Assignment on Financial Engineering and Derivatives

We use a number of different arbitrages argument to explore the relationships between European option prices, American option prices, and the underlying stock price. The most important of these relationships is put-call parity, which is a relationship between European call option prices and European put option prices. Now we will describe the chapter in brief.

Factors affecting stock prices
1. The current stock price, S0
2. The strike price, K
3. The time to expiration , T
4. The volatility of the stock price, σ
5. Risk free interest rate, r.
6. Dividends expected during the life of the option.

Stock price and the strike price:
Call options become more valuable as the stock price increases and less valuable as the strike price increases. Put options become less valuable as the stock price increases and more valuable as the strike price increases.


The time to expiration:
European put and call options become more valuable as the time to expiration increases but in case of dividend the stock price will decline, so that the short life option could be worth more than the long time option.

Volatility:

As volatility increases, the chance that the stock will do very well or very poorly increases. In general the values of both calls and puts therefore increase as volatility increases.

Risk free interest rate:
The net effect of interest rate increase and the accompanying stock price decrease can be to decrease the value of a call option and increase the value of a put option & vice versa.


Dividends:
Dividends have a negative relation with the value of a Call option and a positive relation with the value of a put option.

The following table shows the effect of increasing one variable while keeping all others fixed: