Final answer:
Without a specific valuation model, it's not possible to give an exact price for American call or put options. Generally, if the stock price goes up, the value of a call option increases, while the value of a put option decreases. The actual valuation would depend on the chosen model and additional details.
Step-by-step explanation:
Valuation of American Options
The question pertains to the valuation of American options on a non-dividend-paying stock that fluctuates by 10% each month, with the risk-free rate at 12% per annum with continuous compounding. Valuing American options, especially without dividends, is very similar to valuing European options since early exercise offers no benefit as there are no dividends to capture. However, without a specified model like Black-Scholes or Binomial for American options, giving an exact numerical answer isn't possible.
We can still discuss the qualitative aspects. If the stock goes up, both the American call and put options' intrinsic values could change. The call option becomes more valuable as it provides the right to buy the stock at a strike price lower than the market price. Conversely, the put option becomes less valuable as the option to sell at the strike price becomes less attractive if the market price is higher.
Since the student's question does not provide enough information for a quantitative answer, a qualitative approach is necessary to explain how the stock price movement impacts the valuation of American options.