Other questions based on the Formula Sheet

Question 1

Which position benefits from an increase in the asset price?

Answer 1

Long position

Question 2

Which position benefits from an decrease in the asset price?

Answer 2

Short position

Question 3

True or false : the profit on a zero-couon bond = 0?

Answer 3

TRUE

Question 4

If I buy a risk-free ZCB, what is the equivalent between borrowing or lending at the risk-free rate?

Answer 4

Lending

Question 5

What is the max gain, the max loss and the strategy behind buying a Forward?

Answer 5

Max gain : Infinite
Max loss : Forward price
Strategy : Lock in purchase price for the underlying asset.

Question 6

What is the max gain, the max loss and the strategy behind selling (shorting) a Forward?

Answer 6

Max gain : Forward price
Max loss : Infinite
Strategy : Lock in sale price for the underlying asset.

Question 7

What is the max gain, the max loss and the strategy behind buying a call?

Answer 7

Max gain : Infinite
Max loss : Accumulated Value of call premium
Strategy : Insurance against high underlying price

Question 8

What is the max gain, the max loss and the strategy behind shorting a call?

Answer 8

Max gain : Accumulated value of call premium
Max loss : Infinite
Strategy : Selling insurance against high underlying price

Question 9

What is the max gain, the max loss and the strategy behind buying a put?

Answer 9

Max gain : Strike price - AV(premium)
Max loss : Accumulated value of put premium
Strategy : Insurance against low underlying price

Question 10

What is the max gain, the max loss and the strategy behind shorting a put?

Answer 10

Max gain : Accumulated value of put premium
Max loss : Strike price - AV(premium)
Strategy : Selling insurance against low underlying price

Question 11

Why would you use a floor and what is the formula for a floor?

Answer 11

Floor = long put + long stock

Guarantees minimum selling price for the asset

Question 12

What combination of option/asset would you use to write a covered put?

Answer 12

written covered put = - Floor

- Floor = short put + short stock

Question 13

Why would you use a cap and what is the formula for a cap?

Answer 13

Cap = long call + short stock

Guaranteed a maximum purchase price for the asset

Question 14

What combination of option/asset would you use to write a covered call?

Answer 14

written covered call = - cap

- cap = short call + long stock

Question 15

Name 2 ways to create a synthetic long forward.

Answer 15

1. Long stock + Borrow money (sell bond)

2. Long call + short put at same strike price

Question 16

Name 2 ways to create a synthetic short forward.

Answer 16

1. short stock + lend money (buy bond)

2. short call + long put at same strike price

Question 17

What is a cash-and-carry?

Answer 17

Arbitrage situation where the forward is over price.

To exploit: long synthetic forward and short real forward.

Question 18

What is a reverse-cash-and-carry?

Answer 18

Arbitrage situation where the synthetic forward is underpriced.
To exploit : short synthetic forward and long real forward.

Question 19

Using d1 or d2 in the lognormal model, what is the formula for Prob[St < K] ?

Answer 19

Prob[St < K] = N[-d2]

Question 20

Using d1 or d2 in the lognormal model, what is the formula for Prob[St >K] ?

Answer 20

Prob[St > K] = N[d2]

Question 21

What are the assumptions for the Black-Scholes Formula?

Answer 21

1. Continuously compounded returns are normally distributed and independent over time
2. Volatility and risk-free rate are known and constant
3. Future dividends are known
4. No transaction costs
5. Investors can borrow/lend at risk-free rate
6. Short selling is allowed at no costs.