You would like to be holding a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Co.
-Suppose the desired put options with X = 50 were traded.How much would it cost to purchase?
A) $1.19
B) $2.38
C) $5.00
D) $3.33

Question

Quizplus · Accepted Answer

The cost of the put option can be calculated using the binomial option pricing model. The stock can go up to $55 or down to $45. The risk-neutral probability of the stock going up is (1.05 - 0.9) / (1.1 - 0.9) = 0.75. The expected payoff of the put option is 0.25 * $5 = $1.25. Discounting this at the risk-free rate of 5% gives $1.25 / 1.05 = $1.19.

You Would Like to Be Holding a Protective Put Position