Euro type.
If I choose to use MC simulating jump process to price it.
I am goint to generate path in this way.
First, I generate 1000 paths following GBM, then I generate 1000 paths
containing pure jumps.
Then I took the cross product, i.e. 1 mm path.
Then I use these 1mm path to price the options.
The question is what's the difference here if I generate 1mm paths directly?
Thank you. | x********o
发帖数: 519 | 2 I do not think this is good, but not very sure.
wait for someone else to give a reasonable explanation.
directly?
【在 J*****n 的大作中提到】
: Say, I would like to price a barrier or Asian otions in Euro type.
: If I choose to use MC simulating jump process to price it.
: I am goint to generate path in this way.
: First, I generate 1000 paths following GBM, then I generate 1000 paths
: containing pure jumps.
: Then I took the cross product, i.e. 1 mm path.
: Then I use these 1mm path to price the options.
: The question is what's the difference here if I generate 1mm paths directly?
: Thank you.
| w**********y
发帖数: 1691 | 3 I bet Compound Poisson should be general enough for your application.
1. Generate X_t, 0
2. Generate the Poisson Point process t_1, t_2,…t_k, which is the times
for jumps
3. Generate your jump size from a given distribution..
4. Modify your X_t..for t>=t1, Y_t = X_t + J1…until the last t_K
Glasserman’s book should have a clear step by step description.
When you move to the Levy process, it has two or three different simulation methods: one is truncated and approximate it using a compound poisson; another is based on the conditional distribution/transition density
One part of ViKtor (?) Todorov’s Ph.D. dissertation is about this.
Semimartigale is more complex.. |
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