Immediately after establishing your put options hedge, volatility for LLL stock suddenly jumps to 45 percent. This changes the number of put options required to hedge your employee stock options. How many put option contracts are now required? (Except for the new volatility, use the same assumptions specified in Problem 18.)

Data From Problem 18

Suppose you hold LLL employee stock options representing options to buy 10,000 shares of LLL stock. You wish to hedge your position by buying put options with three-month expirations and a $22.50 strike price. How many put option contracts are required? Use the same assumptions specified in Problem 17. (That such a trade may not be permitted by the covenants of many ESO plans. Even if the trade were permitted, it could be considered unethical.)

In its 10Q dated February 4, 2016, LLL, Inc., had outstanding employee stock options representing over 272 million shares of its stock. LLL accountants estimated the value of these options using the Black-Scholes-Merton formula and the following assumptions:
S = current stock price = $20.72
K = option strike price = $23.15
r = risk-free interest rate = 0.043
σ = stock volatility = 0.29
T = time to expiration = 3.5 years
What was the estimated value of these employee stock options per share of stock? (LLL pays no dividends.)