SERVING THE QUANTITATIVE FINANCE COMMUNITY

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February 19th, 2019, 2:21 pm
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 336
Views: 21076

### Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

I did not read the paper but usually when someone says that it means that once you have trained the neural network it you want the implied volatility for  T and K and given model parameters it will provide you a value in a time 10000 faster that it would take to compute price with the same parameter...
January 14th, 2019, 2:25 pm
Forum: Brainteaser Forum
Topic: Catch my error
Replies: 3
Views: 3016

### Re: Catch my error

I will try: with CLT you can say that $\frac{ X_N - N \mu }{ \sigma \sqrt{N}}$ tend in law to a normal distribution $\cal{N} (0, 1)$ not that $X_N$ tend in law to  $\cal{N}$ $(N \mu, \sigma \sqrt{N})$.
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January 20th, 2016, 7:39 am
Forum: Student Forum
Topic: Quanto adjustment and Monte-Carlo simulation
Replies: 1
Views: 1713

### Quanto adjustment and Monte-Carlo simulation

<t>If S(t) is price in domestic currency then I expect that a quanto option will pay (S(t) - K )^+ N / X_0 in foreign currency where X_0 is a constant exchange rate.As far as I undertand your payof (S(t) /X(t) - K)^+ is a compo option in foreign currency, but you are doing your simulation under risk...
October 30th, 2015, 9:21 am
Forum: Numerical Methods Forum
Topic: Barrier option with continuous monitoring solved by finite difference
Replies: 42
Views: 37644

### Barrier option with continuous monitoring solved by finite difference

<t>Usualy people want to use CN as it is second order with only 1 trigiagonal system while Richardson need 3 inversion for the same supposed second order of convergence. Again if you want to price product with event in most generality you will make an approximationwhen something happen. In case of b...
October 29th, 2015, 2:38 pm
Forum: Numerical Methods Forum
Topic: Barrier option with continuous monitoring solved by finite difference
Replies: 42
Views: 37644

### Barrier option with continuous monitoring solved by finite difference

<t>QuoteOriginally posted by: CrimsonKodousually a couple of rannacher steps is enough to get rid of the CN oscillations no ?Hum, if Rannacher steps (i.e. fully implicit) is used to dampen high frequencies components coming from non smoothness in the payoff we can expect to apply it every timewe hav...
June 25th, 2015, 6:50 am
Forum: Technical Forum
Topic: Pricing FX Binary Options
Replies: 4
Views: 3003

### Pricing FX Binary Options

Are you almost sure? :)With X_T = EURUSD and expectation on EUR measure that is the price of a digital on EURUSD quanto in EUR and you must have quanto adjustment.
February 13th, 2015, 11:40 am
Forum: General Forum
Topic: fast calculation of BS implied volatility
Replies: 8
Views: 4313

### fast calculation of BS implied volatility

February 13th, 2015, 7:18 am
Forum: General Forum
Topic: Prize for solving the Financial Paradox
Replies: 36
Views: 8344

### Prize for solving the Financial Paradox

<t>Not a numerical example with figures properly fitting your way. You must write price of all securities involved (F1, F2, F3, F3',...) at time t when you set up your portfolio, then write rebalancing at time t+dt with new prices watever they are.By the way your first attempt was static arbitrage, ...
February 11th, 2015, 8:31 am
Forum: General Forum
Topic: Prize for solving the Financial Paradox
Replies: 36
Views: 8344

### Prize for solving the Financial Paradox

<t>Static arbitrage is set up strategy at t_0 which give you positive value today and zero value at time T WHATEVER happen."If min(Sp_T) < S_T < max(Sp_T) then it is possible to make S_T = Sp_T by choosing T_3.If S_T is not in this range..."is different it is : at time T sometime it is possible but ...
February 10th, 2015, 11:11 am
Forum: General Forum
Topic: Prize for solving the Financial Paradox
Replies: 36
Views: 8344

### Prize for solving the Financial Paradox

"If min(Sp_T) < S_T < max(Sp_T) then it is possible to make S_T = Sp_T by choosing T_3.If S_T is not in this range..."OK. You can't set up static arbitrage here which show S'_0 <= S_0.So you try dynamic one. In this case you must look the concept of autofinancing.
February 9th, 2015, 8:33 am
Forum: General Forum
Topic: Prize for solving the Financial Paradox
Replies: 36
Views: 8344

### Prize for solving the Financial Paradox

<t>I won't discuss the first part to show S_0<S'_0 as it is the one where everyone agree.You can use a second F'_3 if you want and define the ratio with F_2 as S''. Can you elaborate your proof on the second part? I did not understand what come after "Price of portfolio at t_0 is 0.5*S'_0 + 0.5*S''_...
February 6th, 2015, 8:48 am
Forum: General Forum
Topic: Prize for solving the Financial Paradox
Replies: 36
Views: 8344

### Prize for solving the Financial Paradox

<t>" I have described you such strategy and showed that it allows arbitrage if S'0!=S0. "No you didn't: you just have make the same (siegel paradox) MISTAKE again!Take one currency, whatever you want . Price of F_1, F_2, F_3 (with your definition of F_3 product) in this currency at any time t. Defin...
February 4th, 2015, 10:20 pm
Forum: General Forum
Topic: Prize for solving the Financial Paradox
Replies: 36
Views: 8344

### Prize for solving the Financial Paradox

<t>This is my last try Sergei, I predicted you what happen now(no proud for this): You are sure you are right and even when you say "'I'm trying to find a mistake" in fact you think : "I am right, they are all wrong and i am not paranoid and even paranoid can have all world against them when they ar...
February 4th, 2015, 12:04 pm
Forum: General Forum
Topic: Prize for solving the Financial Paradox
Replies: 36
Views: 8344

### Prize for solving the Financial Paradox

<t>To see it you need not just saying "otherwise arbitrage opportunity exist". You must set up the arbitrage strategy. Can you show us the strategy which allow to make sure profit if S'0 != S0?In fact S0<=S'0. If you make a simplification of your case by : F1 pays 1 at time T1 and no interest rate b...
February 3rd, 2015, 1:27 pm
Forum: General Forum
Topic: Prize for solving the Financial Paradox
Replies: 36
Views: 8344

### Prize for solving the Financial Paradox

<r>May be you must talk with Sambian (<URL url="http://www.nuclearphynance.com/Show%20Post.aspx?PostIDKey=162316&PageIndex=1"><LINK_TEXT text="http://www.nuclearphynance.com/Show%20P ... ageIndex=1">http://www.nuclearphynance.com/Show%20Post.aspx?PostIDKey=162316&PageIndex=1</LINK_TEXT></URL...
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