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What is “Lambda” in Heston's original paper on stochastic volatility models?

2

1

$begingroup$

In his paper (link), he has the equations:

b1 = k + ƛ - (ρ * σ)

b2 = k + ƛ

k is the rate of mean reversion, ρ is the correlation between the two Wiener processes, σ is vol of vol, what is ƛ?

I have yet to figure out what ƛ is.

Thanks!

options stochastic-processes

share|improve this question

edited 2 days ago

Alex C

6,74211123

asked 2 days ago

vt_ogvt_og

233

$endgroup$

add a comment | 

2

1

$begingroup$

In his paper (link), he has the equations:

b1 = k + ƛ - (ρ * σ)

b2 = k + ƛ

k is the rate of mean reversion, ρ is the correlation between the two Wiener processes, σ is vol of vol, what is ƛ?

I have yet to figure out what ƛ is.

Thanks!

options stochastic-processes

share|improve this question

edited 2 days ago

Alex C

6,74211123

asked 2 days ago

vt_ogvt_og

233

$endgroup$

add a comment | 

$begingroup$

In his paper (link), he has the equations:

b1 = k + ƛ - (ρ * σ)

b2 = k + ƛ

k is the rate of mean reversion, ρ is the correlation between the two Wiener processes, σ is vol of vol, what is ƛ?

I have yet to figure out what ƛ is.

Thanks!

options stochastic-processes

share|improve this question

edited 2 days ago

Alex C

6,74211123

asked 2 days ago

vt_ogvt_og

233

$endgroup$

share|improve this question

edited 2 days ago

Alex C

6,74211123

asked 2 days ago

vt_ogvt_og

233

share|improve this question

edited 2 days ago

Alex C

6,74211123

asked 2 days ago

vt_ogvt_og

233

edited 2 days ago

Alex C

6,74211123

edited 2 days ago

Alex C

6,74211123

asked 2 days ago

vt_ogvt_og

233

asked 2 days ago

vt_ogvt_og

233

2 Answers
2

active

oldest

votes

3

$begingroup$

It is on page 329 (which is the third page of the article) and represents the market price of volatility risk. I have copied below from the original article:

share|improve this answer

answered 2 days ago

Magic is in the chainMagic is in the chain

1,20915

$endgroup$

add a comment | 

1

$begingroup$

That is the "price of volatility risk" (see Page 329)

When volatility can change the "attitude" of investors to these changes becomes important for pricing options. This like/dislike for vol increases is captured in the parameter $lambda$. In practice vol goes up i.e. $dv$ is positive, in bad economic times, such as recessions, when $dC$ is negative. So $lambda$ is negative.

share|improve this answer

edited yesterday

answered 2 days ago

Alex CAlex C

6,74211123

$endgroup$

add a comment | 

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3

$begingroup$

It is on page 329 (which is the third page of the article) and represents the market price of volatility risk. I have copied below from the original article:

share|improve this answer

answered 2 days ago

Magic is in the chainMagic is in the chain

1,20915

$endgroup$

add a comment | 

3

$begingroup$

It is on page 329 (which is the third page of the article) and represents the market price of volatility risk. I have copied below from the original article:

share|improve this answer

answered 2 days ago

Magic is in the chainMagic is in the chain

1,20915

$endgroup$

add a comment | 

$begingroup$

It is on page 329 (which is the third page of the article) and represents the market price of volatility risk. I have copied below from the original article:

share|improve this answer

answered 2 days ago

Magic is in the chainMagic is in the chain

1,20915

$endgroup$

share|improve this answer

answered 2 days ago

Magic is in the chainMagic is in the chain

1,20915

answered 2 days ago

Magic is in the chainMagic is in the chain

1,20915

answered 2 days ago

Magic is in the chainMagic is in the chain

1,20915

1

$begingroup$

That is the "price of volatility risk" (see Page 329)

When volatility can change the "attitude" of investors to these changes becomes important for pricing options. This like/dislike for vol increases is captured in the parameter $lambda$. In practice vol goes up i.e. $dv$ is positive, in bad economic times, such as recessions, when $dC$ is negative. So $lambda$ is negative.

share|improve this answer

edited yesterday

answered 2 days ago

Alex CAlex C

6,74211123

$endgroup$

add a comment | 

1

$begingroup$

That is the "price of volatility risk" (see Page 329)

When volatility can change the "attitude" of investors to these changes becomes important for pricing options. This like/dislike for vol increases is captured in the parameter $lambda$. In practice vol goes up i.e. $dv$ is positive, in bad economic times, such as recessions, when $dC$ is negative. So $lambda$ is negative.

share|improve this answer

edited yesterday

answered 2 days ago

Alex CAlex C

6,74211123

$endgroup$

add a comment | 

$begingroup$

That is the "price of volatility risk" (see Page 329)

When volatility can change the "attitude" of investors to these changes becomes important for pricing options. This like/dislike for vol increases is captured in the parameter $lambda$. In practice vol goes up i.e. $dv$ is positive, in bad economic times, such as recessions, when $dC$ is negative. So $lambda$ is negative.

share|improve this answer

edited yesterday

answered 2 days ago

Alex CAlex C

6,74211123

$endgroup$

share|improve this answer

edited yesterday

answered 2 days ago

Alex CAlex C

6,74211123

answered 2 days ago

Alex CAlex C

6,74211123

answered 2 days ago

Alex CAlex C

6,74211123