In this question, you need to price options with different valuation approaches and comment on your results. You will co
Posted: Wed May 18, 2022 9:34 pm
In this question, you need to price options with different
valuation approaches and comment on your results. You will consider
puts and calls on a share with spot price of $60. Strike price is
$64. The riskfree interest rate is 5% per annum with continuous
compounding.
Binomial trees:
Furthermore, assume that over each of the next two
two-month periods, the share price is expected to go up by 6% or
down by 6%.
a. Use a two-step binomial tree to calculate the value of a
four-month European call option using the no-arbitrage approach. [3
marks]
b. Use a two-step binomial tree to calculate the value of a
four-month European put option using the no-arbitrage approach. [3
marks]
c. Show whether the put-call-parity holds for the European call
and the European put prices you calculated in a. and b. [1
mark]
d. Use a two step-binomial tree to calculate the value of a
four-month European call option using risk-neutral valuation. [1
mark]
e. Use a two step-binomial tree to calculate the value of a
four-month European put option using risk-neutral valuation. [1
mark]
f. Verify whether the no-arbitrage approach and the risk-neutral
valuations lead to the same results. [1 mark]
g. Use a two-step binomial tree to calculate the value of a
four-month American put option. [1 mark]
h. Without calculations: What is the value of a four-month
American call option with a strike price of $64? Why? [2 marks]
Note: When you use no-arbitrage arguments, you need to show in
detail how to set up the riskless portfolios at the different nodes
of the binomial tree. Black-Scholes-Merton model: Furthermore,
assume that the volatility of the underlying asset is 15%.
i. What is the Black-Scholes-Merton price of a four-month
European call option? [1 mark]
j. What is the Black-Scholes-Merton price of a four-month
European put option? [1 mark]
k. Show whether the put-call-parity holds for the European call
and the European put prices you calculated in i. and j. [1
mark]
l. Without calculations: What would happen to the option prices
you calculated in i. and j. if the interest rate drops to 4%? Why?
[2 marks]
Comparison across models:
m. Compare the call option prices you calculated in d. and i.
Compare also the put option prices you calculated in e. and j. Do
expect these prices to be the same? Why/Why not? [2 mark]
valuation approaches and comment on your results. You will consider
puts and calls on a share with spot price of $60. Strike price is
$64. The riskfree interest rate is 5% per annum with continuous
compounding.
Binomial trees:
Furthermore, assume that over each of the next two
two-month periods, the share price is expected to go up by 6% or
down by 6%.
a. Use a two-step binomial tree to calculate the value of a
four-month European call option using the no-arbitrage approach. [3
marks]
b. Use a two-step binomial tree to calculate the value of a
four-month European put option using the no-arbitrage approach. [3
marks]
c. Show whether the put-call-parity holds for the European call
and the European put prices you calculated in a. and b. [1
mark]
d. Use a two step-binomial tree to calculate the value of a
four-month European call option using risk-neutral valuation. [1
mark]
e. Use a two step-binomial tree to calculate the value of a
four-month European put option using risk-neutral valuation. [1
mark]
f. Verify whether the no-arbitrage approach and the risk-neutral
valuations lead to the same results. [1 mark]
g. Use a two-step binomial tree to calculate the value of a
four-month American put option. [1 mark]
h. Without calculations: What is the value of a four-month
American call option with a strike price of $64? Why? [2 marks]
Note: When you use no-arbitrage arguments, you need to show in
detail how to set up the riskless portfolios at the different nodes
of the binomial tree. Black-Scholes-Merton model: Furthermore,
assume that the volatility of the underlying asset is 15%.
i. What is the Black-Scholes-Merton price of a four-month
European call option? [1 mark]
j. What is the Black-Scholes-Merton price of a four-month
European put option? [1 mark]
k. Show whether the put-call-parity holds for the European call
and the European put prices you calculated in i. and j. [1
mark]
l. Without calculations: What would happen to the option prices
you calculated in i. and j. if the interest rate drops to 4%? Why?
[2 marks]
Comparison across models:
m. Compare the call option prices you calculated in d. and i.
Compare also the put option prices you calculated in e. and j. Do
expect these prices to be the same? Why/Why not? [2 mark]