Question
Suppose today is 2nd August 2021, when the Afterpay share (APT.AX) is priced at $114.8. Consider an Afterpay option that expires on 18th November 2021,
Suppose today is 2nd August 2021, when the Afterpay share (APT.AX) is priced at $114.8. Consider an Afterpay option that expires on 18th November 2021, with a strike price of $120. Assume no dividends are paid on this stock. The annual historical standard deviation of Afterpay stocks is 51.27%. The risk-free rate is 0.153% with annual compounding. Ignore transaction costs (e.g. bid-ask spread).
a) Using a three-step binomial tree model, calculate theoretical prices today for a) a November American call option, b) a November American put option, c) a November European call option, and d) a November European put option on Afterpay. Draw the trees and show all calculation workings at each node.
b) Suppose that you observe that the market option price of European put on this stock is currently $4.5. Is there an arbitrage opportunity? If you see an arbitrage opportunity, present a strategy to earn riskless profit and construct a table showing the cashflows at initiation and expiration to demonstrate that your strategy is correct.
c) Suppose that you observe that the market option prices of European call and put on this stock are currently $12.5 and $18.7, respectively. Is there an arbitrage opportunity? If you see the arbitrage opportunity, construct a strategy that leads to inevitable gain and no loss. (Construct a table showing the cashflows at initiation and expiration to demonstrate that your strategy is correct). Note part c) is independent of part b).
d) Now, you wish to connect the Binomial model to the continuous-time equivalent provided by the Black-Scholes-Merton model. The continuously compounded equivalent of 0.153% is 0.1529%. Calculate the theoretical option price of November European call and put using the BSM model. Show the formulas and calculations.
e) Compare the theoretical option price of European call and put obtained from the two pricing models in Task (5a) and (5d). What do you notice?
f) What are the advantages and disadvantages of a binomial option pricing model relative to BSM model?
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started