Analysis of Time Series data
Speaking as someone from a finance background, the `usual' model for a stock price process is

$\frac{dS}{S}=r dt + \sigma dW_t$

i.e. we assume the returns (not the absolute price changes, i.e. dS/S is approximately the daily percentage change in price) as having a 'drift' equal to the risk free rate (the interest rate r) and a random shock $dW_t$ with standard deviation $\sigma$

So it's basically the opposite of what you've been asked, I would expect a trend (but it's very hard to estimate with confidence) and I would not expect any seasonality, you could fit an arithmetic model by taking the daily differences though.