Question

A stock has a price of $84 and a volatility of 25% per annum. European options on the stock have a strike price of $80 and a time to maturity of 180 days. The risk free interest rate is 5% per annum on a continuously compounded basis. The stock pays dividends at a continuously compounded rate of 3.0%. Use the BSMOPM. Use this information to answer this and the next 4 questions.

The risk-neutral probability that the put option will be worth exercising on the expiration date is closest to:
a.0.5973
b.0.3372
c.0.4027

Answer 1

To calculate the risk-neutral probability that the put option will be worth exercising on the expiration date, you can use the Black-Scholes-Merton option pricing model (BSMOPM). The risk-neutral probability is the probability that the option will end up in the money based on the risk-neutral measure. In this case, the risk-free interest rate is 5% per annum, the stock price is $84, the strike price is $80, the time to maturity is 180 days, and the volatility is 25% per annum.

Step-by-step explanation:

To calculate the risk-neutral probability that the put option will be worth exercising on the expiration date, you can use the Black-Scholes-Merton option pricing model (BSMOPM). The risk-neutral probability is the probability that the option will end up in the money based on the risk-neutral measure. In this case, the risk-free interest rate is 5% per annum, the stock price is $84, the strike price is $80, the time to maturity is 180 days, and the volatility is 25% per annum.

Using the BSMOPM formula, you can calculate the risk-neutral probability as:

Risk-neutral probability = N(d2)

where N represents the cumulative distribution function of the standard normal distribution and d2 is given by:

d2 = (ln(S/K) + (r - q - 0.5 * sigma^2) * time) / (sigma * sqrt(time))

Substituting the given values into the equations and using a financial calculator or software, the closest risk-neutral probability is approximately 0.5973 (Option A).