1. No category

Computational Finance - Forward pricing
Lina von Sydow, Josef Höök, Elisabeth Larsson, Slobodan
Milovanoviç, Victor Shcherbakov
Option pricing
∂u
1
∂2u
∂u
+ rs
+ σs 2 2 − ru = 0,
∂t
∂s
2
∂s
Forward
PCA
u(T , s) = φ(s).
L. von Sydow, MSc Projects Sep 2015
(1 : 2)
Computational Finance - Forward pricing
Lina von Sydow, Josef Höök, Elisabeth Larsson, Slobodan
Milovanoviç, Victor Shcherbakov
Option pricing
∂u
1
∂2u
∂u
+ rs
+ σs 2 2 − ru = 0,
∂t
∂s
2
∂s
Forward
PCA
u(T , s) = φ(s).
∂p
1 ∂ σ2 s 2 p
∂ (rsp)
−
+
= 0,
∂t
2
∂s 2
∂s
p(s, 0) = δ(s0 − s).
u(K , T ) = e
−rT
Z
p(s, T )φ(s, K , T )ds
s∈R+
COS, FD, RBF, RBF-PUM, RBF-FD,...
L. von Sydow, MSc Projects Sep 2015
(1 : 2)
Computational Finance - PCA
Lina von Sydow, Josef Höök, Slobodan Milovanoviç, Per
Lötstedt
Option pricing
Forward
d
d
X
∂u
1 X
∂2u
∂u
+r
si
+
ρij σi σj si sj
− ru = 0
∂t
∂si
2
∂si ∂sj
i=1
i,j=1
PCA
L. von Sydow, MSc Projects Sep 2015
(2 : 2)
Computational Finance - PCA
Lina von Sydow, Josef Höök, Slobodan Milovanoviç, Per
Lötstedt
Option pricing
Forward
d
d
X
∂u
1 X
∂2u
∂u
+r
si
+
ρij σi σj si sj
− ru = 0
∂t
∂si
2
∂si ∂sj
i=1
i,j=1
PCA
d
∂u
1 X ∂2u
+
λi 2 − ru = 0
∂t
2
∂ xi
i=1
u≈u
(1)
+
d
X
i=2
∂u λi
∂λi λ̄(1)
L. von Sydow, MSc Projects Sep 2015
(2 : 2)
Computational Finance - PCA
Lina von Sydow, Josef Höök, Slobodan Milovanoviç, Per
Lötstedt
Option pricing
Forward
d
d
X
∂u
1 X
∂2u
∂u
+r
si
+
ρij σi σj si sj
− ru = 0
∂t
∂si
2
∂si ∂sj
i=1
i,j=1
PCA
European Call Basket Option
d
3
∂u
1 X ∂2u
+
λi 2 − ru = 0
∂t
2
∂ xi
2.5
12
i=1
10
i=2
∂u λi
∂λi λ̄(1)
2
8
s3
u ≈ u (1) +
d
X
1.5
6
4
1
2
u ≈ u (1,2) +
d
X
i=3
λi
∂u ∂λi λ̄(1)
L. von Sydow, MSc Projects Sep 2015
(2 : 2)
0
0
0
2
0.5
4
6
5
8
10
s2
10
12
s1
0