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A Difference between Local Vol and Stochastic Vol Models

For the purpose of this question a local vol model is a 1d SDE which specifies the price process and we have a contingent claim that depends on those prices (in general, at multiple times). e.g. ...
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2answers
113 views

Why dynamics of local volatility is wrong?

In Dupire's local volatility model, the volatility is is a deterministic function of the underlying price and time, chosen to match observed European option prices. To be more specific, given a ...
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1answer
128 views

Local volatility SVI parametrization

In this paper Gatheral presents the following parametrization of the implied total variance $w(k,T) = \sigma_{BS}(k,T)^2T$ for each slice $k \mapsto w(k,T)$: $$ w(k) = a + b\{\rho (k-m) + ...
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4answers
111 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 ...
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0answers
35 views

Stochastic Volatility in current market environment

Some price exotics with stochastic vol, some use other models such as local vol. What is the impact/advantage/disadvantage of using stochastic volatility in the current market environment? In other ...
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1answer
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In Dupire's paper, why is $(S_t, t)$ in the $(K, T)$ space?

I'm new to local volatility model. From Dupire's paper and most of the textbooks, they derived the local volatility $\sigma(K, T)$ in the $(K, T)$ (i.e., strike and maturity) space, from call prices ...
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2answers
122 views

Time-independent local volatility

Suppose somebody provides us with a surface of European call prices $C(\tau,K)$ where $\tau$ stands for time-to-maturity and $K$ for the strike. By Dupire's results, there is a unique local volatility ...
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2answers
127 views

Dupire model and Local Volatility model

In the context of Option pricing model. Is there a difference between the Dupire Model and the Local volatility model ? Thanks Achal
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2answers
186 views

How to estimate the greeks with a Monte Carlo simulation?

I am simulating the path of three indices to price a 1 year basket option. All the indices are domestic, so there is no currency component. At each time step I am using the local volatility ...
0
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1answer
110 views

Black-box local volatility pricer

I am testing a local volatility pricer by comparing its results under two settings: Pricing a 5yr ATM call option with a flat volatility of $0.194$ Pricing the call option with the typically shaped ...
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0answers
159 views

Which size of constant range bar gives the most persistent chart?

A constant range bar chart is like a candle chart, only the candles don't close after a certain amount of time (i.e. 30 min, 4 hours), but after a certain range (i.e. 5 ticks) has been crossed. So if ...
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2answers
143 views

What information about the stochastic process is available from path-dependent options?

Assume the stock follows a process, which is defined by the following stochastic differential equation $$\frac{dS}{S}=r(t)dt+\sigma(S,t)dW,$$ so that the stock price process has local volatility. ...
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0answers
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For pricing, what types of Exotic Options are suitable using Local Volatility Model / Stochastic Volatility Model?

I understand that Stochastic Vol Models should be used when Exotic Option payoff is Volatility dependent (such as Variance Swaps and Volatility Swaps). Stochastic Vol Models should also be used when ...
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2answers
4k views

What causes the call and put volatility surface to differ?

I currently have a local volatility model that uses the standard Black Scholes assumptions. When calculating the volatility surface, what causes the difference between the call volatility surface, ...
6
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2answers
1k views

Recommendation for a library to calculate the local volatility surface?

I'd like a library to calculate the options local volatility surface, i.e. the options implied volatility surface for a collection of strikes and their bid/ask prices. Here are the libraries I've ...
8
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1answer
422 views

What are the main differences in Jump Volatility and Local Volatility

Is a JV model simply Local Vol + Jump Diffusion? If so, it seems logical that an existing JV model be able to be used for valuation of both Vanilla and Exotic options. Is this true? Does a Local ...
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4answers
2k 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?