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## Search found 19 matches

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March 3rd, 2021, 7:43 pm
Forum: General Forum
Topic: Martingale Correction
Replies: 15
Views: 1106

### Re: Martingale Correction

solved it... I work on both the curves for model calibration: part1: squared error in swaption prices.    part2: matching P(t, t+1) from the analytical and the model formula Of course, I lose some information on the swaption vol part, but this seems to be a reasonable approach to deal with the two c...
March 3rd, 2021, 12:21 am
Forum: General Forum
Topic: Martingale Correction
Replies: 15
Views: 1106

### Re: Martingale Correction

Using quasi-MC techniques won't make any big difference, I have already tried the Halton sequence. that would fix some variance issues with the factors x and y, but the real problem lies in the deterministic part of the short-rate, which is actually driving the short-rate process.
March 3rd, 2021, 12:17 am
Forum: General Forum
Topic: Martingale Correction
Replies: 15
Views: 1106

### Re: Martingale Correction

thanks, Bearish and JohnLem! In my opinion, I must work always under the risk-adjusted measure for this particular problem. Please consider that the goal is to match the entire yield curve and not only a specific maturity T.  Let me put it again in more detail: I am calibrating the G2++ model to ATM...
February 25th, 2021, 5:05 pm
Forum: General Forum
Topic: Martingale Correction
Replies: 15
Views: 1106

### Re: Martingale Correction

Thanks, Bearish and HS. I am working on G2++ and the curve that I am using in calibration (to calculate swap rates to price swaptions) is different from the curve that I have to simulate. Insurance analytics problem; we have to simulate the EIOPA curve.  So, it is basically a moment matching problem...
February 24th, 2021, 2:11 pm
Forum: General Forum
Topic: Martingale Correction
Replies: 15
Views: 1106

### Martingale Correction

Am I allowed to do the following to exactly match the term structure of rates? P( t, T)_coorected  = P( t, T)_simulated - P( t, T)_simulated_mean + P( t, T)_market The expectation of the above expression  will be equal to the market value of P(t, T) If this is the case, then this approach would be m...
February 16th, 2021, 11:34 am
Forum: Technical Forum
Topic: Moments Matching: G2++
Replies: 0
Views: 452

### Moments Matching: G2++

How do we apply moments matching-variance reduction technique to the G2++ model? In a one-factor short rate model, it is achieved by adding instantaneous forward rate from the market and subtracting the same obtained from the empirical distribution.  r_corrected = r_simulated + f(0,t) - \bar f(0,t),...
February 5th, 2021, 8:53 am
Forum: General Forum
Topic: Brigo/Mercurio Theorem 4.2.3
Replies: 8
Views: 4614

### Re: Brigo/Mercurio Theorem 4.2.3

I encountered the same problem, use scipy.optimize.fsolve, it should work...

cheers
K
February 5th, 2021, 8:47 am
Forum: General Forum
Topic: Calibration Errors
Replies: 7
Views: 918

### Re: Calibration Errors

February 2nd, 2021, 10:56 am
Forum: General Forum
Topic: Calibration Errors
Replies: 7
Views: 918

### Re: Calibration Errors

Thanks, DavidJN! The errors that I reported are for the entire swaption surface, 110 swaptions in this case. Are those numbers too large to get a good fit for the vol surface? what is an acceptable range of errors in this case? I started with a Milliman document that reports comparable error using t...
February 1st, 2021, 4:23 pm
Forum: General Forum
Topic: Calibration Errors
Replies: 7
Views: 918

### Re: Calibration Errors

Thank you, Bearish! The end goal is to generate 'market consistent' interest rate scenarios for insurance analytics, so, I am not really concerned about the bid-ask spread. (not sure if I should be) The idea is to capture the current volatility structure to generate IR scenarios. I am calibrating th...
January 29th, 2021, 11:41 am
Forum: General Forum
Topic: Calibration Errors
Replies: 7
Views: 918

### Calibration Errors

Hi all, I am working on several interest rate models, calibrating them to ATM swaption prices. I would like to know what is an acceptable range for relative errors in swaption prices? I observed a strange pattern in my analysis. Hull-White 1 Factor model:- 35% average error G2++ model:- 7% average e...
December 28th, 2020, 5:27 pm
Forum: Student Forum
Topic: Derivation for two independent brownian motions
Replies: 6
Views: 8799

### Re: Derivation for two independent brownian motions

is it not going to be max( F(x1), F(x2)....F(xn) )? when n is infinite, the value of the function will be equal to 1.
December 22nd, 2020, 9:27 pm
Forum: Technical Forum
Topic: LMM + Heston Model Simulation
Replies: 0
Views: 867

### LMM + Heston Model Simulation

Hi all,  I am trying to simulate the Libor Market Model and the Heston Model together. I have got 30 forward rates to be simulated using LMM and 20 equities using the Heston model.  For the forward rate correlation, I am using a parametrized form, corr(t,T) = \beta_0 + (1 - \beta_0) * exp(-\beta_1 *...
December 22nd, 2020, 9:15 pm
Forum: Student Forum
Topic: Black volatility from SABR
Replies: 2
Views: 1631

### Re: Black volatility from SABR

Thank you, Alan. This explanation is insightful

Kind regards,
K
November 16th, 2020, 11:59 pm
Forum: Student Forum
Topic: Black volatility from SABR
Replies: 2
Views: 1631

### Black volatility from SABR

Hi all,

why do we use SABR model to calculate Shifted Black implied volatility? why can't the shift be applied simply in the BS formula? Can I use any other model to calculate Black Implied vols?

thank you,
K
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