Podcast
Questions and Answers
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 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?
- 11.1
- 40
- 0 (correct)
- 0.9
What should the payoff for a put option at Node V be if the stock price is $39.1?
What should the payoff for a put option at Node V be if the stock price is $39.1?
- 0
- 11.1
- 1.1
- 0.9 (correct)
What is the correct relationship to reflect in the equations for a synthetic portfolio?
What is the correct relationship to reflect in the equations for a synthetic portfolio?
- The equations have no relation to the option values.
- The option payoff equals the portfolio value at corresponding nodes. (correct)
- The value of the synthetic portfolio equals the risk-free loan.
- The synthetic portfolio is only a function of the stock price.
What discount rate should be used for discounting options in this context?
What discount rate should be used for discounting options in this context?
What is incorrect about the discounting method mentioned?
What is incorrect about the discounting method mentioned?
Flashcards
Put Option Payoff Calculation
Put Option Payoff Calculation
The value of a put option at a node is calculated by taking the maximum of the difference between the strike price (K) and the stock price (S) at that node, and zero. This ensures the option holder only exercises the option if it is profitable.
Synthetic Portfolio
Synthetic Portfolio
A synthetic portfolio replicates the payoff of an option using a combination of the underlying asset and a risk-free loan. The delta of the option determines the amount of the underlying asset to hold or short.
Risk-Neutral Probability
Risk-Neutral Probability
The risk-neutral probability is used to discount expected future cash flows when calculating the present value of an option. It reflects the risk-adjusted likelihood of different possible outcomes.
Discounting
Discounting
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Continuous Risk-Free Rate
Continuous Risk-Free Rate
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Study Notes
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%).
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Description
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.
