- Yesterday, 7:29 pm
- Forum: Numerical Methods Forum
- Topic: One-liner questions of a numerical kind
- Replies:
**31** - Views:
**1392**

The PDE for this greek does indeed contain terms in the bond price. The far-field BC sounds reasonable. At the near field the Feller condition for the 'greek PDE' is always satisfied which means we have a drift PDE at that boundary. It must be solved numerically (upwinding) in the worst case. I get...

- Yesterday, 2:17 pm
- Forum: Numerical Methods Forum
- Topic: One-liner questions of a numerical kind
- Replies:
**31** - Views:
**1392**

The nice thing about NDSolve (in Mathematica) is that it automatically adopts a high order inward pointing derivative at boundaries, which then couples the system smoothly to the behavior of the solution at the interior points.

[Erroneous second comment deleted]

[Erroneous second comment deleted]

- August 21st, 2019, 8:11 pm
- Forum: Numerical Methods Forum
- Topic: One-liner questions of a numerical kind
- Replies:
**31** - Views:
**1392**

Consider the well-known PDE for the bind price [$]B[$] in the CIR model.Then differentiate the PDE with respect to [$]r[$] to get a PDE in [$]\frac{\partial B}{\partial r}[$] (this is a bespoke CSE equation). Some points: 1. The Fichera/Feller conditions implies that no BC is given at [$]r= 0[$] a...

- August 12th, 2019, 8:00 pm
- Forum: Politics Forum
- Topic: Trump -- the last 100 days
- Replies:
**2970** - Views:
**86732**

Here's a theory. Like Hannibal Lecter in Silence of the Lamb's, they simply found a dead man with Epstein's face. He, instead, is on his way to parts unknown. When you have zillions, anything is possible, including bribing the coroner.

- August 7th, 2019, 3:50 am
- Forum: Student Forum
- Topic: Vol and T coupling in Derivative Price
- Replies:
**6** - Views:
**284**

I will make a guess. If the payoffs are level invariant as in your examples, and you have 'continuous monitoring', and no cost-of-carry parameters, then what you want might follow simply from dimensional analysis of the value function. After all, you need dimensionless factors. But once you introduc...

- August 6th, 2019, 7:07 pm
- Forum: Student Forum
- Topic: Vol and T coupling in Derivative Price
- Replies:
**6** - Views:
**284**

If the derivative value is just the expectation of an arbitrary terminal payoff, then 'yes'. That follows from writing the value as an integral over a normal density with variance [$]\sigma^2 T[$] (times the payoff, of course). In other words, it's exactly the same normal density you would use to va...

- August 3rd, 2019, 7:15 pm
- Forum: General Forum
- Topic: Circular barrier
- Replies:
**14** - Views:
**443**

With the exception of horizontal lines and maybe parabolas, I believe everything else requires numerics.

- August 2nd, 2019, 7:46 pm
- Forum: General Forum
- Topic: Circular barrier
- Replies:
**14** - Views:
**443**

I think GBM can hit every point on that circle! -- well, possibly excepting one, which doesn't matter. DavidJN's cite may be spot-on, although I haven't looked at that paper in years. Off-hand, the horizontal line through A identifies two key times (t1,t2), and the GBM's location at t1 splits the p...

- August 1st, 2019, 3:11 pm
- Forum: Off Topic
- Topic: Stuff that Physics_(+ &)_mathematicS can explain
- Replies:
**26** - Views:
**5047**

I am enjoying Hossenfelder's book. It's a good read for the beach, but maybe not that interesting to non-physicists (or non-ex-physicists). I'm about half-way through and she's bemoaning her seemingly endless search for the next temporary research position. So, it's a nice mix of general critique, i...

- August 1st, 2019, 2:48 pm
- Forum: General Forum
- Topic: Circular barrier
- Replies:
**14** - Views:
**443**

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:
**36241**

- July 30th, 2019, 11:31 pm
- Forum: Student Forum
- Topic: Derivation for two independent brownian motions
- Replies:
**4** - Views:
**341**

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:
**36241**

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:
**562**

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:
**341**

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...

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