Option Pricing Model

Question 1

Option

Answer 1

Derivative contract which gives the holder the right (not obligation) to exercise option
Buy (call) or sell (put) the underlying asset for a strike Price K and maturity T (European) or prior to Maturity (American)
Price of contact is non-zero at the start (premium)

Question 2

Put-Call-Parity Relation

Answer 2

Ct - Pt = St - K e* - r ( T-t)
Call - exercise if Market Price > Strike Price
Put - exercise if Strike Price > Market Price

Question 3

Binomial Tree

Answer 3

SN follows a binomial distribution (Bernouille Trials)

Question 4

No arbitrage

Answer 4

RV Y takes value u & d with both positive probability and both in between e*r

Question 5

Replicating PF

Answer 5

pay-off (M * shares of stock); Z is amount invested in bank account) of PF need to match pay-off of Stock Price whatever Stock Price movement is)

Question 6

Risk- Neutral Probability Measure

Answer 6

under no arbitrage -> price of option yielding pay-off at T is independent of the “physical probability” P
Current Stock price already takes into account the probability of it experience an up/downward movement in future
Investor only cares about the expected value of return (not risk)

Question 7

Multi -Step Model

Answer 7

a) using Risk- Neutral Measure (evaluating Q(w1), Q(w2) etc.) multiplying along the tree and ignoring Values in between
b) Decompositing model into N-single market models and solve problem backwards in tie with each having a sub-problem (and thus evaluating price at each step)