Questions tagged [local-volatility]
The local-volatility tag has no usage guidance.
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Instability in risks using local volatility
I am valuing vanilla call options using FDM with Crank Nicolson discretization and Rannacher smoothing (mind you, I am having the same issue on MC) and I am getting unstable delta, gamma and theta. I ...
3
votes
1answer
54 views
Price Down and In Barrier Option Using Local Vol and Monte Carlo
As an entry level financial engineer, I'm trying to make sense of a practical case using the concepts I learned including local vol, monte carlo, so I really appreciate your advice if my understanding ...
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56 views
How to derivate Dupire's local volatility?
I want to calculate the expression of local volatility expressed in terms of implied volatility given by Fabrice Douglas Rouah in Derivation of Local Volatility :
$v_{l} = \frac{ \frac{\partial w}{\...
2
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1answer
98 views
How to get the local volatility from IV surface?
I have to work on Dupire's model.
If I understand Fengler's paper well enough we can get the local volatility from implied volatility smoothed surface because if not it would look all bumpy like the ...
4
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1answer
138 views
Different volatility surface ( Local vol, Stochastic vol etc.)
Despite many questions about local and stochastic volatility available on this forum, i still have a few doubts left. Essentially I am seeking validation whether I am interpreting things correctly.
...
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1answer
119 views
Local volatility and Stochastic Volatility
Please help me understand similarity and differences between local volatility and Stochastic Volatility both intuitively and mathematically.
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62 views
Local volatility Formula and How To use it
I'm new to Volatility Modelling, so the content of this question may be completely wrong and th question naive. I'm reading "The volatility surface" by Gatheral. I'm trying to get a sense of the first ...
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0answers
31 views
How to derive the half slope rule from asymptotic relation between implied and local volatility?
In their paper(https://www.sciencedirect.com/science/article/pii/S0764444200017493) BERESTYCKI, BUSCA, and FLORENT proved an asymptotical relation(for short maturity) between implied and local ...
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49 views
looking for a simple realistic parametric volatility model
Which parametric volatility is realistic to test quickly and qualitatively a model?
I do not wish to fit market quotes but would like to have a non-trivial volatility with skew or smile to do some MC ...
4
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1answer
377 views
Local Volatility with Monte Carlo Simulation
I am trying to implement a Monte Carlo Simulation using Local Volatility Model (Dupire’s Equation).
I’m pretty sure I can build a very good LV surface, however, I do not know how to use it in the MC ...
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1answer
96 views
Pricing with local volatility for derivatives beside options
Say I have calibrated an local volatility mode to market data on a forward on stock X. Say I want to price a derivative Y that is NOT a call/put option. What is the (or one of many) general strategy ...
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1answer
176 views
How frequently is local volatility calibrated to implied vol surface, in practice?
This has two related questions -
How frequently do equity derivative traders re-mark the implied volatility surface -
(i) once a day (e.g. at start of trading day, or end-of-day), or
(ii) ...
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199 views
How to price the american options using local volatility
I have given with a surface of american option prices $C_{am}(T, K)$. From these american option prices the implied volatility surface is deduced.
Now I want to find the local volatility $\sigma(s,t)$...
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59 views
Difference between local volatility and implied volatility [duplicate]
I have read several articles about local volatility and implied volatility, but I am still confused with the difference between the two.
Please correct me if I am wrong: Implied volatility is the ...
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2answers
297 views
Model calibration volatility surface
Let's say i have an exotic structure that is to be vega hedged dynamically. I choose to price it with a local volatility (which means the model prices in your future vega hedges using all options for ...
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0answers
104 views
Pricing forward start Cliquet option with implied volatility with Dupire
I have the following implied volatility matrix of a stock index downloaded the 15th February 2019, the value of the stock was 3188.44 at the time:
...
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0answers
85 views
Is there an arbitrage free option model that treats volatility as a deterministic function of strike?
I am trying to get a good understanding of the different models out there, and thus be able to study hedging errors, and strengths and weaknesses. My understanding of the Local Volatility model in ...
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56 views
Local volatility model equivalent reformulation
Do we have a equivalent formulation of the local volatility model, where the SDE of the model would be on the volatility and S would be a functional of the the volatility and time?
Thanks.
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2answers
955 views
Local Volatility calculation in Python
I am trying to price Local Volatility in Python using Dupire (Finite Difference Method).
I have following set of information
Spot: 770.05, Strike: 850, Type: 'C', rfr: 0.0066, time to maturity = ...
2
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1answer
336 views
Dupire Formula question
I want to calculate the local volatility from Dupire's formula:
$\sigma _{VL}^{2} (K,T,S_{0}) = \frac{\frac{\partial C}{\partial T}}{\frac{1}{2} K^{2} \frac{\partial^2 C}{\partial K^2}}$
So I use ...
2
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1answer
285 views
LSV model calibration with only few quotes per maturity
At this link I have asked what is the market standard when pricing options in different asset classes. Based on the answers, the standard for FX and equities seems to be the local-stochastic ...
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272 views
Mixed local-stochastic volatility model in Quantlib
At a conference the speaker mentioned that it is a standard approach today to use a mix of local and stochastic volatility model in equity, FX and interest rates.
Can you please suggest the most ...
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0answers
191 views
How do you numerically solve the Dupire Local Volatility PDE in log moneyness-time space?
I am trying to implement a numerical solution to price vanilla calls. I am using the Dupire equation in log moneyness-time (k = ln(F/T)) space as per below PDE
I have tried solving it using a fully ...
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1answer
280 views
Vanilla Option Prices from Local Vol Surface (using neither MC nor PDE)
There are numerous papers that describe the derivation of the Local-Vol equation using available market prices of options. For example:
Dupire's formula (see e.g. OpenGamma (2013)) gives us LV in ...
2
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2answers
219 views
Probability Density Function sign problem when using Call Price
Given the call price $C_t = e^{-\int_t^Tr(s)ds}\int (s-K)^{+}\phi_{S_T}(T,s)ds $
we know that $$\frac{dC}{dK}=-e^{-\int_t^Tr(s)ds}\int_K^{\infty} \phi_{S_T}(T,s)ds$$
Now when I use dirac delta ...
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1answer
164 views
Deriving Dupire's Volatility Formula : Why $\lim_{s \rightarrow \infty} (s-K) \frac{d}{ds} \big[ \sigma^2(T,s)s^2\phi(T,s)\big] = 0 $
In deriving Dupire's formula for the local volatility, using European call option, this is used in the integration by part :
$$\lim_{s \rightarrow \infty} (s-K) \frac{d}{ds} \Big[ \sigma^2(T,s) s^2\...
5
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2answers
308 views
Local volatility implied by implied vol surface
In his book volatility and correlation, Rebonato tries to explain intuitively the shape of local volatility surface (depending on stock level and time) from the implied volatility surface in the OTM ...
4
votes
2answers
1k views
What are the benefits of using Dupire model
I'm trying to understand what is the point of the local volatility model in practice. Rather than asking a question I will explain what is what for me hoping someone will spot where I'm wrong:
The ...
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1answer
665 views
how to price barrier option under local vol model using QuantLib
I use QuantLib in Python. Now I have implied volatility surface data. How can I get the local vol surface than using finite difference method to price a barrier option in QuantLib?
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1answer
180 views
Drift of Local Volatility Model - Dupire
i understand that the local volatility function can be computed from the implied volatility surface.(i.e there is no calibration to option prices, we just need the full implied volatility surface only)...
7
votes
2answers
422 views
Vega of exotic options
I'am wondering if there is a standard definition to the Vega of an exotic product when the underlying model is not Black-Scholes.
Let me give some examples :
What is the Vega if the price is ...
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0answers
177 views
Finite Difference with SVI Vol Model
I am attempting to implement a local vol pricing model in finite difference for equity index options.
I have followed Gatheral's Lectures and fitted an SVI Model bringing me to the following local ...
4
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1answer
169 views
Break even Levels Local volatility
I came across a presentation where it is stated that using a local volatility model the PnL of an option is
and
What does he mean by spot/vol correl = -100%?
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119 views
Dynamically adjusting the size of a Constant Range Bar (on an intraday fx chart)
Constant Range Bars (CRB) is a type of candlestick charting method that does not draw a new candle every unit of time (like every 1/5/15/30 minutes), but every time the range (high-low) of the ...
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0answers
46 views
Trying to understand Strike Adjusted Spread, can someone explain using a simple example?
I should start by saying that I am not a quant, I am someone interested in options but I perhaps lack the mathematics background to always follow along. I recently stumbled upon a terrific article ...
5
votes
1answer
360 views
Calibration of Cox-Ingersoll-Ross process that hits zero (Feller condition violation)
I'm considering a Cox-Ingersoll-Ross (CIR) process
$$
dx_{t} = \alpha\left(\theta - x_{t}\right)dt + \sigma \sqrt{x_{t}}\,dW_{t}\,,\qquad \alpha,\beta,\sigma > 0
$$
which by assumption has $2\...
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1answer
490 views
Forward Skew in the Local Volatility Model
How does the local volatility model cause a forward skew? How is this different to the skew observed for future tenors in the vol surface?#
Also how do LV models underestimate vol of vol?
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3answers
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Problems with local volatility models (vs stochastic volatility models)
Why is pricing with local volatility models are problem with exotics, mainly due to "the volatility surface is the market's current view of volatility and this will change in the future meaning the ...
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2answers
2k views
Autocallable pricing under stochastic vs. local volatility
I am interest in the reason why an Autocallable (structured product) is cheaper under local volatility compared to stochastic volatility.
I thought this was due to the following:
when thinking in ...
5
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0answers
248 views
Dupire's calibration
I'm trying to implement a method for calibrating the local volatility model (Dupire's one). I'm working on the paper from Andreasen and Huge : Volatility interpolation (SSRN). Is this considered to be ...
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0answers
93 views
Local variance derivation by Gatheral
I've bought Gatheral's book on Local Volatility and I have troubles with understanding a part where he shows that local variance is a conditional expectation of instantaneous variance.
Why in the ...
2
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1answer
175 views
Proof for ATM delta with Local col
I am looking at a time-homogeneous local volatility model where
ATM implied volatility equals ATM local volatility: $\sigma_{imp}(S_0)=\sigma_{local}(S_0)$
ATM IV Skew = half of LV slope
In general $\...
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0answers
164 views
How to compute SABR's probability density function
I am trying to compute the probability density function of the forward rate implied by the SABR formula approximation in order to see how the density implied by the approximation has negative ...
5
votes
1answer
674 views
SSR definition in Bergomi in relation to sticky strike and sticky delta
In Bergomi [Stochastic Vol Modelling] (Sec. 2.5.2), in the section on surface dynamics, the following definition of the "Skew Stickiness Ratio" (SSR) is made:
$$ SSR = \dfrac{1}{\mathcal{S}_T}\frac{d\...
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0answers
296 views
Implied Vol skew VS Local Vol skew (as presented by Derman 1995)
I am reading Derman's article/notes regarding local volatilty:
http://www.emanuelderman.com/writing/entry/the-local-volatility-surface.
I am examining the graph on page 13.
The Implied volatility (...
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1answer
409 views
Mixture models of Stochastic Volatility and Local Volatility
As far as I can see on this website the stochastic volatilty models seem to be preferred to local volatility models, mainly due to the fact that stochastic volatility is 2D diffusive process whilst ...
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1answer
943 views
Local Volatility implementation
The Dupire equation is well-known and mentioned in thousands of articles. Although I could not find a lot of documentation about a consistent and proper way of implementing the formula (The difficulty ...
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2answers
1k views
Marking implied vol surface daily with sticky strike and sticky delta
Suppose that implied vol surfaces are calibrated once per month due to data restrictions (i.e. option data is only available at month end). How can a trading desk remark their vol surfaces on a daily ...
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733 views
Local Stochastic Volatility - Break even levels
In Chapter 12 of his excellent book Stochastic Volatility Modeling, Lorenzo Bergomi discusses the topic of local-stochastic volatility models (LSV).
As most of you are probably aware of, the idea is ...
5
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1answer
154 views
Motivation of the singular perturbation solution formulation for local volatility model
I am puzzled by the motivation of the particular choice of the (singular) perturbation method used in Equivalent Black Volatilities. Equation (A.6a) sets
$$\epsilon:= A(K)\ll 1.$$
What is the ...
