Suppose you hold LLL employee stock options representing options to buy 10,700 shares of LLL stock. You wish to hedge your position by buying put options with three-month expirations and a $29.98 strike price. LLL accountants estimated the value of these options using the Black-Scholes-Merton formula and the following assumptions:

S = current stock price = $28.2

K = option strike price = $30.63

r = risk-free interest rate = 0.032

= stock volatility = 0.24

T = time to expiration = 3.5 years

How many put option contracts are required? (Note 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.) (Round your answer to the nearest whole number.)

Put option contracts

Here is an explanation of a similar problem:

Suppose you hold LLL employee stock options representing options to buy 10,600 shares of LLL stock. You wish to hedge your position by buying put options with three- month expirations and a $27.2 strike price. LLL accountants estimated the value of these options using the Black-Scholes-Merton formula and the following assumptions: S = current stock price = $25.42 K = option strike price = $27.85 r = risk-free Interest rate = 0.043 O = stock volatility = 0.24 T = time to expiration = 3.5 years How many put option contracts are required? (Note 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.) (Round your answer to the nearest whole number.) Put option contracts 103 : 1% Explanation This is a hedging problem in which you wish to hedge one option position with another. Your employee stock option (ESO) position represents 10,600 shares, and you need to know how many put option contracts are required to establish the hedge. First, we need to calculate deltas for both options. The ESO delta is ESO (Call) Delta = N(C4) = 0.6392 For the put option, we get this value for dy di In (25.42/27-2)+(0.043+0.242/2) x 25 0.24 x 25 -0.4144 These standard normal probabilities are given: N(C) = 0.339282 N(-1) = -0.6607 Put option Delta =-N(-09) = -0.6607 The number of put option contracts is then calculated as ESO delta x 10,600 0.6392x10,600 Number of option contracts = Put option delta x 100 -0.6607x100 Performing the calculation ylelds 102.55, or about 103, put option contracts