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by hgeorgako
March 12th, 2008, 6:54 pm
Forum: Numerical Methods Forum
Topic: Richardson extrapolated penalty method
Replies: 7
Views: 59137

Richardson extrapolated penalty method

Mustached Bouzouki Player ---> The great Greek bouzouki master Zabetas Haven't tried the Richardson extrapolation penalty method though.
by hgeorgako
February 5th, 2008, 2:27 pm
Forum: Numerical Methods Forum
Topic: Finite Difference error
Replies: 27
Views: 63776

Finite Difference error

<t>For Calls: V[0] = 0V[Smax] = Smax * exp(b-r)*(T-t) - K*exp(-r * (T-t))For Puts:V[0] = K * exp(-r * (T-t))V[Smax] = 0------------------------------Can you folks comment on the type of grid refinement that should be employed if the Spot price is far removed from the strike price.A simple log transf...
by hgeorgako
February 1st, 2008, 9:43 pm
Forum: Numerical Methods Forum
Topic: Finite Difference error
Replies: 27
Views: 63776

Finite Difference error

<t>No dividends. American case. Dirichlet boundary conditions at S = 0 and Smax = ATMF * exp(sigma^2/2 * T + 6*sigma*sqrt(T)) ; ATMF = So*e^(r-q)T - FV of DivsExtreme case of 1000 * 1000 grid ( Call = 61.30295, Put = 7.17124) Actual values should be closer to 61.09639 and 6.94701 (computed using ano...
by hgeorgako
February 1st, 2008, 7:13 pm
Forum: Numerical Methods Forum
Topic: Finite Difference error
Replies: 27
Views: 63776

Finite Difference error

<t>Even for European i see a discrepancy. It doesn't have to do with the free boundary condition. I would also like to stay away from logS space since i'm dealing with discrete dividends and the transformation messes me up. So let's say i price a European way ITM call, put with high vol in S-space u...
by hgeorgako
January 30th, 2008, 9:52 pm
Forum: Numerical Methods Forum
Topic: Finite Difference error
Replies: 27
Views: 63776

Finite Difference error

<t>Here's a simple American Put and Call.S=100, K=50, sigma=70%, r=5%, b=5%, T=1.81My grid is an implicit method with respect to the actual S and not log(S)Question: How far should i extend Smax and how many asset steps should i use? I seem to be pricing all other options correctly except for deep I...
by hgeorgako
May 8th, 2007, 7:23 pm
Forum: Trading Forum
Topic: Best Model for trading Vanilla Options
Replies: 2
Views: 73228

Best Model for trading Vanilla Options

<t>I know there is no single "Best" model out there but bear with me for the sake of argument. Let's assume you want a model that will give you correct prices and correct hedge parameters. What are the model choices that you folks recommend for a real trading + market making environment. My question...
by hgeorgako
March 23rd, 2007, 1:13 pm
Forum: Numerical Methods Forum
Topic: C++/C# code for inverting an N * N matrix
Replies: 11
Views: 85280

C++/C# code for inverting an N * N matrix

Is there anything similar out there for C# (free libraries).Ones i found are (not extensive): http://www.dnanalytics.net/doku.php http://www.cdrnet.net/projects/nmath/
by hgeorgako
February 27th, 2007, 8:20 pm
Forum: Numerical Methods Forum
Topic: Exonential Fitting Scheme
Replies: 10
Views: 84693

Exonential Fitting Scheme

In Duffy (Financial Instrument Pricing using C++) pg 205, the exponentially fitted parameter gamma replaces the sigma(x,t) function (diffusion term) of the PDE. (fully implicit in the time direction).Can this method be applied to a Crank Nicolson scheme with the same effectiveness?
by hgeorgako
February 22nd, 2007, 3:00 am
Forum: Technical Forum
Topic: volatility adjustments for long dated, discrete dividends
Replies: 6
Views: 79877

volatility adjustments for long dated, discrete dividends

<t>From what i understand thus far, it is best not to adjust volatility but rather propagate the actual stock price process down your grid and when you encounter and ex-div date, simply decrease the stock price at that point by the dividend amount. S - D. Subsequently, apply the continuity condition...
by hgeorgako
February 13th, 2007, 1:41 pm
Forum: Numerical Methods Forum
Topic: FEM Scheme for American Options with Discrete Divs?
Replies: 8
Views: 80050

FEM Scheme for American Options with Discrete Divs?

Very interesting indeed. Thank you all for your comments.I'm sure glad I switched from Engineering into Finance. No standard way of doing anything and no "correct" answers for the most part!Good times...
by hgeorgako
February 12th, 2007, 8:46 pm
Forum: Numerical Methods Forum
Topic: FEM Scheme for American Options with Discrete Divs?
Replies: 8
Views: 80050

FEM Scheme for American Options with Discrete Divs?

<t>Thanks Cuch.I have a MSc in Electrical Engineering and Financial Math. I figure that if I spend a few weeks with the relevant books and papers underneath my pillow at night, i should be able to come up with something reasonable. When you say 3 seconds, do you mean 3 seconds for a single option?! ...
by hgeorgako
February 12th, 2007, 3:05 pm
Forum: Numerical Methods Forum
Topic: FEM Scheme for American Options with Discrete Divs?
Replies: 8
Views: 80050

FEM Scheme for American Options with Discrete Divs?

<r>I have managed to successfully incorporate a discrete dividend stream into an FDM Crank-Nicolson-based pricing DLL (thanks in part to help from a few people on this forum.)I get "decent" prices for American options of various maturities. With multiple dividends and longer maturities, though, my a...
by hgeorgako
January 22nd, 2007, 12:02 am
Forum: Numerical Methods Forum
Topic: Can someone spot the error in my ways? (Crank Nicolson with Discrete Dividends)
Replies: 8
Views: 83011

Can someone spot the error in my ways? (Crank Nicolson with Discrete Dividends)

<t>Thank you gentlemen for the input.So how does the algorithm that Wilmott describes work then? (Volume 2. page 909)Does the S(i) he refers to have different values prior to the td date and similarly after the td date? That's what outrun's method seems to suggest.If i have multiple dividends then m...
by hgeorgako
January 20th, 2007, 6:41 pm
Forum: Numerical Methods Forum
Topic: Can someone spot the error in my ways? (Crank Nicolson with Discrete Dividends)
Replies: 8
Views: 83011

Can someone spot the error in my ways? (Crank Nicolson with Discrete Dividends)

<t>Wilmott Volume 2: pg 909Haug's latest: pg 343I am given a table with ex-div dates and discrete div amounts.I go through my initial loop and i set my dt = T/(N - numberOfDividends) initially.This pretty much gives me a larger time span to work with. I subsequently make the dividend dates a grid po...
by hgeorgako
January 19th, 2007, 11:07 pm
Forum: Numerical Methods Forum
Topic: Can someone spot the error in my ways? (Crank Nicolson with Discrete Dividends)
Replies: 8
Views: 83011

Can someone spot the error in my ways? (Crank Nicolson with Discrete Dividends)

<t>The following fragment of the C# code determines whether i have hit a discrete dividend point (td date falls on a time grid point) and then proceeds to implement the Wilmott suggested jump condition.Since it is an American type option, i include the comparison of max(Vold, payoff)Am i using the r...
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