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by Mars
January 5th, 2021, 4:45 pm
Forum: General Forum
Topic: Proof of the risk-neutral assumption
Replies: 70
Views: 14276

Re: Proof of the risk-neutral assumption

" easier than a sledgehammer approach" Really?  Second order term in time of exp(A+B)t ,  exp(At) and exp(Bt) are quite easy to calculate using known Taylor expansion of exponentials , then second order polynomial multiplication (non commutative one) show that exponential equality implies...
by Mars
December 21st, 2020, 4:48 pm
Forum: General Forum
Topic: Proof of the risk-neutral assumption
Replies: 70
Views: 14276

Re: Proof of the risk-neutral assumption

(3) is not a premiss. As I said B&S model => PDE => expectation with a specific measure coming from Feynmann-Kac theorem => (3) is true with the expectation using the same measure. And in that model there are risk premiums. Thanks. Are there any simpler ways to derive the Formula direct from th...
by Mars
December 21st, 2020, 4:26 pm
Forum: General Forum
Topic: Proof of the risk-neutral assumption
Replies: 70
Views: 14276

Re: Proof of the risk-neutral assumption

(3) is not a premiss. As I said B&S model => PDE => expectation with a specific measure coming from Feynmann-Kac theorem => (3) is true with the expectation using the same measure.

And in that model there are risk premiums.
by Mars
December 21st, 2020, 3:42 pm
Forum: General Forum
Topic: Proof of the risk-neutral assumption
Replies: 70
Views: 14276

Re: Proof of the risk-neutral assumption

When they solve the PDE the equation (4) only stand when [$]E[ \ ][$] means expectation with a probability measure where the spot log normal diffusion as a drift coefficient [$]r S_t dt[$], i.e. what is called risk neutral measure. So the BS Formula is true only when there is no risk premium? False...
by Mars
December 21st, 2020, 3:30 pm
Forum: General Forum
Topic: Proof of the risk-neutral assumption
Replies: 70
Views: 14276

Re: Proof of the risk-neutral assumption

When they solve the PDE the equation (4) only stand when [$]E[ \ ][$]
means expectation with a probability measure where the spot log normal diffusion as a drift coefficient [$]r S_t dt[$], i.e. what is called risk neutral measure.
by Mars
December 21st, 2020, 1:54 pm
Forum: General Forum
Topic: Proof of the risk-neutral assumption
Replies: 70
Views: 14276

Re: Proof of the risk-neutral assumption

"Why do people think it is generally true?"

Why do you think that people think it is generally true?
by Mars
October 26th, 2020, 10:28 am
Forum: Numerical Methods Forum
Topic: alternative to cubic splines
Replies: 21
Views: 7232

Re: alternative to cubic splines

Could someone suggest interpolation algorithm alternative to cubic splines? Interpolated function has to be continuous, with continuous first differential and perfect fit with input data.
What about Stineman interpolation ( https://pages.uoregon.edu/dgavin/software/stineman.pdf )
by Mars
October 2nd, 2020, 9:59 am
Forum: Trading Forum
Topic: Cleanest expression of a single currency?
Replies: 5
Views: 9146

Re: Cleanest expression of a single currency?

Currencies are expressed as pairs, eg AUD/USD. However if I wanted to express the value of the (somewhat nonsensical) AUD alone (or changes in its value), how might we attempt/approximate this? I realise that this is an intractable problem and also is very much based on what objective function you ...
by Mars
October 2nd, 2020, 8:27 am
Forum: Numerical Methods Forum
Topic: Monotone Schemes: what are they and why are they good?
Replies: 78
Views: 17817

Re: Monotone Schemes: what are they and why are they good?

I do not agree, if  [$] \lambda_i[$] are thre eigenvalues of [$]A[$] then [$]\frac{1 - \lambda_i}{1 + \lambda_i}[$] are the eigenvalues of  [$](I_d + \tau A)^{-1}(I_d - \tau A)[$].   Let us suppose that you missed a [$]\tau[$] here. So there exists eigenvectors [$] v^i [$] such that [$]v^i(\tau) = ...
by Mars
October 1st, 2020, 7:49 am
Forum: Numerical Methods Forum
Topic: Monotone Schemes: what are they and why are they good?
Replies: 78
Views: 17817

Re: Monotone Schemes: what are they and why are they good?

When I look in the Lawson and Morris article you provide, just below eq 1.7 there is a discussion where the oscillation is linked to the negative (close to -1) eigenvalues when timestep is too large. The problem studied is heat equation, without first order derivatives the coefficient below and abo...
by Mars
September 30th, 2020, 8:36 am
Forum: Numerical Methods Forum
Topic: Monotone Schemes: what are they and why are they good?
Replies: 78
Views: 17817

Re: Monotone Schemes: what are they and why are they good?

Am I missing something or in Crank Nicolson oscillations come when H (or A in the Daniel post) got real but NEGATIVE eigenvalues (for the high frequency eigenvectors)? No, complex eigenvalues! See Strang and Fix 1974, Lawson and Morris 1978 for a full answer. There was a time (until I came along) t...
by Mars
September 29th, 2020, 2:38 pm
Forum: Numerical Methods Forum
Topic: Monotone Schemes: what are they and why are they good?
Replies: 78
Views: 17817

Re: Monotone Schemes: what are they and why are they good?

Am I missing something or in Crank Nicolson oscillations come when H (or A in the Daniel post) got real but NEGATIVE eigenvalues (for the high frequency eigenvectors)?
by Mars
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: 341
Views: 72683

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...
by Mars
January 14th, 2019, 2:25 pm
Forum: Brainteaser Forum
Topic: Catch my error
Replies: 3
Views: 9199

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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by Mars
January 20th, 2016, 7:39 am
Forum: Student Forum
Topic: Quanto adjustment and Monte-Carlo simulation
Replies: 1
Views: 2157

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...
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