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16
votes
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?
8
votes
1answer
447 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 ...
7
votes
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
votes
2answers
222 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 ...
6
votes
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 ...
5
votes
2answers
200 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 ...
3
votes
2answers
127 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 ...
3
votes
1answer
72 views

Numerical example of how to calculate local vol surface from IV surface

I'm looking for an excel example (not a copy of Dupire's eqn) of how to convert an IV surface to a local vol surface. If unsuccessful I'll work through Dupire's eqn but would be helpful to look at an ...
3
votes
1answer
83 views

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 ...
2
votes
2answers
87 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 ...
2
votes
2answers
147 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. ...
2
votes
1answer
181 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) + ...
2
votes
4answers
174 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
vote
2answers
154 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
1
vote
0answers
222 views

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 ...
0
votes
1answer
62 views

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. ...
0
votes
1answer
118 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 ...
0
votes
1answer
64 views

Local volatility parametrization using the spot

Is it possible to estimate the local volatility using the spot price S at time t instead of the strike price K and the expiry date T ? Any help would be appreciated.
0
votes
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 ...
0
votes
0answers
184 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 ...
-1
votes
0answers
33 views

Local volatility computing

I am trying to compute local volatility using dupire formula after interpolating the implied volatility using a cubic spline. Unfortunaly, I get some negative local volatilities. How can I solve this ...