Can you describe what the payoffs from lookback options depend on? Can you write in a concise notation the payoff of a floating lookback call?
a. What is the payoff of a portfolio with a long position in a floating lookback call and with a short position in a floating lookback call with the same maturity on the same underlying asset?
b. Consider a newly written floating lookback put on a non-dividend paying-stock where the stock price is 50, the stock price volatility is 40% per annum, the risk-free rate is 10% per annum (CONT), and the time to maturity is 3 months. Calculate the value of the put.
c. Does any type of put-call parity hold for lookback option? If so, write this relation and explain the different components.
d. Does a floating lookback call become more valuable or less valuable as we increase the frequency with which we observe the asset price in calculating the minimum?