Options Pricing Errors Analysis

What is the correct payoff for a put option at Node IV if the strike price is $40 and the stock price at that node is $52.9?

What should the payoff for a put option at Node V be if the stock price is $39.1?

What is the correct relationship to reflect in the equations for a synthetic portfolio?

What discount rate should be used for discounting options in this context?

What is incorrect about the discounting method mentioned?

Incorrect Payoff Calculations

Node IV (uu): Correctly calculated payoff for put option as 0. Max(Strike Price (K) - Stock Price (S_uu), 0) = Max(40 - 52.9, 0)
Node V (ud): Correctly calculated payoff for put option as 0.9. Max(40 - 39.1, 0)
Node VI (dd): Correctly calculated payoff for put option as 11.1. Max(40 - 28.9, 0)
Nodes II and III Error: Incorrectly treated as long put positions. Correct calculation requires discounting future expected values using risk-neutral probabilities.

Incorrect Synthetic Portfolio Setup

General Error: Equations for synthetic portfolio do not accurately reflect delta (∆) of underlying asset and risk-free loan.
Specific Error (Node II/III example): Incorrect equation structure; -F + $52.9∆ = $0 and -F + $39.1∆ = $0.9. The correct approach is to work backwards using risk-neutral probabilities to calculate option value at each node.

Incorrect Discounting

Incorrect Discount Rate: Incorrectly used a 5% discount rate. The correct rate is the 6-month risk-free rate, continuously compounded, approximately 5.13%.
Incorrect Exponential Form: Incorrectly applied exponential calculations using percentage rather than decimal value for discounting. Should use e^(-0.0513) instead of e^(-5%).

This quiz examines common errors in calculating payoffs for put options, setting up synthetic portfolios, and discounting future values. Participants will evaluate different nodes, identify inaccuracies, and learn the correct methodologies. Enhance your understanding of options pricing and risk-neutral probabilities.