Lapel Inc.stock price is $32.00.Joe bets Sarah that the price will be above $35.00 in 6 months (180 days).The standard deviation of the stock is 0.25 and the risk free interest rate is 5.0%.If Joe wins the bet,he wishes to be paid with one share of stock.At approximately what stock price will the wager be of equal value to both Joe and Sarah?

Question

Quizplus · Accepted Answer

The value of the wager to both Joe and Sarah can be approximated using the Black-Scholes model for pricing options. Given that Joe wants to be paid with one share of stock if the price exceeds $35.00, this situation resembles a call option with a strike price of $35.00. The Black-Scholes model takes into account the current stock price, the strike price, the time until expiration (6 months in this case), the volatility of the stock (standard deviation of 0.25), and the risk-free interest rate (5.0%). Without performing the exact calculations, which require the Black-Scholes formula, we know that the value of this option (wager) must be less than the difference between the current stock price and the strike price due to the time value of money and the chance the stock price might not exceed the strike price. Therefore, the price that makes the wager of equal value to both parties would be above the current price of $32.00 but below the strike price of $35.00. Among the given options, $33.30 is the only price that fits this description.

Lapel IncStock Price Is $32