Deck 10: Multi-Step Binomial Trees

Question 1

Compute the spot rate duration for a call option on a 1.5 year zero coupon bond with K = 99.00, maturity at t = 1. Assume that p? = 0.7038 is constant over time.

Answer 1

Spot rate duration is -9.2354.

Question 2

In order to compute the spot rate duration do you use risk neutral prob- abilities or risk natural probabilities?

Answer 2

You use risk neutral probabilities, since it is derived from pricing bonds in different scenarios (see spot rate duration formula).

Question 3

You are given the following interest rate tree. Use it when required in the
exercises.

-Using risk neutral pricing obtain the value for a put option on a 1.5 year zero coupon bond with K = 97.40, maturity at t = 1. Assume that p? = 0.7038 is constant over time.

Answer 3

The price is 0.1709.

Question 4

Using risk neutral pricing obtain the value for a straddle on a 1.5 year zero coupon bond with K = 98.00, maturity at t = 1. Assume that p? = 0.7038 is constant over time.

Question 5

How realistic is it to speak about negative interest rate in nominal terms?

Question 6

You are given the following interest rate tree. Use it when required in the
exercises.

-Using risk neutral pricing obtain the value for a call option on a 1.5 year zero coupon bond with K = 99.00, maturity at t = 1. Assume that p? = 0.7038 is constant over time.

Question 7

You are given the following interest rate tree. Use it when required in the
exercises.

-Using risk neutral pricing obtain the value for a 1.5 year zero coupon bond. Assume that p? = 0.7038 is constant over time.

Question 8

How realistic is it to speak about negative interest rate in real terms?

Question 9

Which of the following prices should be higher: a call option, a put option or a straddle. All of them have the same maturity, underlying security and strike price. Explain.

Question 10

What is one major drawback from using empirical estimates to fit the "true" interest rate tree?

Question 11

What is the difference between risk neutral probability and risk natural probability?

Question 12

When talking about options, what is a straddle?

Question 13

Compute the spot rate duration for a put option on a 1.5 year zero coupon bond with K = 97.40, maturity at t = 1. Assume that p? = 0.7038 is constant over time.

Question 14

Why do we say that the dynamic replication strategy is self-financing?

Question 15

Compute the spot rate duration for a straddle on a 1.5 year zero coupon bond with K = 98.00, maturity at t = 1. Assume that p? = 0.7038 is constant over time.