You are given the following information on two European call options written on stock XYZ at a strike of 175.
Maturity 11/16/2018 Maturity 01/17/2020 XYZ price
Price Price
4/11/2018 12.50 20.10 178.10
4/12/2018 9.75 17.50 172.55
Assume an annual rate of interest of 2% and an annual dividend rate of 1%. Both rates are continuously compounded.
a) Compute the implied volatilities of both options on both dates. (You will compute four implied volatilities in total)
b) Create a P&L explanation for these two options. A P&L explanation is an explanation of the change in the option value between the two days. The change in value should be expressed as a function of delta, gamma, vega and time decay.
c) Discuss the main differences between the P&L explanations of the two options.