# Questions tagged [local-volatility]

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### 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 ...
• 466
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### 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 ...
1 vote
94 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 ...
• 57
360 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
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### how to evaluate numerically the equation of Dupire with the method of Implicit Euler?

I shoud evaluate numerically the equation of Dupire with the method of Implicit Euler and then studying the convergence of the implied volatilities predicted by the model toward those of market to the ...
201 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
74 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 ...
• 785
80 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 ...
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1 vote
90 views

### local volatility not reasonable

We are going to generate synthetic option prices using a Heston model, i.e., $$\begin{gather*} dS_t = \sqrt{v_t} S_t dZ_t,\\ dv_t = \lambda (\mu - v_t) d_t + \eta \sqrt{v_t} dW_t, \end{gather*}$$ ...
1 vote
182 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
153 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 ...
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1 vote
90 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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1 vote
152 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 ...
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### 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 ...
• 121
1 vote
161 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 ...
106 views

• 99
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### 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 ...
• 319
412 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 ...
257 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. ...
818 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 ...
224 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 ...
• 41
1k 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 ...
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