346 reputation
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bio website kal@kalx.net
location New York, NY
age
visits member for 3 years, 3 months
seen Jun 8 '12 at 16:10

May
11
comment How to get greeks using Monte-Carlo for arbitrary option?
I beleive AD refers to techniques for automatically generating functions for the derivatives. Dual numbers don't do that for you.
May
9
comment Is the binomial model wrong?
Relax, I'm a friendly troll. :-) Here is another one that I don't have a good answer for. Let $F = fe^{-\sigma^2t/2 + \sigma B_t}$. The (forward) value of a log contract is $v = E[\log F]$ and so $dv/df = 1/f$. No surprise. Now consider the payof $v = E[\log F/f]$. Now $dv/df = 0$! It is easy to see what is going on in this example, but how do you know with more complicated parameterizations when the correct delta is not the derivative of value with respect to underlying? Hope you find this puzzle more interesting.
May
8
awarded  Student
May
8
comment Is the binomial model wrong?
But in a binomial model where $s$ can go to $S^-$ or $S^+$ the option value is $v = ((S^+ - Rs)V(S^-) + (Rs - S^-)V(S^+)/R(S^+ - S^-)$ and $dv/ds = (V(S^+) - V(S^-))/(S^+ - S^-)$. I have to confess I am trolling a little here. See kalx.net/ftapd.pdf for the explanation. Also note that $d(Rv)/dR = s(V^+ - V^-)/(S^+ - S^-)$ is the dollar delta in both models.
May
8
awarded  Editor
May
8
revised Is the binomial model wrong?
edited body
May
8
asked Is the binomial model wrong?
May
8
answered How to get greeks using Monte-Carlo for arbitrary option?
May
7
comment How to get greeks using Monte-Carlo for arbitrary option?
You are reading it wrong. Not all samples need to remain in memory. It is not mathematically equivalent to finite differences, you seem to be completely missing the point of dual numbers. You have the source code, let me know if you need help applying it to a non-trivial estimator. Monte Carlo aside, dual numbers allow you to calculate derivatives down to machine precision.
Apr
27
awarded  Yearling
Apr
27
awarded  Teacher
Apr
27
answered How to get greeks using Monte-Carlo for arbitrary option?
Apr
18
answered Formal proof for risk-neutral pricing formula
Apr
4
answered Paradoxes in quantitative finance
Apr
4
answered What are the limitations of brownian motion in finance?
Mar
31
answered Why does the VIX index have *any* correlation to the market?
Mar
31
answered Fundamental Theorem of Asset Pricing (FTAP)