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September 30th, 2002, 9:26 pm
Forum: Student Forum
Topic: Functional analysis
Replies: 27
Views: 191218

### Functional analysis

<t>This is not related to functional analysis but since we have a good membership on this thread i'll post it here.I wonder if there is a nice formula for the expectationE(exp[(aX+b)]N(uX+v)N(mX+n))where X is a standard normal variable and N(x) the cumulative normal distribution function. I was able...
September 26th, 2002, 12:18 pm
Forum: Student Forum
Topic: Functional analysis
Replies: 27
Views: 191218

### Functional analysis

<t>Paul,I can cope with neither long, nor hard nor ugly.It is due to my limited intellect.Steno,Which book on Functional Analysis do you like?I am thinking of a text that goes beyond the introductory level but is still not specialized. An unrelated question:Does anyone know how to contact Farshid Ja...
September 25th, 2002, 10:51 pm
Forum: Student Forum
Topic: Functional analysis
Replies: 27
Views: 191218

### Functional analysis

Aaron,It seems that you have a very bad impression of functional analysis.I always thought of it as being very elegant certainly more so than stochastic process theory.Dunford and Schwartz, Linear Operators is one of the best references.
September 24th, 2002, 2:02 am
Forum: Student Forum
Topic: Functional analysis
Replies: 27
Views: 191218

### Functional analysis

<t>A modern approach to real analysis notes that the family of integrable functions is a vector space and the expectation f -> E(f) a linear functional on this space. It is continuous in a suitable norm.If you do not want this you have moved back into the last century and the realm of ugly definitio...
September 24th, 2002, 1:06 am
Forum: Technical Forum
Topic: Ito's quotient rule
Replies: 16
Views: 190626

### Ito's quotient rule

<t>If you are dealing with Ito processesdX(t)=mu_X(t)dt+sigma_X(t)dW(t)dY(t)=mu_Y(t)dt+sigma_Y(t)dW(t)and want dQ(t), where Q(t)=X(t)/Y(t) simply take logarithms Z(t)=log(Q(t))=log(X(t))-log(Y(t)) and find dZ(t) (easily) and from thisreconstruct dQ(t)=d exp(Z(t)) also easily. In the frequent case wh...
September 22nd, 2002, 11:07 am
Forum: Technical Forum
Topic: Pricing of the Inverse Floater
Replies: 1
Views: 189514

### Pricing of the Inverse Floater

<r>On my website <URL url="http://martingale.berlios.de/Martingale.html">http://martingale.berlios.de/Martingale.html</URL> I have a paper on the implementation of the Libor Market Model (LMM) which follows ideas ofB. Coffey and J. Schoenmakers. It can be downloaded ("LiborProcessPS"). There is a di...
August 12th, 2002, 8:51 pm
Forum: Numerical Methods Forum
Topic: Quasi Monte Carlo : On Dimensionality
Replies: 42
Views: 178600

### Quasi Monte Carlo : On Dimensionality

<t>Johnny,I do not know which mixing theorem you are referring to.Hadi,You don't have to rely on the Koksma-Hlawka inequality. For example [NDR, p21, theorem 2.13] will do it too for all continuous functions on the unit cubeQ=I^n, I=[0,1]. Here [NDR] is the following reference: Niederreiter, Random ...
August 12th, 2002, 10:06 am
Forum: Numerical Methods Forum
Topic: Quasi Monte Carlo : On Dimensionality
Replies: 42
Views: 178600

### Quasi Monte Carlo : On Dimensionality

<t>Greetings,A while ago I posted a report of simulations comparing Monte Carlo to Quasi Monte Carlo. Dostojewski noticed that the Sobol generator did not perform to expectation. I looked at the code and found a coding mistake.This is fixed now and has been tested. So here is the report again with i...
August 8th, 2002, 2:54 pm
Forum: Numerical Methods Forum
Topic: Benefits of MC method compared to PDE for equity options
Replies: 16
Views: 191311

### Benefits of MC method compared to PDE for equity options

<t>I always test the model on known analytic formulas (caplets for example).This will show you if your code is set up correctly.From theory you know that Monte Carlo will converge to the proper expectation and your question is now how close your particular result is.For this you study the standard d...
August 8th, 2002, 2:47 pm
Forum: Technical Forum
Topic: Yet another model for American options ?
Replies: 29
Views: 191277

### Yet another model for American options ?

<t>I don't know of any on line documentation.Kushner's book is overkill since it deals with stochastic control problems whereas early exercise is an optimal stopping problem which is much simpler. If I get around to it I'll write up a tex file.Meanwhile I'd try a web search +"optimal stopping" +"Mar...
August 7th, 2002, 5:47 pm
Forum: Technical Forum
Topic: Yet another model for American options ?
Replies: 29
Views: 191277

### Yet another model for American options ?

<r>Do you have any benchmarks to compare your least squares Monte Carlo prices against? I find it hard to believe that something like that should work very well but I have never tried it or compared against benchmarks.Basically at each step you want to compute complicated iterated conditional expect...
August 7th, 2002, 5:12 pm
Forum: Numerical Methods Forum
Topic: Benefits of MC method compared to PDE for equity options
Replies: 16
Views: 191311

### Benefits of MC method compared to PDE for equity options

<r>There are a couple of things in favour of Monte Carlo:1. It is a very general method, works for all asset price dynamics.Differential equations can only be used under restricted conditions on the asset price dynamics:dS(t)=mu(t,S(t))dt + sigma(t,S(t))dW(t)where the drift mu=mu(t,s) and volatility...
August 7th, 2002, 3:33 pm
Forum: Technical Forum
Topic: Option Hedging
Replies: 26
Views: 192700

### Option Hedging

<t>I worked tirelessly again for the common good and would like to upload the findings as a file hedge.zip.The paper suggests weights for a hedge which is rebalanced at a finite number of times rather than continously. In this case it is of advantageto modify the classical deltas. The basic formulas...
May 21st, 2002, 4:24 pm
Forum: Technical Forum
Topic: Option Hedging
Replies: 26
Views: 192700

### Option Hedging

Yes please, but how do I turn on private messaging?
May 21st, 2002, 3:59 pm
Forum: Technical Forum
Topic: Option Hedging
Replies: 26
Views: 192700

### Option Hedging

I don't know how to activate or use private messaging but will try t o find out about it.

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