Question

a stock presently valued at $10, you feel could either increase to $14 by the end of the month or decline to $7 and you feel either possibility is equally likely. Given that the risk-free rate is 4% continuously compounded per year, what is the binomial estimated price ($) of a put option with a strike of $9 that expires as the stock attains its new value

Answer 1

If the stock ends up at $14, the put option expires worthless and the price at maturity is higher than the strike price

If the stock ends up at $7, the put option has a positive payoff of $2 (Stock price-strike price)

Both of these have equal probability of 0.5

For estimating the price of the put option, we discount the expected cash-flows at maturity by the risk-free rate

Estimated price of a put option = 0.5*0*e^(-0.04*(1/12)) + 0.5*2*e^(-0.04*(1/12))

Estimated price of a put option = $0.99667