Question 4

Pfizer options are listed on CBOE. Today is 12 October 2020. Pfizer is traded at $36.82 per share (bid $36.81, ask $36.83). Assume that the risk free rate is 0.20% and that the volatility of the stock price is stable and equal to its historical volatility observed since the stock was listed on NYSE. Using 7-step binomial tree model, for options that expire on 30 October 2020, calculate:

a) The option premiums (per 1 share) for the ATM call and put options

b) Early exercise premium for the ATM put option

c) How many times would it be optimal to exercise the American ATM put option until the maturity date?

The Excel spreadsheet provides market data on Pfizer options with different expiration dates as of 12 October 2020. Look at similar ATM options that you used in binomial trees. Check whether there is any mispricing you can exploit. Apply scalings necessary to trade in 10 options (of each type).

d) Assuming that you submit limit orders at the midpoint between the best bid and ask prices, how much money can you make?

• Note: if you cannot make money, enter 0

e) Compare these midpoint prices with the ones you calculated using the binomial tree. You can notice that implied volatilities from the spreadsheet are higher than the volatility estimated with historical data. It means that market makers use higher volatilities to price options. What can explain such behavior?

f) Assuming that you submit market orders, how much money can you make?

• Note: if you cannot make money, enter 0