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发帖数: 1741 | 1 1. Replicate an “Easygoing Double No-Touch Option” given four barriers A,
B, C, and D.
----------------|-----------------|-------------|------------|--------------
----|--------->
A B S(now) C
D
An Easygoing Double No-Touch knocks out after the second barrier is touched
or crossed. You may use barrier and/or touch options. S(now) is the current
spot. State your assumptions.
2. Replicate a Double No Touch using a portfolio of double knock out calls
and puts. State your assumptions.
3. In Quantville the weather follows a peculiar pattern described in the
table below:
Tomorrow's Weather
Sunny Cloudy Windy Rainy
Today's Weather Sunny 40% 40% 20% 0%
Cloudy 20% 20% 30% 30%
Windy 25% 25% 25% 25%
Rainy 10% 40% 20% 30%
The highlight row means: If today’s weather is rainy, tomorrow there is a
10% chance of being sunny, 40% chance of being cloudy, 20% chance of being
windy, and 30% chance of being rainy.
What percent of days in Quantville are sunny, cloudy, windy, and rainy?
4. Simulate the following situation. Attach the code as part of your
submission.
At a post office, customers enter a single line waiting to be served by
any one of two clerks. Every minute there is a 60% chance that a new
customer arrives. If there is no one in line and a server is free, the
customer does not wait to be served. When a customer is being served there
is a 25% chance every minute that they complete their business and leave.
When the clerk is free he will take the next customer in line, in the order
that they arrived. Every minute, there is a 5% chance that a person
standing in line will give up and leave. The post office is always open (24
/7/365).
Note: For simplicity you can assume customers will always arrive at the
beginning of the minute and if they leave they do so at the end of the
minute.
a) What is the average amount of time a customer spends in the post office (
including those not served)?
b) What percentage of customers leave without being served?
c) What percentage of time are the clerks idle? | w**********5
发帖数: 1741 | | T*****u
发帖数: 7103 | 3 they really like markov ah |
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