Calibrating (Fitting) the Dupire Local Volatility Model

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Discusses and explains the various methodologies for calibrating or fitting the Dupire Local Volatility model using the market prices of call options. It starts by explaining the calibration problem, links it to the famous Inverse problem, and then explains various methods for determining the local volatility surface such as spline/linear interpolation, smoothing /thin-plate splines, Tikhonov regularisation, and moving least squares. Also outlines the connection to the similar methods used in other fields.

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6 дек 2019

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Комментарии : 22

@Iamine1981 4 года назад

I must say your series about local and stochastic volatility is the best I have come around. I like the clarity of your explanations and the depth of your knowledge is undeniable. I have learned quite a bit from listening to it. Thank you!

@quantpie 4 года назад

Glad you like them! many thanks!!

@kavinkumarr1518 6 месяцев назад

This is a fantastic video ! Really liked the points related to calendar and butterfly arbitrage check in the Call option prices before we infer the Local volatility from the Call option price surface !

@divdagr8 2 года назад

Thank you for creating these videos. A couple of re-runs of this video, and it'll hopefully settle in well :D

@quantpie 2 года назад

You’re welcome! Thanks!

@charleszhang7090 3 года назад

This lecture covers a lot of numerical things! Thank you! Can you consider open another series talking about interpolation and all the numerical calculating details in Quant Finance?

@quantpie 3 года назад

Great suggestion! We have the linear and cubic spline, plus the vanna/volga kinda interpolations on the website, but have not covered them in video format yet, but sure thing! many thanks!

@JaGWiREE 4 года назад

Thanks as always :-). Really appreciating the lengthier videos as the topics are getting more elaborate.

@quantpie 4 года назад

Thanks Brian for your continued support!! You kept us going!!

@shyamrajgarhia8123 4 года назад

Thank you for the video and the previous videos on Fokker Planck & Dupire PDE. I have a broader question related to calibration as I am little confused. At the 3:25 mark, you showed how given a finite set of prices, we can find the values to plug into the Dupire PDE and hence get the local volatility for a given t and S. Subsequently, you showed how to interpolate further prices (for more strike, time combinations). The procedure after this is what I want to confirm: 1) (time stamp: 9:37) at each grid point (finite number but still more than the number of observed prices due to interpolation), we take the observed price and the price that we will get after using the LV from the Dupire PDE as an input (C^LV(Ki, Tj, sigma(t,S)). 2) we try to minimize the sum of squared errors (with some adjustments). Is this understanding correct? If so, then are we simply trying to find the function sigma(t,S) that will minimize the defined error/cost and in that case, are the parameters to be optimized the expressions in the dupire PDE)? Just trying to understand what 'parameters' are being fitted here. Thanks and really appreciate all your videos - have been following for a while now!

@quantpie 4 года назад

Yes that is about it! We want to find a reasonably shaped function that reproduces the input prices as closely as possible subject to the usual constraints!

@tomasdevoto9646 3 года назад

@@quantpie Thanks you very much for the video. I have the following question: I understand that you are looking for the function sigma(t,S) to minimize the sum of the square errors between C^LV and C^BLS as Shyam previously said. Given that sigma(t,S) can be expressed in terms of implied vol, then are we looking for this implied vol?. It is still not completely clear for me what parameter I should calibrate. Thanks in advance!.

@yianpap6093 3 года назад

Nice and informative video, but didn't address much what I came for, which is how we extend the LV surface outside the given market date (extrapolate). I only played with this for a couple of days, but any extrapolation of the (smoothed or not) IV's I tried results in jumps in the LV surface at the edges of the market data "square".

@quantpie 3 года назад

Great point! We have tried to avoid the extrapolation on purpose - it is a dangerous territory! Thanks for sharing!

@davide467 4 года назад

Very good video! Anyway, Is the stochastic calculus playlist complete or not yet?

@quantpie 4 года назад

Thank you Davide! Nah never finishing! We shall be retuning to it soonish! Need to cover backward equations, feynman kac, sigma algebra and probability spaces, construction of measures, martingale, and then dig a bit deeper into the topics! Slow and steady ... as they say!

@matts2207 Год назад

Super helpful video, subscribed! What is the method of calculating the true price under LV model C^{LV} at 10:17? As far as I know there is not simple pricing equation.

@JitendraSingh-gn3oj 4 года назад

While calibrating the local vol, i have downloaded the data from "yahoo finance" for "AAPL" but the implied vol values for few strikes is not available in the dataset 2020-7-17 2020-07-24 2020 - 07 -31 75.0 0.0 0.0 0.0 80.0 0.0 0.0 0.0 85.0 0.0 0.0 0.0 90.0 0.0 0.0 0.0 so how do we calibrate the local vol for these grids, and how we interpret the missing volatility

@quantpie 4 года назад

Thanks for the question Jitendra! I would ignore these points, assuming the input data for these don't exist, and take the reduced set. Then the fitting algorithm (say cubic spline, or regularisation methods, depending on the approach you have taken) will fill the data for the grid points around these strikes as it would for many other strikes. If the missing strikes happen to be in the middle, then it would be some form of interpolation, which is usually not too bad, but if the missing values are in the extreme (lower or upper end), then that is slighly dangerous territory.

@meanreversion1083 3 года назад

I like your video but have to say struggled with the accent a bit....

@quantpie 3 года назад

Thanks for the feedback!! Please keep providing feedback on the other voices and other attributes of the videos as well, it really helps us improve. More specific the better!

@matts2207 Год назад

Come on... at which point? Everything sounds crystal clear to me.