Week 5

Question 1

What is the number of periods for a binomial tree?

Answer 1

n

Question 2

How do you find S(uu)?

Answer 2

Suu

Question 3

How do you calculate multi-period binomial tree?

Answer 3

1. Calculate Suu, Sud and Sdd
2. Calculate Cuu, Cud, and Cdd
3. Calculate Δ and B for u, and also for d (outermost branches)
4. Use to calculate Cu and Cd
5. Use formula to calculate option price

Question 4

Binomial Pricing of American Options

Answer 4

C = max [ S-K, e^(-rh)[C(u)p* + C(d)(1-p*)] ]
P = max [ K-S, e^(-rh)[P(u)p* + P(d)(1-p*)] ]

Question 5

When are a European call option and an American call option the same price?

Answer 5

When there are no dividends

Question 6

Black-Scholes Formula for Stocks

Answer 6

C = Se^(-δT)N(d1) - Ke^(-rT)N(d2)
P = Ke^(-rT)N(-d2) - Se^(-δT)N(-d1)

d1 = [ln(S/K) + (r-δ+0.5σ^2)T] / σsqrt(T)
d2 = d1 - σsqrt(T)

Question 7

BS Options on Stocks with Dividends

Answer 7

S = S(0) - PV(Div)

Question 8

BS Options on Currencies

Answer 8

Prepaid forward = x(0)*e^(-r(f)T)

Question 9

BS Options on Futures

Answer 9

C = F*e^(-rT)N(d1) - Ke^(-rT)N(d2)

d1 = [ln(F/K) + 0.5*(σ^2)*T] / σsqrt(T)
d2 = d1 - σsqrt(T)

Question 10

Delta(Δ) Definition

Answer 10

Change in option price when stock price increases by $1

The number of shares in the portfolio that replicates the option

Question 11

Delta(Δ) Equations (Call and Put)

Answer 11

Δ(Call) = e^(-δT)N(d1)
Δ(Put) = -e^(-δT)N(-d1) = e^(-δT)[1-N(d1)]

Question 12

Gamma Definition

Answer 12

Change in delta when option price increases by $1

Question 13

Vega Definition

Answer 13

Change in option price when volatility increases by 1%

Question 14

Theta Definition

Answer 14

Change in option price when time to maturity decreases by 1 day

Question 15

Rho Definition

Answer 15

Change in option price when interest rate increases by 1%

Question 16

Greek Measure of a Portfolio

Answer 16

The weighted average of Greeks individual portfolio components

Δ(portfolio) = Σω(i)Δ(i)