Option Pricing and valuation

Question 1

Why do option prices rise during a share price drop?

Answer 1

Implied volatility rises → market expects larger moves → higher option premiums.

Question 2

Futures vs. OTC forwards?

Answer 2

Futures = standardised and low risk. Forwards = customised and higher counterparty risk.

Question 3

Why does an ATM option still have value?

Answer 3

Time value — chance the option moves ITM before expiry.

Question 4

Why are option payoffs non-linear?

Answer 4

Small price moves → large option payoffs. This asymmetry is attractive.

Question 5

What is the put-call parity equation?

Answer 5

C + PV(K) = P + S. If violated → arbitrage opportunity.

Question 6

Valuing European vs. American options in binomial trees?

Answer 6

For European: simple backward valuation. For American: must check for early exercise.

Question 7

What does risk-neutral mean in option pricing?

Answer 7

Assume investors are indifferent to risk → assets grow at risk-free rate → arbitrage-free pricing.

Question 8

What are the Greeks?

Answer 8

• Delta = price sensitivity
• Gamma = sensitivity of Delta
• Theta = time decay
• Vega = volatility sensitivity
• Rho = interest rate sensitivity

Question 9

What does Delta tell us?

Answer 9

How much an option’s price changes per $1 change in stock price.

Question 10

What is Gamma?

Answer 10

Sensitivity of Delta → helps manage dynamic hedging.

Question 11

What is Theta?

Answer 11

Time decay of option value → bad for buyers, good for sellers.