Questions tagged [local-volatility]

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62 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 ...
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1answer
39 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 ...
3
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0answers
76 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^...
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1answer
109 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 ...
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57 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 ...
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1answer
158 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
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2answers
139 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
118 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 ...
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31 views

Pricing deep OTM and short expiry options with Monte Carlo methods

Is there any good variance reduction technique to price with MC deep OTM and short tenor options under Local Volatility? Can importance sampling be used? I couldn’t find any reference which does not ...
3
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2answers
128 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
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1answer
133 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
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0answers
32 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
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1answer
117 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, ...
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1answer
87 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
112 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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0answers
39 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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27 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
121 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
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2answers
86 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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41 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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48 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
111 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 ...
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58 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
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1answer
128 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
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1answer
191 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
91 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
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1answer
117 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
71 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
170 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
322 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
216 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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0answers
120 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
48 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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54 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 ...
5
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1answer
955 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
169 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 ...
5
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1answer
250 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
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0answers
322 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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0answers
150 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
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2answers
708 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
170 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
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0answers
113 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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0answers
63 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
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2answers
2k 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
778 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 ...
3
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1answer
410 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 ...
3
votes
1answer
631 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
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0answers
232 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 ...
9
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1answer
396 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
226 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 ...