Week 4

Question 1

Payoff/Profit Call Option

Answer 1

Long:
Payoff = max[0, spot price at exp. - strike price]
Profit = payoff - FV(premium)
Shape: middle down then up

Short:
Payoff = - max[0, spot price at exp. - strike price]
Profit = payoff + FV(premium)
Shape: middle up then down

Mirror images: Long calls are “tall” at end

Question 2

Payoff/Profit Put Option

Answer 2

Long:
Payoff = max[0, strike price - spot price at exp.]
Profit = payoff - FV(premium)
Shape: up then middle down

Short:
Payoff = - max[0, strike price - spot price at exp.]
Profit = payoff + FV(premium)
Shape: down then middle up

Mirror images: Long puts are “tall” at beginning (at payoff axis)

Question 3

Learn effect of variables (stock price, strike price, time to maturity, volatility, dividend, and interest rate) on option prices

Answer 3

↑Stock price => ↑Call price (opposite P)
↑r => ↑Call price (opposite P) (not as strong of effect)

↑K => ↓Call price (opposite P)
↑Div => ↓Call price (opposite P)

↑σ => ↑ all option prices

Question 4

European vs. American Options Prices

Answer 4

C(Amer) >= C(Eur)

P(Amer) >= P(Eur)

Question 5

Lower Bound of Option Prices

Answer 5

C(Eur) >= max[0, PV(F) - PV(K)]

C(Eur) >= max [S(t) - K]

Question 6

Binomial Pricing Model Assumption

Answer 6

Assumes that the price of the underlying asset follows a binomial distribution

Question 7

No Arbitrage Condition in Binomial Pricing

Answer 7

u > e^([r-δ)*h] > d

Question 8

h equation

Answer 8

T/n