Stoch Proc -Assignment Hints

Scott Alexander

Question 1

(a)

(b)

Look at TNC from Ch 2.

(c)

Look at TNC from Ch 2.

(d)

See page 45 from Ch 3.

Question 2

(a)

Simplify using independence property.

(b)

See Def 9 Ch 4.

Question 3

(a)

See previous Lab work for MC pricing.

(a)

See previous Lab work for MC pricing.

Question 4

(a)

Use network diagram to find (P^jump) and then A.

cov((Subscript[X, 3]),(Subscript[X, 30])) = 𝔼[(Subscript[X, 3])(Subscript[X, 30])]-𝔼[(Subscript[X, 3])]𝔼[(Subscript[X, 30])].

For 𝔼[(Subscript[X, 3])] you need p(3).

For 𝔼[(Subscript[X, 3])(Subscript[X, 30])] you need P((Subscript[X, 3])<x,(Subscript[X, 30])<y) -- see Thrm 4 Ch 5.

(d)

See previous lab work.

Use independence property of (Subscript[B, t]),(Subscript[N, t]).

Question 5

(a)

Check stationarity condition and then determine type of process.

(c)

Check condtion page 31 Ch 8.

Question 6

(a)

Find recursion relationship for (Subscript[X, t+h]) and (Subscript[X, t]).

Then apply condition (re-write condtion in terms of (Subscript[B, t])).

(c)

Refer Lab work on OU process.

(d)

Use Ito.