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Billy7
Posts: 262
Joined: March 30th, 2016, 2:12 pm

Re: Finite Difference Method [Option Pricing]: Optimal Grid Structuring

November 22nd, 2016, 12:36 pm

You're welcome, hope you sort it out. Smin and Smax are not things that should be messing your solution up, they are the least important, as long as they're set safely. Set Smin=0 and Smax to something safely far, your 125 was OK in this case (even 105 would do, but let's be generous). Then make sure you build a grid (uniform or not) that has a point on the barrier H and don't worry about Smax. It obviously doesn't matter if your last point doesn't fall exactly on your arbitrarily chosen Smax. When S passes Smax then that's your last point (could be Smax+0.32453, who cares).
 
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Cuchulainn
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Re: Finite Difference Method [Option Pricing]: Optimal Grid Structuring

November 23rd, 2016, 10:41 am

Question: what happens if the barrier is hit between two monitoring dates? Introduce a hitting probability?
The BGK tends to overshoot it seems..
 
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Billy7
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Re: Finite Difference Method [Option Pricing]: Optimal Grid Structuring

November 23rd, 2016, 11:57 am

Question: what happens if the barrier is hit between two monitoring dates? Introduce a hitting probability?
The BGK tends to overshoot it seems..
You mean when we use Monte Carlo right? Yes, I think that's the exact way, when available, which is the case for BM/GBM as far as I know, not sure for other processes. Though if you use Euler discretization then you could say any process becomes locally BM and you can still use the BM hitting probability formulas.
 
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Cuchulainn
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Re: Finite Difference Method [Option Pricing]: Optimal Grid Structuring

November 23rd, 2016, 12:06 pm

Question: what happens if the barrier is hit between two monitoring dates? Introduce a hitting probability?
The BGK tends to overshoot it seems..
You mean when we use Monte Carlo right? Yes, I think that's the exact way, when available, which is the case for BM/GBM as far as I know, not sure for other processes. Though if you use Euler discretization then you could say any process becomes locally BM and you can still use the BM hitting probability formulas.
I am thinkin out loud, but the approach can be applied to any scheme in between 2 monitoring dates? We don't want to underestimate the likelihood of the option being knocked out and hence overestimate the option' value (for knock out).
For knock-in, does BGK underestimate the price?

BTW Espen Haug in his book uses Brownian Bridge probs for this in the binomial tree and says it's 'very accurate'.
 
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Billy7
Posts: 262
Joined: March 30th, 2016, 2:12 pm

Re: Finite Difference Method [Option Pricing]: Optimal Grid Structuring

November 23rd, 2016, 12:37 pm

Question: what happens if the barrier is hit between two monitoring dates? Introduce a hitting probability?
The BGK tends to overshoot it seems..
You mean when we use Monte Carlo right? Yes, I think that's the exact way, when available, which is the case for BM/GBM as far as I know, not sure for other processes. Though if you use Euler discretization then you could say any process becomes locally BM and you can still use the BM hitting probability formulas.
I am thinkin out loud, but the approach can be applied to any scheme in between 2 monitoring dates? We don't want to underestimate the likelihood of the option being knocked out and hence overestimate the option' value (for knock out).
For knock-in, does BGK underestimate the price?

BTW Espen Haug in his book uses Brownian Bridge probs for this in the binomial tree and says it's 'very accurate'.
Thinking out loud as well, the BGK correction is for turning continuous to discrete. One uses the BB probs to make a discretization "as good as continous".
Never used trees (OK, I implemented some basic ones long time ago)  but I can believe Espen that using the BB probs makes them very accurate for continuous barriers. But for PDE/FDM I don't see the need for it, right?
 
tinomudaishe
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Joined: April 6th, 2017, 11:44 pm

Re: Finite Difference Method [Option Pricing]: Optimal Grid Structuring

April 6th, 2017, 11:59 pm

hello guys. can you all please help me i want to discretize the black scholes partial differential equation using the Crank Nicolson method, so i was wondering what are the steps and the final solution??
 
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Cuchulainn
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Re: Finite Difference Method [Option Pricing]: Optimal Grid Structuring

April 7th, 2017, 7:37 am

hello guys. can you all please help me i want to discretize the black scholes partial differential equation using the Crank Nicolson method, so i was wondering what are the steps and the final solution??
wrong thread

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The way it works here is that you post some concrete question when you have reached an impasse or getting incorrect results.
Feels like a student assignment ..