Questions tagged [local-volatility]
The local-volatility tag has no usage guidance.
192
questions
1
vote
0
answers
50
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) ...
1
vote
0
answers
64
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 ...
- 2,211
0
votes
1
answer
21
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 ...
- 101
0
votes
0
answers
74
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
0
votes
0
answers
97
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
0
votes
0
answers
42
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 ...
- 1
0
votes
0
answers
83
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
0
votes
0
answers
54
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 ...
- 1
3
votes
0
answers
85
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 $\mathcal{F}_t$.
...
- 1,009
0
votes
0
answers
168
views
Barrier options in LSV (local stochastic volatility) / Austing's Smile pricing explained
In his book (chapters 9.5 to 9.7), Peter Austing argues that barrier options are insensitive to the details of the stochastic volatility model used in a LSV model, except for the level of vol of vol. ...
- 1
1
vote
0
answers
72
views
local volatility formula
I try to compute the local volatility in python in both formula, i.e. in terms of call price surface and total variance surface.
However, I get 2 different values. What did I do wrong?
...
- 180
2
votes
0
answers
90
views
Calibration of LSV models to vanna/volga break-even
In this paper, Labordère, the author computes a probabilistic representation of the the vanna/vomma(volga) break-even levels. He mentions that they can be used to calibrate LSV models to historical ...
- 71
1
vote
0
answers
75
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
0
answers
77
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 ...
2
votes
0
answers
92
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'...
4
votes
1
answer
253
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
2
votes
1
answer
153
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 ...
- 21
2
votes
0
answers
129
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
2
votes
2
answers
147
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
2
votes
0
answers
121
views
Is the time derivative of asset returns expressible as an SDE?
Consider the following SDE for $(S_t)_{t\geq 0}$ under $\mathbb{Q}$,
\begin{equation}
\mathop{dS_t}=S_t\left(r\mathop{dt}+\sigma(t,S_t)\mathop{dW_t}\right),
\end{equation}
which (in Langevin form) may ...
- 128
0
votes
0
answers
31
views
How can I use SPX options volatility surface to derive SPY options prices? [duplicate]
I am trying to figure out what is the correct procedure one can use to derive the prices from SPY options given the prices of SPX options.
- 190
0
votes
0
answers
116
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
0
answers
363
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
0
votes
0
answers
177
views
Quantlib Local-Volatility Code
I use QL in python and have had a few questions about how a vol surface is transformed into a local volatility surface. Would anybody be able to point me to the C++ code that does this transformation?
...
- 31
3
votes
1
answer
358
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
1
answer
113
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
0
answers
148
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
0
answers
127
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
4
votes
2
answers
594
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 ...
- 5,998
2
votes
0
answers
74
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....
- 152
5
votes
0
answers
220
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
2
answers
1k
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
0
votes
0
answers
179
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
0
votes
0
answers
236
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
0
answers
178
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 ...
- 180
0
votes
1
answer
79
views
Adequate model to payoff
Consider a payoff that pays a certain amount N of a vanilla Call (underlying: S, Maturity= T, strike:K). Every semester date Ts before T, if S>K(Ts), then N is increased by 1.
This product seems ...
- 365
5
votes
1
answer
223
views
Independence vs correlation in stochastic vol models
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 ...
user34971
4
votes
2
answers
641
views
Introductory material for getting started with local and stochastic volatility modelling
Are you able to provide some suggestions for resources to get started with non-flat volatility modelling? The models I am interested in are the likes of CEV, Heston, SABR etc.
I have tried looking ...
- 152
4
votes
1
answer
2k
views
When to use a Local Vol model vs Stochastic Vol Model?
I'm new to volatility modeling, I'm struggling to understand when to use a Local Vol model and when to use Stochastic Vol Model, Also now we use a hybrid model combining the two models ? Can someone ...
- 616
2
votes
0
answers
393
views
Local volatility implied spot vol correlation
I have a question about local volatility models.
In a lot of articles it is stated that the implied spot vol correlation of this model is -1 and we usually compare this with stochastic volatility ...
- 21
1
vote
1
answer
822
views
Calibration and pricing with the Stochastic Local Volatility model
I'm reading the stochastic local volatility model literature, e.g., the Heston Stochastic Local Volatility model (https://ir.cwi.nl/pub/22747/22747D.pdf); but I'm a bit unsure about its calibration ...
- 301
4
votes
2
answers
454
views
Transformation of local volatility model
Assume we have an SDE
$$dX_t=\mu(X_t)dt + \sigma(X_t)dW_t$$
where $\sigma>0$ and $W_t$ is a Wiener process. Is there a transformation $y(X_t)$ that will make the dynamics of the transformed process ...
- 43
2
votes
2
answers
885
views
Local Vol vs Stoch Vol Option Pricing
This is an interview question:
Imagine you have a double knock-out barrier option: the current spot is 100, the lower barrier is 80, and upper barrier is 120. The barrier is continuous, meaning that ...
- 21
2
votes
0
answers
151
views
Implied Volatility is the harmonic average of Local Volatility
I am trying to demonstrate the famous result that states that when $T \rightarrow 0$, the Implied Volatility is the harmonic average of Local Volatility.
I am st the final stage, and I have the ...
- 853
5
votes
0
answers
196
views
Closed formula for computing Implied Volatility from Local Volatility function
The main result of this paper (Asymptotics and Calibration in Local Volatility Models, Berestycki, Busca, and Florent. Quantitative Finance, 2002) is equation (16) on page 63, that states that:
In the ...
- 853
1
vote
0
answers
104
views
local volatility not reasonable
We are going to generate synthetic option prices using a Heston model, i.e.,
$$
\begin{gather*}
dS_t = \sqrt{v_t} S_t dZ_t,\\
dv_t = \lambda (\mu - v_t) d_t + \eta \sqrt{v_t} dW_t,
\end{gather*}
$$
...
- 11
1
vote
1
answer
413
views
Monte Carlo: How to interpolate Dupire's Local Volatility
I am trying to price barrier options which can have daily or monthly observations. I first calibrated by Black vols into smooth SVI vols (with linear interpolation along time in variance) to obtain ...
- 11
2
votes
1
answer
260
views
Dupire's Formula by a Replicating Portfolio
I understand that the BS equation can be explained by a replicating portfolio, e.g., short an option and long $\Delta$ shares of the underlier [Bergomi's Stochastic Volatility Modeling]. I also ...
- 301
1
vote
1
answer
352
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....
- 853
1
vote
1
answer
736
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 ...
- 853