- August 1st, 2019, 2:48 pm
- Forum: General Forum
- Topic: Circular barrier
- Replies:
**14** - Views:
**588**

To me, a circle requires two dimensions. What are the two dimensions?

- July 31st, 2019, 3:14 am
- Forum: Numerical Methods Forum
- Topic: New Approximation to the Normal Distribution Quantile Function
- Replies:
**14** - Views:
**36418**

- July 30th, 2019, 11:31 pm
- Forum: Student Forum
- Topic: Derivation for two independent brownian motions
- Replies:
**4** - Views:
**464**

Thanks.

No, first, I said "n is large but not infinite", so the puzzle is to provide an asymptotic formula that depends upon n. Keep thinking!

Second, if n were infinite, the expected max is [$]+\infty[$].

Hint: start from bearish's comment, generalize it, and start calculating.

No, first, I said "n is large but not infinite", so the puzzle is to provide an asymptotic formula that depends upon n. Keep thinking!

Second, if n were infinite, the expected max is [$]+\infty[$].

Hint: start from bearish's comment, generalize it, and start calculating.

- July 30th, 2019, 11:24 pm
- Forum: Numerical Methods Forum
- Topic: New Approximation to the Normal Distribution Quantile Function
- Replies:
**14** - Views:
**36418**

The late Graeme West, Wilmott mag, Fig. 2 quoting an alogorithm of Hart (accurate to machine double precision everywhere).

- July 30th, 2019, 4:34 am
- Forum: Numerical Methods Forum
- Topic: Explicit Formula for computing IV
- Replies:
**15** - Views:
**758**

Please justify the need for extreme speed. What is the application?

- July 26th, 2019, 5:56 pm
- Forum: Student Forum
- Topic: Black-Scholes from Random Walk Derivation - Issue
- Replies:
**8** - Views:
**462**

Or, the cookbook recipe to working with stochastic differential equations is the following multiplication table: [$]dt \times dt = dt \times dW_t = dW_t \times dt = 0 [$] [$]dW_t \times dW_t = dt[$] (All higher powers are zero). After all, to drive a car, you don't have to be a mechanic. Of course...

- July 26th, 2019, 5:48 pm
- Forum: Numerical Methods Forum
- Topic: High Accuracy Greeks computation under trinomial model
- Replies:
**12** - Views:
**588**

If you set up the option value pde problem using x = log S with solution [$]f(x,t)[$], you can differentiate it to get the pde for [$]g(x,t) = f_x[$]. Then perhaps simply solve that second pde for [$]g[$] on a trinomial lattice, and convert to delta. You probably need two passes, the first to get t...

- July 26th, 2019, 4:01 am
- Forum: Numerical Methods Forum
- Topic: High Accuracy Greeks computation under trinomial model
- Replies:
**12** - Views:
**588**

If you set up the option value pde problem using x = log S with solution [$]f(x,t)[$], you can differentiate it to get the pde for [$]g(x,t) = f_x[$]. Then perhaps simply solve that second pde for [$]g[$] on a trinomial lattice, and convert to delta. You probably need two passes, the first to get th...

- July 24th, 2019, 12:57 am
- Forum: Technical Forum
- Topic: Why is Bellman Equation solved by backwards?
- Replies:
**14** - Views:
**846**

It's usually solved backwards because of the "principle of optimality", which you can google if you don't know it. The standard finance example is determining an optimal exercise strategy for an American-style put. It's day 1 and the put expires on day N. Whatever the "strategy" on day 1, it should ...

- July 22nd, 2019, 6:41 pm
- Forum: Technical Forum
- Topic: Why is Bellman Equation solved by backwards?
- Replies:
**14** - Views:
**846**

I cannot make a specific example, because I read that in a book.

page1 https://ibb.co/1fhhK2m

page2 https://ibb.co/3WW69NW

page3 https://ibb.co/Zfxt1Ty

I looked briefly. I think I was right: with stationary transition densities, it's a trivial relabeling: [$]n \rightarrow n' = N - n[$].

- July 22nd, 2019, 5:28 am
- Forum: Numerical Methods Forum
- Topic: Smoothing splines (clamped spline)
- Replies:
**22** - Views:
**969**

You could take a look at http://www.netlib.org/dierckx/. concur.f implements the clamped smoothing spline. Disclaimer: I haven’t used this library myself, but Dierckx’s book is quite good. Thank you -- it looks like Dierckx's book may indeed have what I am searching for -- ordered a decently priced...

- July 21st, 2019, 7:11 pm
- Forum: Technical Forum
- Topic: Why is Bellman Equation solved by backwards?
- Replies:
**14** - Views:
**846**

I will take a guess that it is a "trivial" rewrite. That is, if you a have a stationary PDE problem with a terminal condition at T, you can always trivially rewrite it with [$]\tau = T - t[$] and the terminal condition becomes an initial condition. Ditto for the Bellman problem.

- July 19th, 2019, 4:46 pm
- Forum: Numerical Methods Forum
- Topic: Smoothing splines (clamped spline)
- Replies:
**22** - Views:
**969**

For Alan specific problem with the smoothing parameter, the problem was already solved in Carl de Boor (1978), A Practical Guide to Splines (Chapter XIV). While it is solved with "natural" BC (allowing to have a tridiagonal matrix and adding 2 equations to the linear system), solving for your speci...

- July 18th, 2019, 5:30 pm
- Forum: Numerical Methods Forum
- Topic: Smoothing splines (clamped spline)
- Replies:
**22** - Views:
**969**

Thanks, guys but it looks like you are all citing either (i) cubic spline interpolation (the interpolant goes through the data points) or (ii) standard smoothing splines (Green & Silverman, for example, which have a so-called "natural" boundary condition [$]g''(a) = g''(b) = 0[$]). I am asking about...

- July 18th, 2019, 12:47 am
- Forum: Numerical Methods Forum
- Topic: Smoothing splines (clamped spline)
- Replies:
**22** - Views:
**969**

Hi Daniel, Thank you for the code. I haven't opened it yet. Let me know if I will find the solution to the following problem, which will answer your question. I want to find the piecewise cubic polynomial [$]g(t)[$] that solves the following problem: (*) minimize [$] \left( \sum_{i=1}^n \{ y_i - g(t...

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