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March 31st, 2014, 7:57 am
Forum: Student Forum
Topic: VaR Question
Replies: 7
Views: 5173

### VaR Question

<t>I don't think ppauper's answer is in the right area, X is not normally distributed in this problem it is a mixture of 2 normals. The inverse of the VaR function is:f(x) = 0.991 * cum.norm.dist(x,mean=0,std=1) + 0.001 * cum.norm.dist(x,mean=-10,std=1) So do a root find on:g(x) = 0.991 * cum.norm.d...
June 8th, 2012, 9:05 am
Forum: Student Forum
Topic: Infinitely Divisible Density Continuous?
Replies: 6
Views: 12215

### Infinitely Divisible Density Continuous?

Poisson distribution is infinitely divisible and is a discrete distribution (Poisson process is a Levy process), there are several others (negative binomial for example) so your intuition is off the mark.
February 23rd, 2012, 10:36 am
Forum: Student Forum
Topic: iid process with infinite variance - can I scale VaR with sqrt(t)?
Replies: 6
Views: 14981

### iid process with infinite variance - can I scale VaR with sqrt(t)?

No problem
February 23rd, 2012, 9:42 am
Forum: Student Forum
Topic: iid process with infinite variance - can I scale VaR with sqrt(t)?
Replies: 6
Views: 14981

### iid process with infinite variance - can I scale VaR with sqrt(t)?

<t>I think you have everything you need then. The Cauchy distribution is the building block for the Cauchy process, it is an iid and infinite variance process. By the argument below, you cannot scale VaR by sqrt(t). You have a proof from this that it's not valid to do this in general because you hav...
February 21st, 2012, 8:40 am
Forum: Student Forum
Topic: iid process with infinite variance - can I scale VaR with sqrt(t)?
Replies: 6
Views: 14981

### iid process with infinite variance - can I scale VaR with sqrt(t)?

<t>Someone should check I haven't screwed something up here, but if we're assuming iid and infinite variance we can pick a distribution, the Cauchy distribution, that satisfies these conditions and see what happens. This distribution has pdf:Let's choose x0 as 0 over 1 day. This is a stable distribu...
February 3rd, 2012, 12:27 pm
Forum: Student Forum
Topic: Wiener process
Replies: 2
Views: 14256

### Wiener process

I would guess it's Bachelier:Louis Bachelier
October 29th, 2011, 6:22 am
Forum: Student Forum
Topic: Modified Bessel Functions
Replies: 3
Views: 17081

### Modified Bessel Functions

<t>The Generalized Hyperbolic Distribution has one of the Modified Bessel functions in it's pdf. It's quite a flexible distribution can can be used in risk management as something that can capture a few features (fat tails, skewness) that the normal distribution will not and it contain several other...
September 9th, 2011, 11:48 am
Forum: Numerical Methods Forum
Topic: Portfolio Optimization
Replies: 2
Views: 20390

### Portfolio Optimization

To be honest, when an optimizer is used I think most of them use a commercial system - MSCI-Barra's factor model and optimizer (and to a lesser extent its competitors like APT, Axioma, Northfield). How reliable these systems can be I couldn't tell you.
September 7th, 2011, 7:18 am
Forum: Student Forum
Topic: option hedging remark*
Replies: 62
Views: 22698

### option hedging remark*

<t>QuoteOriginally posted by: listchocolatemoney, I think that along with perfectly hedged BS-type solution there always exists another one. This is C ( t , x ) = 0. No one either buyer or seller of an option can lose anything and hence it is also no-arbitrage price.I know I asked you this already, ...
September 4th, 2011, 3:14 pm
Forum: Student Forum
Topic: option hedging remark*
Replies: 62
Views: 22698

### option hedging remark*

<t>QuoteOriginally posted by: list3) The value of our portfolio at time T is either 100 if S(T)=200 (133 1/3 - 33 1/3 = 100) or 0 if S(T)=50 (33 1/3 - 33 1/3 = 0). These are the same values are the payoff of the option./// up to this everything is perfect ///4) No other combination of the stock and ...
September 2nd, 2011, 6:20 pm
Forum: Student Forum
Topic: option hedging remark*
Replies: 62
Views: 22698

### option hedging remark*

<t>QuoteOriginally posted by: listQuoteOriginally posted by: frenchXQuoteOriginally posted by: daveangelWe have tried ignoring him - he keeps popping up and writing the same drivel week in, week out... pathetic.I agree that this is problematic. What I would do to stop him is to point explicitely a m...
September 2nd, 2011, 9:59 am
Forum: Student Forum
Topic: Estimate parameters in SDEs
Replies: 10
Views: 18345

### Estimate parameters in SDEs

<t>Ok, to see it simulate 100, 1000, 10000, 100000 points on the following process 10000 times: And set beta to something close to 1 (0.99, 0.999, 0.9999 or even 1). The estimate the value of beta by MLE and plot a histogram of these estimates for each combination of points and pre-chosen value of b...
September 2nd, 2011, 9:03 am
Forum: Student Forum
Topic: Estimate parameters in SDEs
Replies: 10
Views: 18345

### Estimate parameters in SDEs

<t>Also worth bearing in mind that when the mean reversion is very weak (process is close to having a unit root or actually has one) then the MLE estimate becomes very biased, you'll need to be aware of this when getting/interpreting your results (it can make thing look like they mean revert a lot m...
September 1st, 2011, 6:40 pm
Forum: Student Forum
Topic: option hedging remark*
Replies: 62
Views: 22698

### option hedging remark*

<t>QuoteOriginally posted by: listQuoteOriginally posted by: ACDLast try (I swear, I know that you can get this, I believe in you!):Do you understand the following things:1) What arbitrage is?The definition of the option price based on : call option price is C ( t , x ) = 0 for scenarios from { S ( ...
September 1st, 2011, 5:55 pm
Forum: Student Forum
Topic: option hedging remark*
Replies: 62
Views: 22698

### option hedging remark*

<t>Last try (I swear, I know that you can get this, I believe in you!):Do you understand the following things:1) What arbitrage is?2) If you can construct a portfolio that replicate the payoff of a derivate in *any* future scenario and this portfolio is unique (i.e. no arbitrage is possible) then th...

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