Modelling in Finance Ongoing BC

Question 1

V

Answer 1

value of an option

Question 2

underlying asset

Answer 2

S. Share price, exchange rate underlying assests have dift & are volatile

Question 3

r

Answer 3

interest rate

Question 4

σ

Answer 4

volatility of underlying assest

measure of uncertainty of the drift

Question 5

drift?

Answer 5

μ

the expected % increase in value over a certain period of time

Question 6

delivery price

Answer 6

F

Question 7

exercise price

Answer 7

X

Question 8

C(s,t)

Answer 8

Call option is a function of value and time.
gives the holder the right to buy assest at T for X
C(s,t) = max( S - X, 0 )

Question 9

P(s,t)

Answer 9

put option is a function of value and time
gives the holder the right to sell assest at T for X.
P(s,t) = max( X - S, 0 )

Question 10

(1 + r/m)^m → ?

Answer 10

e^r

Question 11

a compoundly invested assest A, after t years it is worth?

Answer 11

Value = Aexp(rt) or Aexp( ∫r(t)dt )

Question 12

Put Call parity for european options?

Answer 12

C(s,t) + Xexp( -r(T-t) ) = P(s,t) + S

Question 13

Forward contract?

Answer 13

buyer (long position) agrees to buy an assest at T for F of a seller (short position)

Question 14

stochastic differential ?

Answer 14

S_t+dt - S_t = dS = μdt + σdW

Question 15

Geometric Brownian motion

Answer 15

dS = μSdt + σSdW

Question 16

Itos lemma?

Answer 16

if ds = a(s,t)dt + b(s,t)dW and f(s,t) is suitably differentiable then
dF = [a.∂f/∂s + ∂f/∂t + ½b².∂²f/∂s²]dt + [b.∂f/∂s]dW

Question 17

Θ ?

Answer 17

∂V/∂f

Question 18

ν?

Answer 18

∂V/∂σ

Question 19

ρ?

Answer 19

∂V/∂r

Question 20

Γ?

Answer 20

∂²V/∂s²

Question 21

as dt → 0 ?

Answer 21

dW² → dt

dtdW = o(dt)