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.Question: what happens if the barrier is hit between two monitoring dates? Introduce a hitting probability?
The BGK tends to overshoot it seems..
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).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.Question: what happens if the barrier is hit between two monitoring dates? Introduce a hitting probability?
The BGK tends to overshoot it seems..
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".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).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.Question: what happens if the barrier is hit between two monitoring dates? Introduce a hitting probability?
The BGK tends to overshoot it seems..
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'.
wrong threadhello 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??