Questions tagged [local-volatility]
The local-volatility tag has no usage guidance.
5
votes
1answer
100 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) ...
4
votes
0answers
65 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 $\sigma(s,t)$...
1
vote
0answers
41 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 ...
0
votes
1answer
55 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 ...
1
vote
0answers
49 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:
...
4
votes
0answers
68 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 ...
1
vote
0answers
48 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.
2
votes
2answers
301 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
votes
1answer
114 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
votes
1answer
206 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 ...
1
vote
0answers
140 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 ...
2
votes
0answers
114 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 ...
8
votes
1answer
221 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
votes
2answers
214 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 ...
1
vote
1answer
138 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
votes
2answers
241 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
738 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 ...
0
votes
1answer
362 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?
0
votes
1answer
133 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
320 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 ...
3
votes
0answers
149 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
votes
1answer
141 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%?
1
vote
0answers
88 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 ...
1
vote
0answers
37 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 ...
3
votes
0answers
244 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\...
0
votes
1answer
325 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?
6
votes
3answers
3k views
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 ...
4
votes
2answers
1k 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
votes
0answers
216 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 ...
2
votes
0answers
81 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
votes
1answer
156 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 $\...
1
vote
0answers
133 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
431 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\...
2
votes
0answers
247 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 (...
1
vote
1answer
296 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 ...
3
votes
1answer
655 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 ...
1
vote
2answers
825 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 ...
16
votes
0answers
598 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
votes
1answer
125 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 ...
6
votes
2answers
2k views
Local vol, stochastic vol, implied vol
I've been studying volatility modelling over past the few days; in particular, the connections between local vol, stochastic vol, implied vol. I've been reading Gatheral's book "The volatility surface"...
2
votes
0answers
145 views
Problem of negative local volatility:
Consider the displaced log-normal process: $$dS(t) = \lambda(t)(a(t)+b(t)S(t))dW(t), S(0) = S_0>0, $$ where $W(t)$ is a one-dimensional Brownian motion.
We suppose that $(\forall t \ge 0) : \...
3
votes
0answers
290 views
Ill-posed problem: Local volatility calibration. Regularization vs Smoothing
I have asked my question on Mathematics site of Stack Exchange but maybe I will get the answer rather here.
I am working on inverse problem - calibration of local volatility (financial application). ...
1
vote
1answer
238 views
Conditional expectation and Dirac delta function
In the proof of Dupire equation we end up with an identity involving the Dirac delta function.
How to prove that
$$\dfrac{E[\...
0
votes
1answer
138 views
Why/When local volatility is preferred over implied distribution sampling?
Let's say we have an option whose payoff is path dependent (let's say it's asian option with observations every month). Then why these are usually priced with local vol instead of sampling from ...
5
votes
2answers
411 views
Difference between Local Vol and Copula
Let's assume we have ATM European call on a basket of two stocks and price it with:
1) Multivariate Local Vol with constant correlation
2) Gaussian copula
Assuming we use the same correlation ...
0
votes
1answer
362 views
Approximations for Quanto Options pricing
On page 4 of this paper, the auhor provides two good approximations for quanto options pricing: $V^d_{black}$ and $V^d_{blackATM}$. These approximations consist of using the ATM and/or stike ...
4
votes
1answer
567 views
Proof of arbitrage-free implied volatility surface in relation to local volatility surfaces
I'm looking for proof of the following statement:
"The existence of an arbitrage-free implied volatility surface is
equivalent to the existence of a well-defined local volatility
surface."
4
votes
1answer
812 views
Methods to compute Local Volatility surface and price
I am trying to wrap my head around how exactly Dupire's formula is implemented in practice.
We need $\sigma(S,T)$ for every possible $S$ and $T$. If we had that, then we can just run a monte carlo ...
8
votes
1answer
1k views
Is the local volatility linear if smile is linear?
Assume $dS = S_t\sigma(S_t,t)dW$.
Given a implied volatility smile which is linear in, say, $(K - S_0)$, (we know its intercept and slope), we wish to calibrate $\sigma(S_t, t)$ to it. Will it too be ...
1
vote
0answers
42 views
Reference request: local volatility and time-dependent volatility
Is there a good practitioners guide to time-dependent and local volatility models?
