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by rwang716
July 30th, 2019, 11:46 pm
Forum: Numerical Methods Forum
Topic: New Approximation to the Normal Distribution Quantile Function
Replies: 14
Views: 36632

Re: New Approximation to the Normal Distribution Quantile Function

This paper looks like a piecewise rational approximation of cumulative normal distribution, isn’ it?
by rwang716
July 30th, 2019, 11:02 pm
Forum: Numerical Methods Forum
Topic: New Approximation to the Normal Distribution Quantile Function
Replies: 14
Views: 36632

Re: New Approximation to the Normal Distribution Quantile Function

Have tried many uniform approximation formulas for normal distribution CDF function, none of them is accurate enough.
I guess by partition the x into different subintervals it would be much easier to approximate.
by rwang716
July 30th, 2019, 12:44 pm
Forum: Numerical Methods Forum
Topic: New Approximation to the Normal Distribution Quantile Function
Replies: 14
Views: 36632

Re: New Approximation to the Normal Distribution Quantile Function

Does anyone have papers related to rational approximation of normal distribution?
I guess the uniform approximation would have to much error so the piecewise approximation is better?
by rwang716
July 30th, 2019, 6:05 am
Forum: Numerical Methods Forum
Topic: Explicit Formula for computing IV
Replies: 15
Views: 1038

Re: Explicit Formula for computing IV

I have pretty much solved the problem myself. Anyway, thanks guys for the help. BTW, by extreme speed, I mean I hope the time for computing the BS implied vol is less than 0.02us, hopefully 0.01us. My current speed is 0.022us on my laptop but I think with further code optimization I can reduce it to...
by rwang716
July 29th, 2019, 11:44 pm
Forum: Numerical Methods Forum
Topic: Explicit Formula for computing IV
Replies: 15
Views: 1038

Re: Explicit Formula for computing IV

I tried c = 15.3559 and get iv = 0.10979904 using both Differential Evolution (DE) and Brent's method in Boost C++.  A benign problem, numerically. // The approach taken in LI 2005 (Taylor series, >>) does not appeal to me at all. I've lost count of the number of time that 'explicit formula' is men...
by rwang716
July 29th, 2019, 11:38 pm
Forum: Numerical Methods Forum
Topic: Explicit Formula for computing IV
Replies: 15
Views: 1038

Re: Explicit Formula for computing IV

As far as the paper I have read, this is an inevitable problem for all formulas that stem from Taylor expansion. All of these formulas works for a small range of option prices and moneyness, which makes them much less useful in practice. I guess I might just have to read a lot more papers to find th...
by rwang716
July 29th, 2019, 3:21 pm
Forum: Numerical Methods Forum
Topic: Explicit Formula for computing IV
Replies: 15
Views: 1038

Re: Explicit Formula for computing IV

Do you mean Li(2005) formula?
I don't think so. I have tried this formula and it produces imaginary numbers.
Try the input: S = 2800, K = 3050, T = 1/12, r = 0.02, divi = r, call price = 15.36.
The result is a negative value in the square root bracket.
by rwang716
July 29th, 2019, 10:57 am
Forum: Numerical Methods Forum
Topic: Explicit Formula for computing IV
Replies: 15
Views: 1038

Re: Explicit Formula for computing IV

There are some approximation IV formulas that are 99.9% accurate. However, the problem is that those formula only works for near-ATM options, for options that are, e.g., 25% ITM/OTM, the formula becomes nonsense. So I just wonder if there are some approximation formulas that does not have this kind ...
by rwang716
July 29th, 2019, 7:39 am
Forum: Numerical Methods Forum
Topic: Explicit Formula for computing IV
Replies: 15
Views: 1038

Explicit Formula for computing IV

Working on the fast computation of BS implied volatility. I have read some papers regarding the explicit formula ofr BS IV. Like the Li(2005) paper: A new formula for computing implied volatility. However, I met a very serious problem in their formulas because the terms in the square root bracket ca...
by rwang716
July 29th, 2019, 7:33 am
Forum: Numerical Methods Forum
Topic: High Accuracy Greeks computation under trinomial model
Replies: 12
Views: 815

Re: High Accuracy Greeks computation under trinomial model

Have increased the accuracy of deltas computation by roughly 20 times, using the non-cenctered difference methods. The accuracy problem is solved. Thanks, guys.
by rwang716
July 19th, 2019, 12:51 am
Forum: Numerical Methods Forum
Topic: High Accuracy Greeks computation under trinomial model
Replies: 12
Views: 815

Re: High Accuracy Greeks computation under trinomial model

the reason why we choose to use tree models is that it is stable, accuracy controlable, intuitive and straightforward to calculate greeks. Since we are doing option HFT, the speed is equally important as accuracy. I have tried many other approximation methods like BAW, JZ, Bjerksund etc. But all the...
by rwang716
July 18th, 2019, 6:27 am
Forum: Numerical Methods Forum
Topic: High Accuracy Greeks computation under trinomial model
Replies: 12
Views: 815

High Accuracy Greeks computation under trinomial model

I am currently working on the Tian4 trinomial model for vanilla American call/puts. The performance of price accuracy turns out to be quite good. However, I am wondering if there is any way to increase the computation accuracy of delta. The traditional way of computing delta = (up price - down price...
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