BLACK- SCHOLES-MERTON MODEL

CHANGES IN STOCK PRICES

     The graphs shows that as the current stock price increase, the call price also increase which means call options become more valuable as the stock price increases. Meanwhile, put options behave in the opposite way from call options: they become less valuable as the stock price increases as we can see from the graphs.

CHANGES IN VOLATILITY

     Volatility is simply a measure of risk (uncertainty), or variability of price of an option's underlying security. Volatility of a stock price is a measure of how uncertain we are about future stock price movements. Higher volatility estimates reflect greater expected fluctuations (in either direction) in underlying price levels. 

     This expectation generally results in higher option premiums for puts and calls alike. As we can see from the graph, the values of both calls and puts increase as volatility increases. 

CHANGES IN STRIKE PRICES

     The strike price is defined as the price at which the holder of an options can buy (in the case of a call option) or sell (in the case of a put option) the underlying securities when the option is exercised. Hence, strike price is also known as exercise price.

  According to the graph above for call options, the blue one is the line for the call option's price. The call option price is going down as far as the strike price is going up. This symbolizes that the higher the strike price, the cheaper the option.

     Conversely, for put option, we can see from the above graph, the red line one is the put price. The theory same goes for put option's price as mentioned for call option's price above. The price is going up throughout the increasing of the strike price, so we can say the higher the strike price, the more expensive the option.

     The strike price intervals vary depending on the market price and asset type of the underlying.

CHANGES IN TIME

Based on the graph above, blue line represent the call price and the red line represent the put price. As we can see, the call price is going up as time increases and same goes to the put price, the put price is going up as time increases.

This indicates that as long as the period of the maturity date is long, so there is high possibility that the call and put price to  be increases because the price is more volatile.

CHANGES IN INTEREST RATE

     An increase in interest rates will tend to increase call prices and decrease put prices. To understand why this is, think about the effect of interest rates in the context of comparing an option position to simply owning the stock. 

     For call option, it is much cheaper to buy a call option than 100  shares of the stock, the call buyer is willing to pay more for the option when rates are relatively high, since they can invest the differences in the capital required between the two positions.

     While for put options, however, higher interest rates are disadvantageous. When interest rates are higher, investors lose more interest while waiting to sell the underlying when using puts. Thus, the opportunity cost of waiting is higher when interest rates are higher.