Questions tagged [local-volatility]
The local-volatility tag has no usage guidance.
137
questions
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65 views
Implied and Local Volatility relation in Monte Carlo
I am implementing a Monte Carlo engine with the local volatility model based on Dupire.
Obviusly, I obtain the local volatility surface from the implied volatility surface and that surfaces has ...
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23 views
How to calculate Vega using Dupire and MonteCarlo engine with Autograd?
I have implemented a Monte Carlo pricer engine which includes the volatility local model based on Dupire formula.
For now I can value several (european) options which I used to validate the model, but ...
2
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1answer
59 views
Calibration Heston Local Stochastic Volatility (LSV) Model
The Heston Local Stochastic Volatility (LSV) model has the following dynamics:
$$dS_{t}=r S_{t} d t+L\left(S_{t}, t\right) \sqrt{V_{t}} S_{t} d W_{t},$$
$$d V_{t}=\kappa\left(\theta-V_{t}\right) d t+\...
6
votes
1answer
136 views
Negative Density in Local Stochastic Volatility (LSV) Model Calibration
I'm trying to calibrate Local stochastic volatility model using finite difference method, and I'm mainly following this referece: Tian (2015).
I met a problem when calibrating leverage function - the ...
1
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0answers
39 views
How to use log moneyness in a local volatility context
I am implementing a monte carlo to price various options using a local volatility model.
The implied volatility surface from which the local volatility is derived is a function of logmoneyness and ...
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0answers
36 views
Local volatility (dupire equation) for monte Carlo, discretisation - need help understanding spatial and TEMPORAL dimensions
As proven in Gatheral notes (or in this discussion)
The equations of the local volatility as a function of the vanilla calls can be written as
$$
\sigma^2(T,K) = \frac{\frac{\partial C}{\partial T} +...
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55 views
Local Vol from Implied Vol formulas different
I am wondering why "LOCAL VOLATILITY MODELLING Roel van der Kamp July 13, 2009" (formula 2.23) has a different numerator compared to "The Volatility Surface. JIM GATHERAL" (formula ...
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0answers
24 views
When is the effect of skew most potent for an early exercise option?
Let us say I have a Bermudan option which I can terminate at 3 possible dates. When can I expect the discrepancy between a local vol and a stochastic vol model to be highest (assuming both are ...
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22 views
Local vol vs stochastic vol in the context of American digital options
I have two models of some spot. One is under local vol and the other is under stoch vol. Both are calibrated to the prevailing vanilla prices. I then consider the option that pays $1$ if the spot ...
1
vote
1answer
114 views
calibration of a local volatility model
Generally speaking, when calibrating a local volatility model a la Dupire to European vanilla calls, should I use the numerically (PDE or Monte Carlo) solved price for the vanilla call in the cost ...
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29 views
Local Volatility Monte Carlo option price - different starting index level
I constructed the local volatility surface of S&P 500 from implied vols and was able to price the options accurately using Monte-Carlo. Let's say I priced a 80% of S0 put option with S0 = 4000. ...
5
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2answers
289 views
Correct Monte Carlo simulation of local volatility models
I am using Monte Carlo simulation to evolve the following SDE over a grid of timepoints $0,t_1,...,t_N$.
\begin{equation}
dS(t)=\sigma(t, S(t))dw(t)
\end{equation}
Here $\sigma(t_i,S(t_i)), i=1,...,N$ ...
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0answers
36 views
calibration of local volatility to
I'm looking to understand the practical details of calibrating local volatility to option prices for a range of different expiries using the Dupire local volatility equation. Would appreciate some ...
0
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1answer
64 views
Price a contingent claim with payoff $(S_T-K)1_{\{S_T>K\}}1_{\{L\leq X_T\leq U\}}$
I'd like to price the following contingent claim using a copula model.
$$V_T = (S_T-K)1_{\{S_T>K\}}1_{\{L\leq X_T\leq U\}}$$
where $S$ and $X$ are two stock price processes which follow a non-flat ...
0
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1answer
97 views
Is there a Dupire's Formula for put options?
Generally, Dupire's formula is taking derivatives on the call option prices. Here it only uses information of the call options.
If now we have the data including both call and put options, is there a ...
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66 views
Arbitrage Free Interpolation of Implied Volatility on Time Dimension
I’m working on a project to build a local volatility model out of implied volatility data and I’m currently testing the no-arbitrage version of SVI model as described in this paper Section 5.1 [...
2
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2answers
196 views
Question About SVI and SSVI Tradeoff between Fitness and No-Arbitrage
I’m currently working on a project to build a local volatility model out of implied volatility data and am struggling in the selection of an appropriate method to interpolate the volatility surface. I ...
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0answers
109 views
SABR vs Dupire: when to use what?
I was wondering for which products one would use the (AF)SABR model and for which ones Dupire's Local Volatility model.
If I understand correctly, Dupire is by construction Arbitrage-Free but produces ...
6
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0answers
157 views
Hedging : effect of not matching the term structure of skew
Let us assume that we construct a pure stochastic volatility model calibrated to the implied volatility surface, but that the model does not replicate accurately the observed term structure of the ...
0
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1answer
63 views
Basket option: volatility surface
I would like to calculate a basket European option with Black Scholes local volatility model.
I want to simplified the basket option into a single underlying European option. Should we get the local ...
4
votes
0answers
95 views
$\frac{\partial C_{BS}}{\partial T}$ in local volatility derivation in terms of implied volatility
In Gatheral's book, in the derivation of local volatility in terms of implied volatility, we use the regular Dupire formula
$$
\frac{\partial C}{\partial T} = \frac{1}{2} \sigma^{2}K^{2}\frac{\partial^...
2
votes
1answer
149 views
Calibrate Stochastic Volatility Model
For stochastic volatility models, and any vol model I know, it seems the standard approach is to calibrate the model from option prices. As other user said, this seems a chicken egg problem - how do I ...
6
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0answers
132 views
Autocallable option Delta
There have been numerous exotic trading desk blow ups lately, related to various reasons. However, in particular, one bank had some issues where they were pricing autocallable notes with Local ...
0
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1answer
191 views
Implied Volatility vs Actual Volatility Calculation
To build a term structure I need different volatilities; as I don't get them at every strike, I use interpolation technique to calculate the rest and plot. This is how I calculate the implied vols. ...
3
votes
2answers
274 views
Forward skew generated by Local Vol model
I'm digging into the properties of the Local Vol model and I become confused with statements made by authors in papers/textbooks (without explanations) like, "The forward skew in local vol model ...
3
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1answer
142 views
LIBOR market model with stochastic volatility
I have read that there are 3 types of pricing models: local volatility, stochastic volatility and stochastic-local volatility models (LSV).
I am now looking at interest rates exotics pricing models ...
3
votes
2answers
378 views
Interpolation of FX Vol Surface from non-uniform strike vs tenor grid
TL;DR
I'm trying to fit a vol surface to market FX options quotes in order to build a local vol model to price with. Unlike listed options that typically have a nice rectangular grid of strikes and ...
6
votes
1answer
252 views
Local Volatility Model Error
I am implementing my local volatility pricer using the finite difference method in MATLAB. I parametrise the implied volatility surface using the SSVI parametrisation (Gatheral & Jacquier), which ...
3
votes
0answers
38 views
Infinitesimal Generators and Expectation of First Hitting Time as Solution of Differential Equation
I've been learning about Linear Diffusions and how their infinitesimal generators can be used to relate expectations and deterministic differential equations.
Let $X$ be an one-dimensional diffusion ...
4
votes
1answer
207 views
Euler Discretization to use with Monte Carlo simulation and Local Volatility Model
Like in the title, I am working on running Monte Carlo simulations to price options with the Local Volatility model as a project. I just want to make sure that I am understanding the process, ...
0
votes
1answer
109 views
Book/ Articles recommendation for Volatility models
I am looking for references on volatility models. I want to gain more insights on these models but have a little background as of now. Thus, looking for references that can pick the topic from basics ...
3
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1answer
206 views
Three questions regarding local volatility implementation (based on the Andreasen, Huge article “Volatility interpolation”)
I am new to the area of local volatility interpolation and I am trying to make a decent implementation for calculating the local volatility surface from option prices using the basic methodology from ...
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48 views
Intuition behind local volatility curve shapes in interest rate environments
I have some questions regarding the intuition behind shapes for the local volatility (LV) curve as seen in quite popular models. Let's say we have the following generalized stochastic-local volatility ...
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40 views
Dupire formula and stochastic rates
I was reading a proof of Dupire's formula from Ch. 2 of Lorenzo Bergomi's Stochastic Volatility modeling and a question came up: what if the repo rate and the risk-free rate are stochastic? Do we have ...
3
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0answers
157 views
Rigorous proof of Dupire formula (e.g. using Gyöngy's theorem)
Where can I find a rigorous proof of the Dupire formula (for example, using using Gyöngy's theorem)? I imagine this would be covered by a paper or by a standard financial math text, but I could not ...
2
votes
2answers
160 views
What is the difference between parametric and non-parametric models?
I'm reading about volatility modelling and I came across the concept of parametric and non-parametric models. For example, GARCH is a parametric model and Realized Volatility is a non-parametric model....
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48 views
what is the formula for local vol , as a function of implied vol, AND why am i getting a negative denominator?
i am seeing different formulas at different places on stack exchange, so not sure!
eg if denominator has a term y^2/w^2, or y/w^2 or
1/w or -1/w
and also, whatever formula i use, i get a negative ...
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vote
0answers
60 views
Dupire Vomma and Stochastic volatility
Suppose that you are short an option on asset $X_t$ following a pure diffusion. Suppose you are hedging your position using (Dupire) Local volatility model. Suppose that the option is concave with ...
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2answers
222 views
Testing an implementation of Dupire's local volatility model
I have implemented Dupire's local volatility function $\sigma(K,T)$ using call option price time and strike derivatives. $\sigma(K,T)$ uses a fixed spot $S_0$. The surface $\sigma(K,T)$ closely ...
3
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0answers
59 views
For any twice differential continuous function C(T, K), does there exist a sigma(t, S) that can reproduce C(T, K)?
In the Dupire's paper, he assumes that there exits a function $\sigma(t,S)$ that can reproduce $C(T, K)$. My question is that: is the assumption true for any twice differential continuous function $C(...
5
votes
1answer
176 views
Is Dupire's local volatility model path independent to recover historical option price?
Generally when we implement Dupire's local volatility model, we follow the steps below:
Calculate implied volatility from given historical data
Fit the implied volatility skew. So we also know the ...
3
votes
1answer
227 views
Calculating local volatility from option prices?
I'm attempting to calculate local volatility given a set of option prices using $$ \sigma(T,K)=\sqrt{2\frac{\frac{\partial C}{\partial T}+rK\frac{\partial C}{\partial K}}{K^2\frac{\partial^2C}{\...
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0answers
166 views
Expected value and variance of the stock log-returns under Local Volatility framework
I want to calculate the expected value and the variance of the stock process log-returns in the Local Volatility setting (and the realized/terminal correlation but let us begin in the one-dimentional ...
3
votes
1answer
162 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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0answers
83 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}{\...
3
votes
1answer
254 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
votes
1answer
499 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.
...
2
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1answer
301 views
Local volatility and Stochastic Volatility
Please help me understand similarity and differences between local volatility and Stochastic Volatility both intuitively and mathematically.
2
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0answers
181 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 ...
2
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0answers
54 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 ...
