Questions tagged [local-volatility]

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1answer
104 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. ...
2
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0answers
54 views

Impact of Discrete and linear dividends on Local Volatility model

I am trying to understand the assumptions and weaknesses of a Dupire Local Volatility model. If dividends are assumed linear, is it a problem for model calibration? If yes, why? Why would large values ...
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0answers
22 views

Calibrate Local Volatility model to price quanto options

I have a Local Volatility model. I compute the LV surface $\sigma_{S}^{local}$ on vanilla option of $S$. Assume the vol of foreign exchange is constant and know, and the correlation equity/FX is known....
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1answer
83 views

Why Local Volatility model underestimate price of double no touch options

By reading this great answer, on points 2 and 3, it is stated that the Local Volatility model is not adapted to price barrier double-no-touch options. But I don't understand exactly why. Could you ...
6
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1answer
2k 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 ...
0
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1answer
60 views

Dupire pricing equation derivation vs Black Scholes PDE

I know the Dupire pricing equation is derived in similar way to Black Scholes PDE, but it is not exactly the same equation. Dupire equation reads: $\boxed{\frac{\partial C}{\partial T} = \frac{\sigma^...
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0answers
48 views

Forward volatility smile: Local Volatility vs Stochastic volatility

I was reading this great answer: What are the advantages/disadvantages of these approaches to deal with volatility surface? And I have the following question: How to show that the forward volatility ...
2
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0answers
45 views

Correlation Spot Vol - when is it important?

I know that a local volatility model does not allow to control the correlation between Spot and Vol. I know also that the correlation Spot Vol is important for products like autocalls. Why is ...
3
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1answer
133 views

How is Emanuel Derman's implied tree model implied volatility skew derived?

I am reading Emanuel Derman's paper Patterns of Volatility Change. The section, Implied Volatility In The Sticky Implied Tree Model has the linear skew approximation near the old underlying $S_0$ $$\...
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0answers
17 views

Local volatilty models for fixed maturity curves with sparse equity data

I'm implementing an options analytics platform - with sparse market data going out a few months. Mostly equities and fx options. Building a fixed maturity curve like the one on quikstrike by bantix is ...
0
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1answer
103 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 ...
1
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1answer
107 views

How to extract volatility smile implied by a mixture model?

If one had to extract the implied volatility smile from a local volatility model, one can simply use the relationship: $\sigma^2_{imp}(t, x)T = \int_t^T \sigma^2_{loc}(s, x)ds$ with $\sigma_{loc}$ the ...
1
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0answers
39 views

Question on model recalibration upon a spot shift scenario analysis

I am given a plot of the fair value of a complex derivative against a scenario spot shift for a range odd possible shifts (-40% to 40%). Let us say the pricing model is a local vol model. I am unable ...
2
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1answer
87 views

Finding Option Probability Density Using Local Volatility from Dupire Model

This question is different than pricing using dupire local volatility model and Is Dupire's local volatility model path independent to recover historical option price? I also asked this on Math ...
1
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0answers
75 views

Price difference digital option : constant vol vs local vol

I got the following interview question: Consider a digital option, it will be priced by using two approaches: 1)constant volatility; 2)local volatility. At the strike, both volatilities are equal. (...
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0answers
65 views

Vega Surface with Local Volatility Model

I am trying to obtain the Vega of some equities with the Dupire local volatility model. For this I have already validated the pricing model (I am using Monte Carlo) and now I am able to obtain the ...
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0answers
47 views

How to match simulated local vol european prices with closed formula

Say an implied volatility is given by $\sigma_{imp}(T, log(F_T/K))$ and we note the Dupire local volatilty $\sigma_{loc}(T, log(F_T/K))$ with $F_t$ the forward rate and $K$ the strike. The price of a ...
4
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3answers
3k 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 ...
27
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5answers
11k views

Local Volatility vs. Stochastic Volatility

Are there any empirical observations or practices when to prefer Local Volatility Model for pricing over Stochastic Model or vice versa?
6
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2answers
2k 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 ...
7
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1answer
187 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 ...
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0answers
99 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 ...
0
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0answers
45 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 ...
3
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1answer
226 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+\...
1
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0answers
109 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 ...
0
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0answers
56 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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0answers
89 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 ...
9
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4answers
11k views

Local volatility surface corresponding to the implied volatility surface

In Derman/Kani/Zou paper about local vol they rebuilt a local vol surface from an implied vol surface. Each implied volatility depicted in the surface of the "implied Vol" is the Black-Scholes implied ...
1
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0answers
28 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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0answers
38 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 ...
2
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1answer
328 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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1answer
229 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 ...
5
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2answers
402 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
52 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 ...
8
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1answer
529 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
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1answer
131 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 ...
2
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2answers
374 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 ...
0
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0answers
149 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 [...
4
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0answers
147 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
187 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 ...
3
votes
2answers
3k views

How to interpret Realized Volatility and TSRV using R

I am looking at some high frequency data and I would like to know how to interpret and compare Realized volatility (RV) and Two Scale Realized Volatility (TSRV). References below. Given X is the log ...
3
votes
2answers
857 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 ...
0
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1answer
96 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
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0answers
102 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
188 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 ...
0
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1answer
227 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. ...
6
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0answers
272 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 ...
4
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1answer
269 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, ...
4
votes
2answers
471 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 ...
6
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1answer
375 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 ...