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

Re: One-liner questions of a numerical kind

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

Re: One-liner questions of a numerical kind

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

Re: One-liner questions of a numerical kind

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

Re: Trump -- the last 100 days

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.  :D
by Alan
August 7th, 2019, 3:50 am
Forum: Student Forum
Topic: Vol and T coupling in Derivative Price
Replies: 6
Views: 284

Re: Vol and T coupling in Derivative Price

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

Re: Vol and T coupling in Derivative Price

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...
by Alan
August 3rd, 2019, 7:15 pm
Forum: General Forum
Topic: Circular barrier
Replies: 14
Views: 443

Re: Circular barrier

With the exception of horizontal lines and maybe parabolas, I believe everything else requires numerics. 
by Alan
August 2nd, 2019, 7:46 pm
Forum: General Forum
Topic: Circular barrier
Replies: 14
Views: 443

Re: Circular barrier

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

Re: Stuff that Physics_(+ &)_mathematicS can explain

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...
by Alan
August 1st, 2019, 2:48 pm
Forum: General Forum
Topic: Circular barrier
Replies: 14
Views: 443

Re: Circular barrier

To me, a circle requires two dimensions. What are the two dimensions? 
by Alan
July 30th, 2019, 11:31 pm
Forum: Student Forum
Topic: Derivation for two independent brownian motions
Replies: 4
Views: 341

Re: Derivation for two independent brownian motions

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. 
by Alan
July 30th, 2019, 11:24 pm
Forum: Numerical Methods Forum
Topic: New Approximation to the Normal Distribution Quantile Function
Replies: 14
Views: 36241

Re: New Approximation to the Normal Distribution Quantile Function

The late Graeme West, Wilmott mag, Fig. 2 quoting an alogorithm of Hart (accurate to machine double precision everywhere). 
by Alan
July 30th, 2019, 4:34 am
Forum: Numerical Methods Forum
Topic: Explicit Formula for computing IV
Replies: 15
Views: 562

Re: Explicit Formula for computing IV

Please justify the need for extreme speed. What is the application?
by Alan
July 26th, 2019, 5:56 pm
Forum: Student Forum
Topic: Black-Scholes from Random Walk Derivation - Issue
Replies: 8
Views: 341

Re: Black-Scholes from Random Walk Derivation - Issue

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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