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Financial Derivatives (N1559) – Spring 2024
Seminar Questions Week 9
Seminar Questions
1. (JC 20.16) What is a volatility smile with respect to the Black-Scholes-Merton model?
2. (JC) Replicate Table 20.4 in the core textbook (the table is also provided in the lecture notes): given the strike, stock price, interest rate, maturity of the option and their market prices (the first 5 columns of the table) calculate the implied volatility and compare to column 6.
3. (Data) The following data are on Apple options recorded on 13 December 2021. The full dataset is available on canvas.
(a) Estimate the price of the underlying given only the data provided in the spreadsheet.
(b) Given only the data in the spreadsheet, do you think the price of the underlying went up or down over the last trading day?
(c) Plot the implied volatility curve for this stock. Is the pattern you observe similar to what you observe for other equity markets?
(d) For the same strike and maturity, does the implied volatility need to be identical for calls and puts?
(e) What would be the impact of non-synchronous quotes (the time stamp of the stock price quote does not coincide with the time stamp of the option quotes) on the calculation of implied volatilities?
(f) Use other internet sources to provide an estimate of the dividend that should have been used in pricing the stock.
(g) Calculate the relative bid-ask spread on the options. Compared to the underlying stock, are the bid-ask spreads small or large?
(h) Which options are the most liquidly traded?
4. (Data) Download option data for a company of your choice with an earnings announcement in the next week. Discuss the patterns you observe in the implied volatility curves for different option maturities.