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Jul
11
answered Estimate price movement per unit of volume for daily data
Jul
10
answered Do Bond Put Dates always fall on Coupon Dates (for non-zero coupon bonds). Calculation rules for Coupon Dates
May
18
comment Measuring co-movement at non-constant intervals
Well, really correlation has nothing to do with the data points coming from time series realizations. You may do better looking through the literature for the (numerous) treatments of cointegration.
May
10
comment How to get greeks using Monte-Carlo for arbitrary option?
For the curious, the "dual number" approach referenced here is an automatic differentiation package, where the bookkeeping mostly handled by C++ templates and extensions to the standard numeric types. Derivatives of transcendental functions are handled by automatic differentiation of the numerical analytic series approximations used to calculate function values. (Please correct any mistakes I have made in that)
May
7
comment How to get greeks using Monte-Carlo for arbitrary option?
I'll also note that, as @Dirk and I read the question, Alexey does not necessarily have the source code to the option pricer.
May
7
comment How to get greeks using Monte-Carlo for arbitrary option?
You're right, I now see it is not finite differences. I would find the simplicity of your example far more convincing if you demonstrated calculating, say, delta of an average strike option under the the Black-Scholes stochastic model. It seems to me the transcendental functions involved make this difficult even for vanilla options. Path dependencies will make the problem much worse.
May
7
comment Can American options with no dividends and zero risk-free rate be treated as European?
Technically, call options can be optimal to exercise early if $r<0$. $r$ rarely if ever goes sufficiently negative on its own, though.
May
4
answered Why use swap-rates in a yield curve?
Apr
27
comment What is an appropriate hedge ratio for hedging a credit instrument with equity of the same issuer?
You can get numbers from the classical Merton structural model using Bloomberg. In both theory and practice the hedge ratio is highly dependent on leverage so you will get results even poorer than the usual dismal ones for equity/credit if you do not take that into account.
Apr
27
comment How to get greeks using Monte-Carlo for arbitrary option?
A novel method. It appears mathematically equivalent to finite differences. Also worth noting is that all samples need to remain in memory, at least if I read this stuff right. It would be informative to see code applied to a nontrivial estimator function.
Apr
27
comment How to get greeks using Monte-Carlo for arbitrary option?
That vibrato Monte Carlo thesis is very interesting.
Apr
26
comment definition for “the viscosity” in financial market data series
You can measure whatever you want...there is no standard definition of viscosity in financial mathematics. Most stochastic modelers would take it to mean terms involving $\nabla^2 V$ in the associated Feynman-Kac PDE, which is clearly very different from the simple heuristics you have in mind here.
Apr
25
revised How to get greeks using Monte-Carlo for arbitrary option?
add not beng able to control $M$
Apr
24
answered How to get greeks using Monte-Carlo for arbitrary option?
Apr
20
comment application of lie groups in finance
Well, we do use $\mathbb{R}^n$ all the time.
Apr
20
comment Analytical relationship between a covariance matrix and cross-sectional dispersion
Interesting question. I wonder if there really exists a convenient expression for it. I would say you should try playing with the 3-variable version in Mathematica and work to $N$ variables only if you succeed in getting an acceptably simple expression in 3 variables. You may need to switch to variance, and use convecity corrections to adapt that to standard deviation.
Apr
12
revised calculating arbitrage-free ranges based off outright, spread, and fly prices
add flag
Apr
11
comment A few questions about signs of the Greek letters
Well consider just the zero-vol value of an in-the-money option. Here $C=e^{-rT}(S_0 e^{rT} - K)^+$ or $S_0 - e^{-rT}K$ and so the rho is simply $T e^{-rT} K$, very positive. Basically, the increase in forward value has overwhelmed the decrease due to discounting. Pathological setting of parameters may give negative rho in some cases, but this is the gist of why rho of calls is generally positive.
Apr
10
answered calculating arbitrage-free ranges based off outright, spread, and fly prices
Apr
10
answered A few questions about signs of the Greek letters