Final answer:
The deltas for an at-the-money call and put option using the Black-Scholes model, given the stock price equals the exercise price, would typically be around 0.5 and -0.5 respectively. However, the actual values could deviate due to the specified high volatility.
Step-by-step explanation:
To determine the deltas of a call and a put option with given characteristics, we can use the Black-Scholes model. This model requires inputs including the current stock price, the exercise price, the risk-free rate, the maturity time, and the standard deviation of the stock's returns. Without carrying out the actual calculations, because the stock price and exercise price are equal, and assuming that no dividends are paid, we can expect the call delta to be close to 0.5 and the put delta to be close to -0.5. These deltas would reflect the change in the option's price for a small change in the stock price. However, because volatility is high at 65% per year, this could skew the delta values slightly away from 0.5 because of the increased likelihood of the stock moving significantly in or out of the money before maturity.