Option Pricing with Fourier Transform and Exponential Lévy Models [pdf]
1–10 of 20 posts
Re: Option Pricing with Fourier Transform and Exponential Lévy Models [pdf]
#2I'm not sure whose voting up such a technical paper. I could understand if the subject was control theory or robotics, but economics with engineering-level math seems out of most of our purviews.
I'm not complaining - I'm happy to see more math on HN. I'm just wondering about HN's demographics.
Re: Option Pricing with Fourier Transform and Exponential Lévy Models [pdf]
#3I'm not sure whose voting up such a technical paper. I could understand if the subject was control theory or robotics, but economics with engineering-level math seems out of most of our purviews. I'm not complaining - I'm happy to see more math on HN. I'm just wondering about HN's demographics.
Especially since the result is not new (it was written in 2004). Even though the topic is within my interests I'm confused that this is on the front page of HN.
Re: Option Pricing with Fourier Transform and Exponential Lévy Models [pdf]
#4I'm not sure whose voting up such a technical paper. I could understand if the subject was control theory or robotics, but economics with engineering-level math seems out of most of our purviews. I'm not complaining - I'm happy to see more math on HN. I'm just wondering about HN's demographics.
There are a lot of engineers here who would have ended up in finance (possibly as quants), myself included. This sort of thing is right up our street.
Re: Option Pricing with Fourier Transform and Exponential Lévy Models [pdf]
#5I'm not sure whose voting up such a technical paper. I could understand if the subject was control theory or robotics, but economics with engineering-level math seems out of most of our purviews. I'm not complaining - I'm happy to see more math on HN. I'm just wondering about HN's demographics.
Especially since the result is not new (it was written in 2004). Even though the topic is within my interests I'm confused that this is on the front page of HN.
I guess it's interesting to see an alternative to Black Scholes. Fourier transform (FFT) is a common topic in advanced algos.
Re: Option Pricing with Fourier Transform and Exponential Lévy Models [pdf]
#6I'm not sure whose voting up such a technical paper. I could understand if the subject was control theory or robotics, but economics with engineering-level math seems out of most of our purviews. I'm not complaining - I'm happy to see more math on HN. I'm just wondering about HN's demographics.
Folks interested in this, but finding it too long, so waiting for someone to summarize/explain maybe :)
Re: Option Pricing with Fourier Transform and Exponential Lévy Models [pdf]
#7Being a geophysicist, I got sucked into this by the mention of the Fourier Transform.
I found this paper to be very wordy and littered with mathematics that was at times impenetrable. Thank God for the Appendix to help decipher some of the non-geophysical industry symbology. I'm familiar with the derivations of the equations used but it's been several decades since I had taken differential equations so there is a lot left for me to absorb.
I understand this is an old paper but I am cursed with an eye for detail and some of the little things ended up grabbing my attention more than they should have. I found myself wondering if, prior to publication, anyone had bothered reading the full text with an eye for identifying simple spelling errors or whether they had used a spell checker or other tool to maintain consistency of spelling of uncommon words or terms. I think not. Just in my own reading these things popped out at me:
p. 92 in the sentence just after Figure 6.1 sock is used instead of stock.
p. 153 just after Eq 9.8 is defined Meron is used instead of Merton.
p. 166 the page has all but one mention of Black-Sholes spelled as Black-Shoels.
p. 244 the third sentence uses Bronwian instead of Brownian.
Also, they made a typical math funny on pages 190-191. On p.190 the second sentence reads:
>Because the CF of VG process cannot be obtained by simply substituting 0 α = in (11.23), we need to do this step-by-step.
So now they promise me some interesting step-by-step derivations in their algebra. Instead I get the standard upper-level math statement on p. 191 after Eq. 11.28:
>After tedious algebra:
You're almost to the appendix and you find the first mention that some of the math got hairy. Fun stuff.
I expected the last page to read "This page intentionally left blank."
Re: Option Pricing with Fourier Transform and Exponential Lévy Models [pdf]
#8From the abstract
>Merton jump-diffusion model (1976) which is an exponential Lévy model with finite arrival rate of jumps,
This is funny because my graduate thesis is about models based on Hawkes processes, that is, jump with a path-dependent and self-exciting intensity process. Instead of taking the arrival time of jumps (often the parameter lambda) to be constant, in a Hawkes process a jump increases the probability of another jump (positive feedback), leading to clusters of jumps we often see in crises.
I love how this paper might seem "magic" and voodoo and most importantly "true" to people who don't know much about mathematical finance. The point is that the models here are most likely wrong and have GLARING flaws in them, yet are still used to price REAL things in REAL life. All models are wrong, some are less wrong than others. The point is, how wrong do our models have to be before we get some really bad consequences (2008 financial crisis, anyone?)
P.S. Please rewrite this in LaTeX, posting a 250 page document written in Word makes me 90% less likely to read it (compared to something written in LaTeX)
Re: Option Pricing with Fourier Transform and Exponential Lévy Models [pdf]
#9>> The answer is that these three models are special cases of
more general exponential Lévy models. Options cannot be priced with general exponential Lévy models using the traditional approach of the use of the risk-neutral
density of the terminal stock price because it is not available.
Does this mean there is no hedging strategy in these general exponential models? My understanding is the Black-Scholes gives the price, such that if the price was different, there would be an arbitrage strategy (under some assumptions on the variance). And this arbitrage strategy is used for hedging.
Re: Option Pricing with Fourier Transform and Exponential Lévy Models [pdf]
#10Being a geophysicist, I got sucked into this by the mention of the Fourier Transform. I found this paper to be very wordy and littered with mathematics that was at times impenetrable. Thank God for the Appendix to help decipher some of the non-geophysical industry symbology. I'm familiar with the derivations of the equations used but it's been several decades since I had taken differential equations so there is a lot…
>I found this paper to be very wordy and littered with mathematics that was at times impenetrable.
don't understand this comment. if someone asked you to read a QFT paper would you claim it were "littered" with impenetrable mathematics? or vice versa: if a cond mat physicist read a geophysics paper would they be justified in claiming the same? you're reading a paper outside of your domain of expertise; expect to be challenged.