Lecture 3_Pricing

Question 1

How to convert discretely compounding rate to continuously compounding rate? And the other way around

Answer 1

Rc = e^(rt)
Rd = (1+r)^t
Conversion –> make them equal and solve for the rate

Question 2

What are the assumptions underlying the pricing formulas for futures?

Answer 2

The Future RATT!!!
R - risk-free rate
A - arbitrage opportunity can be exploited
T - transaction costs
T - tax rate

Question 3

What parameters are important when calculating the future prices?

Answer 3

The current price and the interest rate

Proof by contradiction - future price should be current price * interest rate

Question 4

What is the price of future contracts?

Answer 4

current spot rate compounded by risk-free rate

Question 5

What is the difference between value and price of future contracts?

Answer 5

1. Value of future contracts - PV of future cash flows; (difference between delivery price and future price; discount back)
2. Price of future contracts - spot rate compounded to future rates or expected future price

Question 6

What are the types of questions on investment assets?

Answer 6

1. No-income: future price = current price roll over
2. Income: future price = (current price - PV dividends) roll over
3. Investment assets with dividend yield

a. Price of future contract
b. Value of future contract (gain/loss through this contract)

Question 7

What is the Value of the future contract?

Answer 7

PV ( St - K ): Assume St = F0

Question 8

What is the intuition behind the pricing of investments with income (dividend)?

Answer 8

1. Assets with income - subtract the PV of the income first - this makes sense because the current price contains that income, however, you will never get the income when you purchase a future. As if the current spot rate is overvalued

Question 9

What is the intuition behind the pricing of investments with income (dividend yield)?

Answer 9

The difference between income in terms of dividend yield - is just that the income is expressed in a different form.

Subtract the value of the dividend in the exponent.

Question 10

What are some examples of hedging with future contracts?

Answer 10

1. Hedging with stock index: (Use the dividend yield calculation)
2. Pricing of futures of currency: Arbitrage -

F = S *(1+ rate (numerator))/ (1+rate (denominator)) - discrete –> infer –> continuous

Question 11

What about futures on commodity?

Answer 11

Before rolling over to future price, add the storage costs to the current spot rate.

You want flower in 3 months, you cannot simply assume that you can also buy the flower today and roll over - you need to take into considerations of watering, storage and others.

Question 12

Can you short commodities?

Answer 12

No, so certain arbitrage opportunities cannot be taken. They are used for consumption. Future price is more often below the normal price.

Question 13

How to treat convenience yield in pricing future contracts?

Answer 13

Convenience yield, similar to income of investment, is the benefit that is priced in the current spot price, but the future contract holders cannot enjoy. Subtract.