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Theoretical physics phd student.


Nov
17
comment How to price zero coupon bonds with the Monte Carlo method?
As a consistency check you could benchmark your generated paths against the exact solution. The error in the Euler scheme can grow quite quick for large discretizations, so it's good to know how well the distribution of the final points of the paths matches the exact distribution.
Nov
17
comment float64 to store price data: is precision sufficient?
Also, like rhaskett said, what you described in Option 1 is essentially how floating point numbers are stored.
Nov
17
comment float64 to store price data: is precision sufficient?
No, you're correct. NumPy does not support NaN for int types. Only for floats. Note that this is not some universal property of NaN's -- it was a choice made by the authors from NumPy not to support NaN for int.
Oct
26
comment Incompatibility of Lognormal Forward Model (LMM\BGM) and Lognormal Swap Model
Yea, you got it right. Swap rates and forward rates depend non-linearly on each other, so it would be quite weird to assume that both follow a lognormal distribution. If you try to derive $dS$ from (11) using (10), then there is no way you can end up with (12).
Oct
25
revised General way to solve Partial differential equation using Feynman kac representation
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Oct
25
comment General way to solve Partial differential equation using Feynman kac representation
That's a general method to make the original PDE easier. Just substitute $F = e^{rT} G$ into the PDE and you will get a new PDE in terms of $G$. This PDE is the same as the old one, but without the $rF$ term. So we then perform the same manipulations for $G$, obtain the final result and then transform the final expression back to $F$.
Oct
25
answered General way to solve Partial differential equation using Feynman kac representation
Oct
13
revised Proof oriented introductory text?
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Oct
13
answered Proof oriented introductory text?
Oct
12
answered What are the textbooks used to teach Quantitative Trading at universities?
Oct
9
revised Show that $E[B_t|\mathscr{F}_s] = B_s$
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Oct
8
revised Show that $E[B_t|\mathscr{F}_s] = B_s$
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Oct
8
comment Show that $E[B_t|\mathscr{F}_s] = B_s$
It's better to work on the higher power first. So first eliminate the quadratic term in $W_t$, as this will generate more linear terms in $W_t$. However, if you just want to compute the term you mentioned, then: $E[tW_t|F_s] = t E[(W_t - W_s) + W_s|F_s] = t E[(W_t - W_s)|F_s] + tE[W_s|F_s] = t W_s$. This term alone is of course not a martingale.
Oct
8
comment Show that $E[B_t|\mathscr{F}_s] = B_s$
Not sure I follow, so please correct me if I'm wrong. But I think that $E[C]$ can again be be completely rewritten in terms of $E[(W_t - W_s)^2|\mathcal{F}_s]$, $E[(W_t - W_s)|\mathcal{F}_s]$ and terms that only depend on $W_s$. And these are all known.
Oct
8
revised Show that $E[B_t|\mathscr{F}_s] = B_s$
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Oct
7
answered Show that $E[B_t|\mathscr{F}_s] = B_s$
Sep
24
awarded  Autobiographer
Dec
5
awarded  Yearling
May
21
awarded  Enthusiast
May
13
comment What are the best Journals & Conferences in Quantitative Finance?
FYI vixra.org is considered a "crackpot site" when it comes to the physics and mathematics articles. It is mostly filled with articles that didn't make it onto arxiv.org. So beware..