Lecture 9: Features of interest rate models, Black scholes

Question 1

Exchange traded futures options

Answer 1

Futures options gives the buyer the right to buy or sell to the writer a designated futures contract at a designated price at any time.

if the option is a call, the buyer has the right to buy one contract at the exercise price

if the option is a put, the buyer has the right to sell one contract at the exercise price.

Question 2

mechanics of trading futures options

Answer 2

upon exercise, the futures price for contracts will be set equal to the exercise price.

the position of the counterparties is then immediately market to market in terms of the then-current futures price.

• thus the futures position of the counterparties will be at the prevailing futures price.
• at the same time the option buyer will receive the economic benefit from the option seller.

writer of an option bares all risk, and thus is required to deposit the margin required on the interest rate of the position, if that is the underlying instrument, and also deposit the option price received for writing the option.

Question 3

Specifications for actively traded futures options

Answer 3

All futures options are of the american type. trading of the futures option on treasury bonds steps in the month prior to the underlying futures contracts delivery month.

in order to compete with the over the counter market, flexible treasury bonds were introduced
- these allow counterparties to customize options with certain limits such as strike price, expiration date, and type of exercise.

Question 4

Intrinsic value of an option

Answer 4

intrinsic value of an option is the economic value of the option is exercised immediately.

Call option
- intrinsic value is the difference between the bond price and strike price

Put option
- intrinsic value is equal to the amount by which the bond price is below the strike price.

Question 5

In the money/out the money

Answer 5

for a call option, when the option has intrinsic value, it is in the money
when the strike price exceeds the bond price, it is out of the money.
if equal it is at the money.

for a put option, it is the opposite, when strike price is lower than bond price, it is out of the money.

Question 6

Time value of an option

Answer 6

the time value of an option is the amount by which the option price exceeds the intrinsic value of an option.

Question 7

option prices: 6 factors influencing

Answer 7

1. current price of underlying instrument
2. strike price
3. time
4. short term risk free rate over life of an option
5. coupon rate on the bond
6. expected volatility of yields over the life option.

Question 8

Why is black scholes model deemed fair

Answer 8

fair in the sense that if any other price existed, it would be possible to earn riskless arbitrage profit by taking an offsetting position in the underlying stock.

Question 9

3 assumptions in the BS model

Answer 9

1. if the probability distribution for the return assumed by the black scholes model permit same probability that the return can take on any positive value.
2. the short term interest rate is constant over the life of the option.
3. the variance in prices is constant over the life of the option.