# Questions tagged [local-volatility]

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• 99
119 views

### In the Stochastic-Local Volatility (SLV/LSV) calibration procedure, which surface is used when calibrating the Leverage function

Before we match the leverage function $L(S_t,t)$ to the implied volatility surface generated from the market, we are supposed to calibrate the pure Heston parameters, $(\theta, \kappa, v_0, \rho, \xi)$...
• 99
80 views

### Vol-Vol Breakeven (MC Estimation)

I am currently reading the paper Computation of Break-Even for LV and LSV Models. This paper defines the vol-vol breakeven \begin{align*}\tag{1} B_t(T,K,T',K') &\ :=\ d\langle \ln \sigma^{T,K}...
• 1,042
1 vote
227 views

### Arbitrage-Free implied/local volatility surface with Cubic Spline Interpolation

I am trying to create a local volatility surface using a cubic spline interpolated implied volatility surface. In other words, I have a function $\sigma(T,K)$, that is arbitrage-free $\forall T,K$ (...
78 views

### Does Gatheral formula for local volatility translate to a constraint on implied volatility

In Gatheral's "The Volatility Surface : A Practitioner's Guide", Equation (1.10) page 13, the following relation linking squared local volatility and squared implied volatility is expressed :...
• 171
312 views

• 99
1 vote
67 views

### Intuition behind the benefits of Stochastic Local Volatility (SLV) models [duplicate]

There have been various posts on this topic, but they don't really discuss the intuition behind the benefits of the stochastic local volatility (SLV) models over normal stochastic volatility (SV) ...
119 views

### Hagan's 2002 SABR paper "Managing Smile Risk" on Dupire local vol model

I'm reading Hagan's 2002 paper Managing Smile Risk originally published on the WILMOTT magazine, and got something confusing on his comment on Dupire's local volatility model. The set up: Consider a ...
• 2,231
1 vote
53 views

### Change of expansion point for singular perturbation solution in Equivalent Black Volatilities

In the paper Equivalent Black Volatilities, an peturbative solution is derived for the equivalent Black volatility of a vanilla call option under the dynamics $dF_t = a(t) A(F_t) dW_t$ by Taylor ...
• 111
100 views

### What would be the practitioner way of hedging jump risks?

I have developed a keen interest in volatility strategies and have implemented various approaches based on practitioner delta. This delta is meticulously calibrated using a no-arbitrage implied ...
• 43
244 views

### Dupire Formula with Discrete Cash Dividend

For stocks when there is cash dividend, the Dupire formula should still hold according to Bergomi. In the book "Stochastic Volatility Modeling", he says: In the presence of cash-amount ...
• 101
73 views

### Local Volatility Derivation

In Jim Gatheral's book (The Volatility Surface), in the first chapter, it says below while deriving Dupire Equation for Local Volatility. I do not understand how the drift term got removed. Can ...
116 views

### Neural Network to learn Heston Model parameters

I am trying to solve this question: Write down pseudocode to learn a local stochastic volatility for finitely many given option prices: assume a Heston stochastic variance and parametrize local ...
• 43
61 views

### Valuation via decomposition or via simulation of the underlying?

My question might be very straight forward but I have seen both approaches being followed in practice so I am curious to see if there are arguments in favor or against each one. I am explaining my ...
127 views

### Construction of stochastic volatility model from a given local volatility model

The Gyongy's theorem: Let $X_t$ be a stochastic process satisfying $$dX_t = \mu_t dt+\sigma_tdW_t$$ where $\mu_t, \sigma_t$ are bounded stochastic process adapted to the filtration $\mathcal{F}_t$. ...
• 1,033
1 vote
112 views

### From model vega matrix to market vega matrix

I'm reading Antonie Savine's fascinating book Modern Computational Finance AAD and Parallel Simulations. However, I got a bit confused while reading and couldn't make sense of how it works in his work....
• 11
1 vote
86 views

### Questions on limitations of local volatility model

I am currently studying local volatility for equity models and I am trying to understand some limitations of the model: 1. under local volatility, the forward smile gets flatter and higher. Lorenzo ...
103 views

### Good resources about Volatility Calibration with code Snippet

As I just landed in the quantitative finance world, I would like to dig deeper into Volatility Surfaces construction. I have a good theoritical background ( I'm familiar with volatility models ) but I'...
333 views

### Vega hedge of a barrier option

I was re-reading Lorenzo Bergomi's paper Smile Dynamics I. On the first page, he makes the point that it is necessary for a model to match the vanilla smile observed in markets in order to incorporate ...
• 747
252 views

### Pricing Quantos with Local-Stochastic Volatility model

I would like to price equity quanto options with the Heston Local-Stochastic Volatility model (LSV) but I am having hard time understanding how to apply quanto adjustment in such complex setup. When ...
205 views

### Barrier on realized volatility

I am trying to understand the risk exposures of vanilla options that also have a European barrier on realized volatility. For example, the option could knock out if the realized volatility over the ...
• 747
213 views

### Use LocalVolTermStructureHandle in Python QuantLib

I would like to simulate a local volatility underlying $$dS_t = S_t\sigma(t, S_t)dW_t$$ and have looked at QuantLib's LocalVolTermStructureHandle to do so. So far:...
• 21
130 views

### Is the time derivative of asset returns expressible as an SDE?

Consider the following SDE for $(S_t)_{t\geq 0}$ under $\mathbb{Q}$, $$\mathop{dS_t}=S_t\left(r\mathop{dt}+\sigma(t,S_t)\mathop{dW_t}\right),$$ which (in Langevin form) may ...
• 128
164 views

### Quantlib Monte Carlo using regular Volatility Surface, not Local Volatility surface

I am trying to run a Quantlib Python Monte Carlo simulation using either the ql.BlackScholesMertonProcess or the ql.GeneralizedBlackScholesProcess. I have a vol surface that I have generated using ql....
• 31
1 vote
717 views

### Implied volatility to local volatility via Dupire

I am doing some self study on stochastic local volatility modelling and am having a hard time replicating some results from the paper "FX Option Pricing with Stochastic-Local Volatility Model&...
• 11
556 views

### Quantlib vol surface issue 'the black vol surface is not smooth enough'

I create a vol surface from the market and do smoothing(interpolation and extrapolation), and explicitly correct for any total variance decreasing on a given strike as we increase maturity. I create a ...
• 31
1 vote
137 views

### Impact of stochastic rates on varswaps and volswaps

Let us consider that we are looking at issuing some varswaps or volswaps on some FX rate. By longer term I mean something longer than 3 months. Different from this time two years ago, now the interest ...
• 747
1 vote
231 views

### how to understand Black-Scholes volatility is average of local volatilities

Black-Scholes volatility is average of local volatilities. It is from: https://bookdown.org/maxime_debellefroid/MyBook/all-about-volatility.html First what's the meaning of ...
• 545
1 vote
173 views

### Implied volatility from local volatility versus market implied volatility

Does the local volatility flattens the (existing not forward) skew faster than what we observed in the implied volatility surface? The process is: Get market implied volatilities Fit a IV model (i.e. ...
• 11
842 views

### Is Local Volatility a function of the Strike or the Underlying price?

Long story cut short: I am asking why the Local Volatility function can be thought of as a function of the underlying, when in fact it appears to be a function of the strike. Additionally, I wonder ...
• 6,223
93 views

### How do I proceed with pricing after calculating local vol volatilities?

What are the next steps for pricing under the local volatility formula? It feels like I'm missing the trick (as I only see the numerical methods used to obtain prices after calculating local vol). I.e....
311 views

### Very close local volatility and implied volatility using Dupire's equation

I used Dupire's equation to calculate the local volatility as in https://www.frouah.com/finance%20notes/Dupire%20Local%20Volatility.pdf and Numerical example of how to calculate local vol surface from ...
• 61
1 vote
2k views

### How to calculate the local volatility from implied volatility in practice

The local volatility can be derived from the implied volatility. But in practice how we deal with the first-order and second-order derivatives? I have seen this formula  \sigma_{\mathrm{Dup}}(T, K)^{...
• 61
258 views

### Stochastic vs. local volatility model choices for greeks

As a follow-up of another question (which is I feel slightly separate, hence a new question). Assume we want to fit a volatility surface with the goal of calculating good greeks, not prices. We can ...
• 113
298 views

### How to price american barrier with Local-Stochastic Volatility

I have attended a conference where one speaker mentioned that the market standard to price FX and Equity derivatives is now the Local-Stochastic volatility model. I understand this class of model is a ...
• 113
1 vote
233 views

### how to interpolate and extrapolate the local volatility surface?

Local volatility can be computed in terms of call prices using Dupire's formula. Assume we have a rectangle call price surface, let's say $I = [30,60]\times[1 day, 1year]$. For interpolation, should ...
• 170
I am struggling a bit with some basic stuff lately: Consider a SV model \begin{align} dS_t &= \sigma_t S_t dW_t \\ d\sigma_t &= b(\sigma_t,t) dZ_t \end{align} with $dW_t dZ_t = 0$. I know that ...