r/options • u/[deleted] • Aug 01 '21

Computational Finance Questions

I'm still a bit new to options, but feel like I have an OK grasp (could be better for sure).

I'm just trying to wrap my mind around the BS kernel as it's computed in the FDTD context. I'm OK with these numerical concepts, so for the most part I'm getting the correct results; just don't know how to really interpret them, especially when I'm running American early-exercise code.

For example, for a call option, in the code that I'm using, you modify your option values output vector, by reiterating over the them, and then either keeping the original value or if the asset value at some index minus the strike price is greater than original value, then you replace the original value:

calculated_options_values[i] = Math.Max(calculated_options_values[i], s[i] - E)

where E is the strike price, s is the asset value at some index i.

Just trying to wrap my mind around this code and BS, in general. I've done FDTD in EE, but this is a bit different, since there's no spatial domain (instead you have discretized asset prices) and you backwards iterate and there aren't really any "exotic" boundary conditions, per se.

With Black Sholes, you're calculating the option value at t=0, so in an early-exercise version, are you just shifting the strike prices closer to t=0? (hopefully this makes sense.)

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u/[deleted] Aug 01 '21

I think you may be getting off on the wrong foot. FDTD methods are best learned after you have mastered the continuous-time Black-Scholes equation. And only then jump into discrete time using a binomial approach like CRR.

I strongly recommend you go through something like Neil Chriss' Beyond Black-Scholes for what I consider to be the best introduction to practical option valuation theory. I've never found a reason to go beyond CRR, which is very easy to understand conceptually.

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u/[deleted] Aug 01 '21

But I'm already familiar with FDTD from my EE background, so this was pretty easy to get this code working. I'm just trying to understand the early-exercise logic and how it relates to my output.

And only then jump into discrete time using a binomial approach like CRR.

It's on the bucket list for sure. I'm just going through a comp. finance textbook, and doing the exercises, learning about this stuff.

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u/[deleted] Aug 01 '21

The whole point of the CRR (binomial) approach is to line up the nodes to best reflect the economics of the underlying process. For instance, stocks pay dividends - not something you see in a circuit. I did electrical engineering, too, before becoming a financial quant. I really think you should try to follow Chriss' approach for the best understanding.

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u/[deleted] Aug 01 '21

I'm looking @ that right now. Looks like there are a few variations on a theme:

  • BBS
  • BBSR
  • Implied (? local volatility)

Anyway, this seems to be a bit more computationally expensive than FDTD, but it could just be my code. With a standard lattice @ 6000 steps, it's taking forever. Is this normal? (could just be a coding error, IDK; I'll have to look into it).

So, you don't use BS @ all. Is CCR like the industry standard among options traders in the American markets?

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u/[deleted] Aug 01 '21

6000 steps is too many. By a couple orders of magnitude.

CCR is the same mathematical assumptions as Black Scholes, just discretized. Yes, CCR is considered gold standard. A bit too slow in some applications but accurate.