December 2013
Intermediate to advanced
484 pages
14h 54m
English
Content preview from Nonlinear Option Pricing
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202 The Uncertain Lapse and Mortality Model
we define u (t
k
, ·) = max
b
i
>x
u
b
i
(t
k
, ·), and
λ
L,p
t
k
=
(
λ
L,p
(t
k
) if u
L,p
t
k
− u
p
t
k
≥ 0
λ
L,p
(t
k
) otherwise
λ
D,p
t
k
=
(
λ
D,p
(t
k
) if u
D,p
t
k
− u
p
t
k
≥ 0
λ
D,p
(t
k
) otherwise
b
∗
(t
k
, ·) = arg max
b
i
>x
u
b
i
(t
k
, ·)
so that we are now able to estimate u(t
k−1
, ·), etc. At the end of the backward
induction, all λ
L
t
k
, λ
D
t
k
, and b
∗
(t
k
, ·) have been estimated as functions of the
regressors, we simulate N
2
new independent paths and compute
1
N
2
N
2
X
p=1
X
t
j
>0
D
0t
j
C
p
t
j
with
C
p
t
j
= 1
E
p,b
i
t
j
¯
C
p
t
j
¯
C
p
t
j
= N
p
t
j
C
c,p
t
j
+N
p
t
j−1
1 − exp
−λ
L,p
t
j
∆t
j
exp
−λ
L,p
t
j
∆t
j
C
L,p
t
j
+N
p
t
j−1
1 − exp
λ
D,p
t
j
∆t
j
C
D,p
t
j
E
p,b
i
t
j
=
n
∀t
l
∈ [t
1
, t
j−1
] ∩ [T
UO
, ∞), X
p
t
l+1
≤ b
∗
(t
l
, ·)
o
∩
X
p
t
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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.