December 2015
Intermediate to advanced
522 pages
20h
English
Content preview from Stochastic Volatility Modeling
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
Local volatility 85
2.9.2 Calibration and its meaningfulness
What do we do once we have the hedge portfolio
Π
? Can we use it in practice?
Consider a constant volatility
bσ
0
and call
P
0
the corresponding Black-Scholes
price. Let us assume that the market smile is not too strong so that
bσ
Kτ
−bσ
0
is small.
Using the above results and expanding at order one in bσ
Kτ
− bσ
0
:
P = P
0
+
Z
T
0
dτ
Z
∞
0
dK µ (τ, K)
C
Kτ
− C
0
Kτ
(2.124)
where
C
0
Kτ
is the Black-Scholes price with volatility
bσ
0
and
C
Kτ
the market price
of the vanilla option of strike K, maturity τ.
(2.124) can be interpreted as expressing the following:
26
•
Choose an implied volatility
bσ
0
for risk-managing the exotic option. ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.