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What's the point of stochastic volatiliy models if you can use local volatility?

For pricing, what types of Exotic Options are suitable using Local Volatility Model or a Stochastic Volatility Model?A Difference between Local Vol and Stochastic Vol ModelsImplied volatility as price transformHow to use a stochastic volatility model to price a quanto optionLocal Stochastic Volatility - Break even levelsProblems with local volatility models (vs stochastic volatility models)Vega of exotic optionsMixed local-stochastic volatility model in QuantlibLSV model calibration with only few quotes per maturityWhy can't we create a “magic” basket of options to sell for no-arbitrage pricing in SVJ model?

1

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Given known call option prices, there is a unique local volatility function consistent with those prices.

So why use stochastic volatility models? We can use the market to find local volatility, and then that's our model, no?

Why do we need to complicate things by introducing a stochastic volatility model?

Doesn't that also mean that we need to find a model that produces the same local volatility given by Dupire's equation, since otherwise it would not match the market prices. How is there any guarantee it does that?

stochastic-volatility

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asked 8 hours ago

BalaBala

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1

$begingroup$

Given known call option prices, there is a unique local volatility function consistent with those prices.

So why use stochastic volatility models? We can use the market to find local volatility, and then that's our model, no?

Why do we need to complicate things by introducing a stochastic volatility model?

Doesn't that also mean that we need to find a model that produces the same local volatility given by Dupire's equation, since otherwise it would not match the market prices. How is there any guarantee it does that?

stochastic-volatility

share|improve this question

asked 8 hours ago

BalaBala

611 bronze badge

New contributor

Bala is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

Given known call option prices, there is a unique local volatility function consistent with those prices.

So why use stochastic volatility models? We can use the market to find local volatility, and then that's our model, no?

Why do we need to complicate things by introducing a stochastic volatility model?

Doesn't that also mean that we need to find a model that produces the same local volatility given by Dupire's equation, since otherwise it would not match the market prices. How is there any guarantee it does that?

stochastic-volatility

share|improve this question

asked 8 hours ago

BalaBala

611 bronze badge

New contributor

Bala is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|improve this question

asked 8 hours ago

BalaBala

611 bronze badge

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Bala is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

asked 8 hours ago

BalaBala

611 bronze badge

New contributor

Bala is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 8 hours ago

BalaBala

611 bronze badge

New contributor

Bala is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 8 hours ago

BalaBala

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1 Answer
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Well, what you find is that the introduction of stochastic vol changes the delta of your options. So what does this mean? If the new delta reduces the variance of your hedged portfolio versus the pure local vol model , then it means that the introduction of stochastic vol has resulted in a better description of market dynamics versus the pure local vol model.

Secondly, what you also find is that you can have different models all of which reprice the vanilla options, but that some exotic options have very different prices in the different models. For example , the introduction of stochastic vol can be done in a way that preserves the vanilla option prices , but it lowers the value of forward implied volatilities in the model versus a simple local vol model. Thus, exotics that depend on forward vols ( cliques, Bermudan etc) are priced very differently. Hence another reason to introduce stochastic vol is to improve the pricing of exotics, given the vanilla market.

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answered 3 hours ago

dm63dm63

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3

$begingroup$

Well, what you find is that the introduction of stochastic vol changes the delta of your options. So what does this mean? If the new delta reduces the variance of your hedged portfolio versus the pure local vol model , then it means that the introduction of stochastic vol has resulted in a better description of market dynamics versus the pure local vol model.

Secondly, what you also find is that you can have different models all of which reprice the vanilla options, but that some exotic options have very different prices in the different models. For example , the introduction of stochastic vol can be done in a way that preserves the vanilla option prices , but it lowers the value of forward implied volatilities in the model versus a simple local vol model. Thus, exotics that depend on forward vols ( cliques, Bermudan etc) are priced very differently. Hence another reason to introduce stochastic vol is to improve the pricing of exotics, given the vanilla market.

share|improve this answer

answered 3 hours ago

dm63dm63

8,08311 gold badge99 silver badges3333 bronze badges

$endgroup$

add a comment | 

3

$begingroup$

Well, what you find is that the introduction of stochastic vol changes the delta of your options. So what does this mean? If the new delta reduces the variance of your hedged portfolio versus the pure local vol model , then it means that the introduction of stochastic vol has resulted in a better description of market dynamics versus the pure local vol model.

Secondly, what you also find is that you can have different models all of which reprice the vanilla options, but that some exotic options have very different prices in the different models. For example , the introduction of stochastic vol can be done in a way that preserves the vanilla option prices , but it lowers the value of forward implied volatilities in the model versus a simple local vol model. Thus, exotics that depend on forward vols ( cliques, Bermudan etc) are priced very differently. Hence another reason to introduce stochastic vol is to improve the pricing of exotics, given the vanilla market.

share|improve this answer

answered 3 hours ago

dm63dm63

8,08311 gold badge99 silver badges3333 bronze badges

$endgroup$

add a comment | 

$begingroup$

Well, what you find is that the introduction of stochastic vol changes the delta of your options. So what does this mean? If the new delta reduces the variance of your hedged portfolio versus the pure local vol model , then it means that the introduction of stochastic vol has resulted in a better description of market dynamics versus the pure local vol model.

Secondly, what you also find is that you can have different models all of which reprice the vanilla options, but that some exotic options have very different prices in the different models. For example , the introduction of stochastic vol can be done in a way that preserves the vanilla option prices , but it lowers the value of forward implied volatilities in the model versus a simple local vol model. Thus, exotics that depend on forward vols ( cliques, Bermudan etc) are priced very differently. Hence another reason to introduce stochastic vol is to improve the pricing of exotics, given the vanilla market.

share|improve this answer

answered 3 hours ago

dm63dm63

8,08311 gold badge99 silver badges3333 bronze badges

$endgroup$

share|improve this answer

answered 3 hours ago

dm63dm63

8,08311 gold badge99 silver badges3333 bronze badges

answered 3 hours ago

dm63dm63

8,08311 gold badge99 silver badges3333 bronze badges

answered 3 hours ago

dm63dm63

8,08311 gold badge99 silver badges3333 bronze badges