and the solution of equation (13) for u(t,x) is (see Appendix)
u(t,x1,x2 )
Xi exp ^-x2 J^ λ1 ∖s)ds)
exp ɑʃ (—λ^2∖r) σy (r) + b(r)^ ^ʃ — ʌɑ∖s)ds) dr)
Hence, Ft is given by
Ft = It exp -~σt ʃ ʌɑ∖s)ds^
exp
exp
^- ʃ (—λ^2∙∖r) σ'^ (r) + b(rɔ ^ʃ ʌɑ∖s)ds) dr)
( f T1 σ (r))2f f ∖s>y dr} , 0 ≤ t ≤ T,
and
Z' = (⅞> )= F ' —'σ'(t)ʃ, <∙ >(^)ds )
The forward price of the asset can be rewritten as
dF = Ftσf (√1 — pt2λ<1 ∖t) + У2∖t)pi)dt
+Ftσξ (√1 — pt2dWt1 + pt dWt, 0 ≤ t ≤ T,
(14)
with
Fiσf := ∖∕(Z<1 >)2 + (Z,<2 <
and
F
.
1∕(zl<'> )2+ (zy)2
(15)
17