Derivative Securities Assignment
Question 1 -
The basics of how options work are being examined in the following questions:
(a) Mr Cheong is an option trader. He has a put option contract whose underlying is 200 shares of a stock and strike price is $80. Analyse how the contract changes in case of
(i) a declaration of a $5 dividend
(ii) a payment of a $5 dividend
(iii) a 6-for-2 stock split
(iv) a payment of a 5% stock dividend
(b) If the payoff at expiration for a call option on the USD is SGD 220, where the underlying is SGD 1.3792 in price and each option is on USD 100,000, find the strike price.
(c) Analyse the factors that affect the price of an American call option. Differentiate between the different actions that you can take when you own an American call option. Substantiate your analysis with real world data and information.
Question 2 -
(a) Explain the Put-Call Parity in three (3) different ways and appraise how it is essential to the theory of option pricing.
(b) Given the following information on the European call and put options of a stock:
- Call price C0 = $4.15
- Put price P0 = $0.80
- Strike price K = $25.60
- Option maturity T = 180 (in days)
- Spot stock price S0 = $29.00
- Risk-free rate r = 5%
(i) Show that the Put-Call Parity is violated.
(ii) Describe how an arbitrageur may take advantage of the situation.
(c) Does the Put-Call Parity hold in the real world?
Question 3 -
Data from the options market are factual and objective. Importantly, the data describes the state of the market. However, these datasets are complicated as many options are traded per underlying and the market is continually changing.
In this question, you will answer questions that require the collection of data on the S&P 500 index (SPX) options from Reuters Eikon.
(a) Are these options American or European? Explain the meaning of the ticker symbol.
(b) Explain the nature of open interest, volume and volatility with regards to how they indicate market activity. Plot graphs to show the relationships between these quantities.
(c) Discuss how options and options-related data may inform us about the market and the challenges in making sense of the datatsets.
Write down the steps that you apply to access the data on Eikon.
Question 4 -
This question examines the basics of the Binomial Model of option pricing.
A commodity stock index is currently 850, the dividend yield on the index and the risk-free rate are both equal to 3%.
(a) Find the price of a 1.5-year European call option with a strike price of 800 if the volatility is 25% per annum by applying a 3-step binomial tree.
(b) Find the price of a 1.5-year American call option with a strike price of 800 if the volatility is 25% per annum by applying a 3-step binomial tree.
(c) How much does the owner of the American option gain exercising early? When does she need to exercise to capture this gain optimally?
(d) Explain how the Binomial Model can be adapted to the pricing of path-dependent options.
Question 5 -
This question examines the basics of the Black-Scholes Model of option pricing.
(a) Apply the Black-Scholes model to find the price of an OTM European call option on a non-dividend paying stock given that the stock price is $150, the risk-free rate is 4%, the maturity is 1-year and the volatility is 25%, given that the option is out-of-the-money by $50.
(b) If a dealer writes 5 options contracts, each of multiplicity 50 shares of the stock, how many shares must he hold in order to hedge his position?
(c) Explain the relationship between the Black-Scholes Model and the Binomial Model.