American options can be exercised at any time before maturity. European options can only be exercised at maturity. In the United States, American options are more common than European options.

A call option's payoff is the determined by how much the stock price exceeds the strike price at maturity. Therefore, as stock price increases before maturity, the chances of the call option being exercised with a large payoff is higher. This, in turn, raises the price of the call. On the flip side, the price of a put option is how much the strike price exceeds the stock price stated in the contract at maturity. Therefore, the price of a put falls as stock price increases.

Based on the same arguments as above, a higher strike price on a call option lowers the price of call option. On the other hand, a higher strike price increases the price of a put option.

If we are dealing with American options, a longer period option has more benefits compared to a shorter period option. Therefore, both puts and calls increase in value as time to expiration increases.

Volatility is a measure of risk in the stock price. For both call and puts, there is a limited downside risk, since the holder of the option would not exercise it if it was not profitable. Therefore, both call and put holders can benefit on profitable stock price movements and are protected on the downside, meaning that both call and put prices increase as volatility increases.

There are two fundamental effects that have to be taken into account as the risk free rate increases. The first effect is the expected growth rate of stocks tends to increase with an increase in the risk-free rate. The second effect is that the present value of a future cash flow from the option decreases. Both these effects decrease the value of a put option. For a call option, however, the first effect increases the call price but the second effect decreases it. The second effect tends to be larger than the first effect, effectively decreasing the price of a call option.

Dividends reduce the stock price on the ex-dividend date. Since the price of the underlying security decreases, call options decrease in value while put options increase in value (see CURRENT STOCK PRICE argument).

Systematic (Pervasive) risk and Unsystematic (Idiosyncratic) risk. Idiosyncratic risk can be diversified away but systematic risk cannot.

• Individual investors are price takers
• Single-period investment horizon
• Investments are limited to traded financial assets
• No taxes or transaction costs
• Information is costless and available to all investors
• Investors are rational mean-variance optimizers
• Homogeneous expectation

Source: Financial Analysis and Securities Trading lecture notes, by Christine Parlour

The Sharpe Ratio is the risk-adjusted rate of return of a portfolio. It is calculated as the average return of the portfolio minus the risk-free rate all divided by the standard deviation of the portfolio.