Week 6

Question 1

Implied Volatility Definition

Answer 1

The volatility that, when put into a pricing formula (typically Black-Scholes), yields the observed option price

Question 2

Volatility Smile

Answer 2

When volatility is symmetric, with volatility lowest for at-the-money options, and higher for in-the-money options and out-of-the-money options

Question 3

Volatility Skew

Answer 3

The difference in volatilities between in-the-money and out-of-the-money options

Question 4

How is implied volatility calculated?

Answer 4

It is calculated by trial and error. We test in a systematic way different volatilities until we find the one that gives the option price when it is substituted into the Black–Scholes formula.

Question 5

Perpetual American Options

Answer 5

They have infinite maturity

They are exercised when the underlying asset reaches the option exercise barrier H(c) or H(p) (for call and put respectively)

Question 6

NPV Rule

Answer 6

Accept project <=> NPV+ and NPV>NPV of all other mutually exclusive alternative projects

Question 7

Perpetuity - Definition and Equation

Answer 7

Constant steam of identical cash flows

PV = C/(1+r) + C/(1+r)^2 + … = C/r

Question 8

Perpetuity with Constant Growth Equation

Answer 8

PV = C/(1+r) + [C(1+g)]/(1+r)^2 + [C(1+g)^2]/(1+r)^3 + … = C/(r-g)

Question 9

How to Treat Project like Option to Find Optimal Time to Invest

Answer 9

Note: σ = 0.00001 -> no uncertainty

1. Price = price of perpetual American call option (formula sheet)
2. Hc = w/(r-g) => w = … (start investing in project when price grows to w)
3. initial price * (1+g)^n = w, solve for n